Chemical Structure and Properties: A Modified Atoms-First, One-Semester Introductory Chemistry Course

Science.gov (United States)

Schaller, Chris P.; Graham, Kate J.; Johnson, Brian J.; Jakubowski, Henry V.; McKenna, Anna G.; McIntee, Edward J.; Jones, T. Nicholas; Fazal, M. A.; Peterson, Alicia A.

2015-01-01

A one-semester, introductory chemistry course is described that develops a primarily qualitative understanding of structure-property relationships. Starting from an atoms-first approach, the course examines the properties and three-dimensional structure of metallic and ionic solids before expanding into a thorough investigation of molecules. In…

Using an Isomorphic Problem Pair to Learn Introductory Physics: Transferring from a Two-Step Problem to a Three-Step Problem

Science.gov (United States)

Lin, Shih-Yin; Singh, Chandralekha

2013-01-01

In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. 382 students from a calculus-based and an algebra-based introductory physics course were administered a quiz in the recitation…

Using Isomorphic Problems to Learn Introductory Physics

Science.gov (United States)

Lin, Shih-Yin; Singh, Chandralekha

2011-01-01

In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the…

Capsule calculus

CERN Document Server

Ritow, Ira

2003-01-01

This brief introductory text presents the basic principles of calculus from the engineering viewpoint. Excellent either as a refresher or as an introductory course, it focuses on developing familiarity with the basic principles rather than presenting detailed proofs.Topics include differential calculus, in terms of differentiation and elementary differential equations; integral calculus, in simple and multiple integration forms; time calculus; equations of motion and their solution; complex variables; complex algebra; complex functions; complex and operational calculus; and simple and inverse

Catwalk: First-Semester Calculus.

Science.gov (United States)

Speiser, Bob; Walter, Chuck

1994-01-01

Describes the use of time-lapse photographs of a running cat as a model to investigate the concepts of function and derivative in a college calculus course. Discusses student difficulties and implications for teachers. (MKR)

A Tale of Two Curricula: The performance of two thousand students in introductory electromagnetism

Science.gov (United States)

Schatz, Michael; Kohlmyer, Matthew; Caballero, Marcos; Chabay, Ruth; Sherwood, Bruce; Catrambone, Richard; Marr, Marcus; Haugen, Mark; Ding, Lin

2009-03-01

Student performance in introductory calculus-based electromagnetism (E&M) courses at four large research universities was measured using the Brief Electricity and Magnetism Assessment (BEMA). Two different curricula were used at these universities: a traditional E&M curriculum and the Matter & Interactions (M&I) curriculum. At each university, post-instruction BEMA test averages were significantly higher for the M&I curriculum than for the traditional curriculum. The differences in post-test averages cannot be explained by differences in variables such as pre-instruction BEMA scores, grade point average, or SAT scores.

Mathematical Rigor in Introductory Physics

Science.gov (United States)

Vandyke, Michael; Bassichis, William

2011-10-01

Calculus-based introductory physics courses intended for future engineers and physicists are often designed and taught in the same fashion as those intended for students of other disciplines. A more mathematically rigorous curriculum should be more appropriate and, ultimately, more beneficial for the student in his or her future coursework. This work investigates the effects of mathematical rigor on student understanding of introductory mechanics. Using a series of diagnostic tools in conjunction with individual student course performance, a statistical analysis will be performed to examine student learning of introductory mechanics and its relation to student understanding of the underlying calculus.

History-Infused Lessons in Introductory Calculus at the Secondary Level: Students' Learning and Perceptions

Science.gov (United States)

Poh, Wei Beng; Dindyal, Jaguthsing

2016-01-01

A history-infused lesson package developed by a team of teachers in a professional learning community was used to teach introductory calculus in a secondary school. First, we report a quasi-experimental design that showed that students in the experimental group performed significantly better than students in the control group. Second, we report on…

Improving Calculus II and III through the Redistribution of Topics

Science.gov (United States)

George, C. Yousuf; Koetz, Matt; Lewis, Heather A.

2016-01-01

Three years ago our mathematics department rearranged the topics in second and third semester calculus, moving multivariable calculus to the second semester and series to the third semester. This paper describes the new arrangement of topics, and how it could be adapted to calculus curricula at different schools. It also explains the benefits we…

Thematization of the Calculus Graphing Schema

Science.gov (United States)

Cooley, Laurel; Baker, Bernadette; Trigueros, Maria

2003-01-01

This article is the result of an investigation of students' conceptualizations of calculus graphing techniques after they had completed at least two semesters of calculus. The work and responses of 27 students to a series of questions that solicit information about the graphical implications of the first derivative, second derivative, continuity,…

Do evidence-based active-engagement courses reduce the gender gap in introductory physics?

Science.gov (United States)

Karim, Nafis I.; Maries, Alexandru; Singh, Chandralekha

2018-03-01

Prior research suggests that using evidence-based pedagogies can not only improve learning for all students, it can also reduce the gender gap. We describe the impact of physics education research-based pedagogical techniques in flipped and active-engagement non-flipped courses on the gender gap observed with validated conceptual surveys. We compare male and female students’ performance in courses which make significant use of evidence-based active-engagement (EBAE) strategies with courses that primarily use lecture-based (LB) instruction. All courses had large enrolment and often had more than 100 students. The analysis of data for validated conceptual surveys presented here includes data from two-semester sequences of algebra-based and calculus-based introductory physics courses. The conceptual surveys used to assess student learning in the first and second semester courses were the force concept inventory and the conceptual survey of electricity and magnetism, respectively. In the research discussed here, the performance of male and female students in EBAE courses at a particular level is compared with LB courses in two situations: (I) the same instructor taught two courses, one of which was an EBAE course and the other an LB course, while the homework, recitations and final exams were kept the same; (II) student performance in all of the EBAE courses taught by different instructors was averaged and compared with LB courses of the same type also averaged over different instructors. In all cases, on conceptual surveys we find that students in courses which make significant use of active-engagement strategies, on average, outperformed students in courses of the same type using primarily lecture-based instruction even though there was no statistically significant difference on the pre-test before instruction. However, the gender gap persisted even in courses using EBAE methods. We also discuss correlations between the performance of male and female students on

Impacts of curricular change: Implications from 8 years of data in introductory physics

Science.gov (United States)

Pollock, Steven J.; Finkelstein, Noah

2013-01-01

Introductory calculus-based physics classes at the University of Colorado Boulder were significantly transformed beginning in 2004. They now regularly include: interactive engagement using clickers in large lecture settings, Tutorials in Introductory Physics with use of undergraduate Learning Assistants in recitation sections, and a staffed help-room setting where students work on personalized CAPA homework. We compile and summarize conceptual (FMCE and BEMA) pre- and post-data from over 9,000 unique students after 16 semesters of both Physics 1 and 2. Within a single institution with stable pre-test scores, we reproduce results of Hake's 1998 study that demonstrate the positive impacts of interactive engagement on student performance. We link the degree of faculty's use of interactive engagement techniques and their experience levels on student outcomes, and argue for the role of such systematic data collection in sustained course and institutional transformations.

Calculus light

CERN Document Server

Friedman, Menahem

2011-01-01

Another Calculus book? As long as students find calculus scary, the failure rate in mathematics is higher than in all other subjects, and as long as most people mistakenly believe that only geniuses can learn and understand mathematics, there will always be room for a new book of Calculus. We call it Calculus Light. This book is designed for a one semester course in ""light"" calculus -- mostly single variable, meant to be used by undergraduate students without a wide mathematical background and who do not major in mathematics but study subjects such as engineering, biology or management infor

Assessing expertise in introductory physics using categorization task

Directory of Open Access Journals (Sweden)

Andrew Mason

2011-10-01

Full Text Available The ability to categorize problems based upon underlying principles, rather than surface features or contexts, is considered one of several proxy predictors of expertise in problem solving. With inspiration from the classic study by Chi, Feltovich, and Glaser, we assess the distribution of expertise among introductory physics students by asking three introductory physics classes, each with more than a hundred students, to categorize mechanics problems based upon similarity of solution. We compare their categorization with those of physics graduate students and faculty members. To evaluate the effect of problem context on students’ ability to categorize, two sets of problems were developed for categorization. Some problems in one set included those available from the prior study by Chi et al. We find a large overlap between calculus-based introductory students and graduate students with regard to their categorizations that were assessed as “good.” Our findings, which contrast with those of Chi et al., suggest that there is a wide distribution of expertise in mechanics among introductory and graduate students. Although the categorization task is conceptual, introductory students in the calculus-based course performed better than those in the algebra-based course. Qualitative trends in categorization of problems are similar between the non-Chi problems and problems available from the Chi study used in our study although the Chi problems used are more difficult on average.

Recursive sequences in first-year calculus

Science.gov (United States)

Krainer, Thomas

2016-02-01

This article provides ready-to-use supplementary material on recursive sequences for a second-semester calculus class. It equips first-year calculus students with a basic methodical procedure based on which they can conduct a rigorous convergence or divergence analysis of many simple recursive sequences on their own without the need to invoke inductive arguments as is typically required in calculus textbooks. The sequences that are accessible to this kind of analysis are predominantly (eventually) monotonic, but also certain recursive sequences that alternate around their limit point as they converge can be considered.

Assessing the Effectiveness of Studio Physics in Introductory-Level Courses at Georgia State University

Science.gov (United States)

Upton, Brianna; Evans, John; Morrow, Cherilynn; Thoms, Brian

2009-11-01

Previous studies have shown that many students have misconceptions about basic concepts in physics. Moreover, it has been concluded that one of the challenges lies in the teaching methodology. To address this, Georgia State University has begun teaching studio algebra-based physics. Although many institutions have implemented studio physics, most have done so in calculus-based sequences. The effectiveness of the studio approach in an algebra-based introductory physics course needs further investigation. A 3-semester study assessing the effectiveness of studio physics in an algebra-based physics sequence has been performed. This study compares the results of student pre- and post-tests using the Force Concept Inventory. Using the results from this assessment tool, we will discuss the effectiveness of the studio approach to teaching physics at GSU.

The Robotic Decathlon: Project-Based Learning Labs and Curriculum Design for an Introductory Robotics Course

Science.gov (United States)

Cappelleri, D. J.; Vitoroulis, N.

2013-01-01

This paper presents a series of novel project-based learning labs for an introductory robotics course that are developed into a semester-long Robotic Decathlon. The last three events of the Robotic Decathlon are used as three final one-week-long project tasks; these replace a previous course project that was a semester-long robotics competition.…

Calculus II For Dummies

CERN Document Server

Zegarelli, Mark

2012-01-01

An easy-to-understand primer on advanced calculus topics Calculus II is a prerequisite for many popular college majors, including pre-med, engineering, and physics. Calculus II For Dummies offers expert instruction, advice, and tips to help second semester calculus students get a handle on the subject and ace their exams. It covers intermediate calculus topics in plain English, featuring in-depth coverage of integration, including substitution, integration techniques and when to use them, approximate integration, and improper integrals. This hands-on guide also covers sequences and series, wit

Calculus refresher

CERN Document Server

Klaf, A A

1956-01-01

This book is unique in English as a refresher for engineers, technicians, and students who either wish to brush up their calculus or find parts of calculus unclear. It is not an ordinary textbook. It is, instead, an examination of the most important aspects of integral and differential calculus in terms of the 756 questions most likely to occur to the technical reader. It provides a very easily followed presentation and may also be used as either an introductory or supplementary textbook. The first part of this book covers simple differential calculus, with constants, variables, functions, inc

Effects of Clicker Use on Calculus Students' Mathematics Anxiety

Science.gov (United States)

Batchelor, John

2015-01-01

This paper reports the results of a survey study of clicker use and mathematics anxiety among students enrolled in an undergraduate calculus course during the Fall 2013 semester. Students in two large lecture sections of calculus completed surveys at the beginning and end of the course. One class used clickers, whereas the other class was taught…

Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

Science.gov (United States)

Patel, Rita Manubhai; McCombs, Paul; Zollman, Alan

2014-01-01

Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student…

Advanced calculus a transition to analysis

CERN Document Server

Dence, Thomas P

2010-01-01

Designed for a one-semester advanced calculus course, Advanced Calculus explores the theory of calculus and highlights the connections between calculus and real analysis -- providing a mathematically sophisticated introduction to functional analytical concepts. The text is interesting to read and includes many illustrative worked-out examples and instructive exercises, and precise historical notes to aid in further exploration of calculus. Ancillary list: * Companion website, Ebook- http://www.elsevierdirect.com/product.jsp?isbn=9780123749550 * Student Solutions Manual- To come * Instructor

The Structure of the Introductory Economics Course in United States Colleges.

Science.gov (United States)

Sweeney, M. Jane Barr; And Others

1983-01-01

This survey examined class size, teaching methods, and the one-semester/two-semester organization of the introductory economics course. Student satisfaction with respect to their institution was also studied. (Author/RM)

Examining issues of underrepresented minority students in introductory physics

Science.gov (United States)

Watkins, Jessica Ellen

In this dissertation we examine several issues related to the retention of under-represented minority students in physics and science. In the first section, we show that in calculus-based introductory physics courses, the gender gap on the FCI is diminished through the use of interactive techniques, but in lower-level introductory courses, the gap persists, similar to reports published at other institutions. We find that under-represented racial minorities perform similar to their peers with comparable academic preparation on conceptual surveys, but their average exam grades and course grades are lower. We also examine student persistence in science majors; finding a significant relationship between pedagogy in an introductory physics course and persistence in science. In the second section, we look at student end-of-semester evaluations and find that female students rate interactive teaching methods a full point lower than their male peers. Looking more deeply at student interview data, we find that female students report more social issues related to the discussions in class and both male and female students cite feeling pressure to obtain the correct answer to clicker questions. Finally, we take a look an often-cited claim for gender differences in STEM participation: cognitive differences explain achievement differences in physics. We examine specifically the role of mental rotations in physics achievement and problem-solving, viewing mental rotations as a tool that students can use on physics problems. We first look at student survey results for lower-level introductory students, finding a low, but significant correlation between performance on a mental rotations test and performance in introductory physics courses. In contrast, we did not find a significant relationship for students in the upper-level introductory course. We also examine student problem-solving interviews to investigate the role of mental rotations on introductory problems.

Putting Differentials Back into Calculus

Science.gov (United States)

Dray, Tevian; Manogue, Corrine A.

2010-01-01

We argue that the use of differentials in introductory calculus courses is useful and provides a unifying theme, leading to a coherent view of the calculus. Along the way, we meet several interpretations of differentials, some better than others.

Effectiveness of Workshop Style Teaching in Students' Learning of Introductory Electricity and Magnetism

Science.gov (United States)

Mehta, Nirav; Cheng, Kelvin

2012-10-01

We have developed an interactive workshop-style course for our introductory calculus-based physics sequence at Trinity University. Lecture is limited to approximately 15 min. at the beginning of class, and the remainder of the 50-min. class is devoted to inquiry-based activities and problem solving. So far, lab is done separately and we have not incorporated the lab component into the workshop model. We use the Brief Electricity and Magnetism Assessment (BEMA) to compare learning gains between the workshop and traditional lecture-based course for the Spring 2012 semester. Both the workshop and lecture courses shared the same inquiry-based lab component that involved pre-labs, prediction-observation and post-lab activities. Our BEMA results indicate statistically significant improvement in overall learning gains compared to the traditional course. We compare our workshop BEMA scores both to traditional lecture scores here at Trinity and to those from other institutions.

TWO-PHASE EJECTOR of CARBON DIOXIDE HEAT PUMP CALCULUS

Directory of Open Access Journals (Sweden)

Sit B.M.

2010-12-01

Full Text Available It is presented the calculus of the two-phase ejector for carbon dioxide heat pump. The method of calculus is based on the method elaborated by S.M. Kandil, W.E. Lear, S.A. Sherif, and is modified taking into account entrainment ratio as the input for the calculus.

Situated Self-efficacy in Introductory Physics Students

Science.gov (United States)

Henderson, Rachel; DeVore, Seth; Michaluk, Lynnette; Stewart, John

2017-01-01

Within the general university environment, students' perceived self-efficacy has been widely studied and findings suggest it plays a role in student success. The current research adapted a self-efficacy survey, from the ``Self-Efficacy for Learning Performance'' subscale of the Motivated Learning Strategies Questionnaire and administered it to the introductory, calculus-based physics classes (N=1005) over the fall 2015 and spring 2016 semesters. This assessment measured students' self-efficacy in domains including the physics class, other science and mathematics classes, and their intended future career. The effect of gender was explored with the only significant gender difference (p gender difference was not explained by a student's performance which was measured by test average. However, a mediation analysis showed that students' overall academic self-efficacy, measured by their math and science self-efficacy, acts as a mediator for the effect of test average on self-efficacy towards the physics class domain. This mediation effect was significant for both female (p < . 01) and male students (p < . 001) however, it was more pronounced for male students.

Introductory Statistics in the Garden

Science.gov (United States)

Wagaman, John C.

2017-01-01

This article describes four semesters of introductory statistics courses that incorporate service learning and gardening into the curriculum with applications of the binomial distribution, least squares regression and hypothesis testing. The activities span multiple semesters and are iterative in nature.

Bringing research into a first semester organic chemistry laboratory with the multistep synthesis of carbohydrate-based HIV inhibitor mimics.

Science.gov (United States)

Pontrello, Jason K

2015-01-01

Benefits of incorporating research experiences into laboratory courses have been well documented, yet examples of research projects designed for the first semester introductory organic chemistry lab course are extremely rare. To address this deficiency, a Carbohydrate-Based human immunodeficiency virus (HIV) Inhibitor project consisting of a synthetic scheme of four reactions was developed for and implemented in the first semester organic lab. Students carried out the synthetic reactions during the last 6 of 10 total labs in the course, generating carbohydrate-based dimeric target molecules modeled after published dimers with application in HIV therapy. The project was designed to provide a research experience through use of literature procedures for reactions performed, exploration of variation in linker length in the target structure, and synthesis of compounds not previously reported in the scientific literature. Project assessment revealed strong student support, indicating enhanced engagement and interest in the course as a direct result of the use of scientific literature and the applications of the synthesized carbohydrate-based molecules. Regardless of discussed challenges in designing a research project for the first semester lab course, the finding from data analysis that a project implemented in the first semester lab had significantly greater student impact than a second semester project should provide motivation for development of additional research projects for a first semester organic course. © 2015 The International Union of Biochemistry and Molecular Biology.

On Flipping First-Semester Calculus: A Case Study

Science.gov (United States)

Petrillo, Joseph

2016-01-01

High failure rates in calculus have plagued students, teachers, and administrators for decades, while science, technology, engineering, and mathematics programmes continue to suffer from low enrollments and high attrition. In an effort to affect this reality, some educators are "flipping" (or inverting) their classrooms. By flipping, we…

Students' Benefit from Video with Interactive Quizzes in a First-Year Calculus Course

DEFF Research Database (Denmark)

Midtiby, Henrik Skov; Nørgaard, Cita; Kjær, Christopher

2017-01-01

The intention of this project was to study the students’ self-reported learning outcome from different formats of videos in an introductory calculus course.......The intention of this project was to study the students’ self-reported learning outcome from different formats of videos in an introductory calculus course....

Sharks, Minnows, and Wheelbarrows: Calculus Modeling Projects

Science.gov (United States)

Smith, Michael D.

2011-01-01

The purpose of this article is to present two very active applied modeling projects that were successfully implemented in a first semester calculus course at Hollins University. The first project uses a logistic equation to model the spread of a new disease such as swine flu. The second project is a human take on the popular article "Do Dogs Know…

Investigating the use of mastery-style online homework exercises in introductory algebra-based mechanics in a controlled clinical study

Science.gov (United States)

Evans, William R.; Selen, Mats A.

2017-12-01

Homework in introductory physics represents an important part of a student's learning experience; therefore, choosing the manner in which homework is presented merits investigation. We performed three rounds of clinical trials comparing the effects of mastery-style homework vs traditional-style homework with students in both algebra-based and calculus-based introductory mechanics. Results indicate a benefit from mastery-style over traditional-style homework, principally for weaker students who are less familiar with the material being covered and on questions that are nearer transfer to the study materials.

A Comprehensive Probability Project for the Upper Division One-Semester Probability Course Using Yahtzee

Science.gov (United States)

Wilson, Jason; Lawman, Joshua; Murphy, Rachael; Nelson, Marissa

2011-01-01

This article describes a probability project used in an upper division, one-semester probability course with third-semester calculus and linear algebra prerequisites. The student learning outcome focused on developing the skills necessary for approaching project-sized math/stat application problems. These skills include appropriately defining…

Topic Order in Introductory Physics and its Impact on the STEM Curricular Ladder

Directory of Open Access Journals (Sweden)

Teresa L Larkin

2017-02-01

Full Text Available Introductory physics courses are an important rung on the curricular ladder in STEM. These courses help to strengthen students critical thinking and problem solving skills while simultaneously introducing them to many topics they will explore in more detail in later courses in physics and engineering. For these reasons, introductory physics is a required element on the curricular ladder. Most often, introductory physics is offered as a two-semester sequence with basic mechanics being taught in the first semester and electricity and magnetism in the second. In fact, this curricular sequence has not been altered in decades. Is there a reason for this? There are many other enduring questions that arise pertaining to these foundation courses in physics. These questions include: Does taking the introductory course sequence “out of order” have an impact on student learning in physics? What topics should be taught? When should these topics be taught? What topics could be left out? The list of questions is essentially endless. This paper will address some of these questions in part, through a brief discussion on student learning in a second-semester algebra-based physics course. Connections will also be made to the broader curricular ladder in STEM. To this end, an illustration that makes connections to an engineering statics course will be presented. This discussion will conclude by presenting some broader implications for the larger STEM communities.

Relationships between Undergraduates' Argumentation Skills, Conceptual Quality of Problem Solutions, and Problem Solving Strategies in Introductory Physics

Science.gov (United States)

Rebello, Carina M.

2012-01-01

This study explored the effects of alternative forms of argumentation on undergraduates' physics solutions in introductory calculus-based physics. A two-phase concurrent mixed methods design was employed to investigate relationships between undergraduates' written argumentation abilities, conceptual quality of problem solutions, as well…

Multivariate calculus and geometry

CERN Document Server

Dineen, Seán

2014-01-01

Multivariate calculus can be understood best by combining geometric insight, intuitive arguments, detailed explanations and mathematical reasoning. This textbook has successfully followed this programme. It additionally provides a solid description of the basic concepts, via familiar examples, which are then tested in technically demanding situations. In this new edition the introductory chapter and two of the chapters on the geometry of surfaces have been revised. Some exercises have been replaced and others provided with expanded solutions. Familiarity with partial derivatives and a course in linear algebra are essential prerequisites for readers of this book. Multivariate Calculus and Geometry is aimed primarily at higher level undergraduates in the mathematical sciences. The inclusion of many practical examples involving problems of several variables will appeal to mathematics, science and engineering students.

Introductory Life Science Mathematics and Quantitative Neuroscience Courses

Science.gov (United States)

Duffus, Dwight; Olifer, Andrei

2010-01-01

We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an…

Using isomorphic problems to learn introductory physics

Directory of Open Access Journals (Sweden)

Shih-Yin Lin

2011-08-01

Full Text Available In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the recitation in which they had to first learn from a solved problem provided and take advantage of what they learned from it to solve another problem (which we call the quiz problem which was isomorphic. Previous research suggests that the multiple-concept quiz problem is challenging for introductory students. Students in different recitation classes received different interventions in order to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. We also conducted think-aloud interviews with four introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. We found that most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem. However, they were not necessarily able to apply the principles correctly. Research suggests that more scaffolding is needed to help students in applying these principles appropriately. We outline a few possible strategies for future investigation.

Using isomorphic problems to learn introductory physics

Science.gov (United States)

Lin, Shih-Yin; Singh, Chandralekha

2011-12-01

In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the recitation in which they had to first learn from a solved problem provided and take advantage of what they learned from it to solve another problem (which we call the quiz problem) which was isomorphic. Previous research suggests that the multiple-concept quiz problem is challenging for introductory students. Students in different recitation classes received different interventions in order to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. We also conducted think-aloud interviews with four introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. We found that most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem. However, they were not necessarily able to apply the principles correctly. Research suggests that more scaffolding is needed to help students in applying these principles appropriately. We outline a few possible strategies for future investigation.

Success in Introductory Calculus: The Role of High School and Pre-calculus Preparation

OpenAIRE

Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles

2017-01-01

Calculus at the college level has significantpotential to serve as a pump for increasing the number of students majoring inSTEM fields. It is a foundation course for all STEM majors and, if mastered well,should provide students with a positive and successful first-year experienceand gateway into more advanced courses. Studies have shown that a high percentage of studentsfailing college calculus has caused a shortage of individuals entering fieldsthat are heavily dependent on mathematics. Many...

The Complex Gradient Operator and the CR-Calculus

OpenAIRE

Kreutz-Delgado, Ken

2009-01-01

A thorough discussion and development of the calculus of real-valued functions of complex-valued vectors is given using the framework of the Wirtinger Calculus. The presented material is suitable for exposition in an introductory Electrical Engineering graduate level course on the use of complex gradients and complex Hessian matrices, and has been successfully used in teaching at UC San Diego. Going beyond the commonly encountered treatments of the first-order complex vector calculus, second-...

Calculus teaching and learning in South Korea

OpenAIRE

Natanael Karjanto

2013-01-01

This article discusses an experience of teaching Calculus classes for the freshmen students enrolled at Sungkyunkwan University, one of the private universities in South Korea. The teaching and learning approach is a balance combination between the teacher-oriented traditional style of lecturing and other activities that encourage students for active learning and classroom participation. Based on the initial observation during several semesters, some anecdotal evidences show that students'...

Calculus teaching and learning in South Korea

OpenAIRE

Karjanto, N.

2015-01-01

This article discusses an experience of teaching Calculus classes for the freshmen students enrolled at Sungkyunkwan University, one of the private universities in South Korea. The teaching and learning approach is a balance combination between the teacher-oriented traditional style of lecturing and other activities that encourage students for active learning and classroom participation. Based on the initial observation during several semesters, some anecdotal evidences show that students' le...

Teaching calculus using module based on cooperative learning strategy

Science.gov (United States)

Arbin, Norazman; Ghani, Sazelli Abdul; Hamzah, Firdaus Mohamad

2014-06-01

The purpose of the research is to evaluate the effectiveness of a module which utilizes the cooperative learning for teaching Calculus for limit, derivative and integral. The sample consists of 50 semester 1 students from the Science Programme (AT 16) Sultan Idris Education University. A set of questions of related topics (pre and post) has been used as an instrument to collect data. The data is analyzed using inferential statistics involving the paired sample t-test and the independent t-test. The result shows that students have positive inclination towards the modulein terms of understanding.

k-Schur functions and affine Schubert calculus

CERN Document Server

Lam, Thomas; Morse, Jennifer; Schilling, Anne; Shimozono, Mark; Zabrocki, Mike

2014-01-01

This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with ...

Two-parameter asymptotics in magnetic Weyl calculus

International Nuclear Information System (INIS)

Lein, Max

2010-01-01

This paper is concerned with small parameter asymptotics of magnetic quantum systems. In addition to a semiclassical parameter ε, the case of small coupling λ to the magnetic vector potential naturally occurs in this context. Magnetic Weyl calculus is adapted to incorporate both parameters, at least one of which needs to be small. Of particular interest is the expansion of the Weyl product which can be used to expand the product of operators in a small parameter, a technique which is prominent to obtain perturbation expansions. Three asymptotic expansions for the magnetic Weyl product of two Hoermander class symbols are proven as (i) ε<< 1 and λ<< 1, (ii) ε<< 1 and λ= 1, as well as (iii) ε= 1 and λ<< 1. Expansions (i) and (iii) are impossible to obtain with ordinary Weyl calculus. Furthermore, I relate the results derived by ordinary Weyl calculus with those obtained with magnetic Weyl calculus by one- and two-parameter expansions. To show the power and versatility of magnetic Weyl calculus, I derive the semirelativistic Pauli equation as a scaling limit from the Dirac equation up to errors of fourth order in 1/c.

Using an isomorphic problem pair to learn introductory physics: Transferring from a two-step problem to a three-step problem

Directory of Open Access Journals (Sweden)

Shih-Yin Lin

2013-10-01

Full Text Available In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. 382 students from a calculus-based and an algebra-based introductory physics course were administered a quiz in the recitation in which they had to learn from a solved problem provided and take advantage of what they learned from it to solve another isomorphic problem (which we call the quiz problem. The solved problem provided has two subproblems while the quiz problem has three subproblems, which is known from previous research to be challenging for introductory students. In addition to the solved problem, students also received extra scaffolding supports that were intended to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. The data analysis suggests that students had great difficulty in transferring what they learned from a two-step problem to a three-step problem. Although most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem, they were not necessarily able to apply the principles correctly. We also conducted think-aloud interviews with six introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. The interviews suggest that students often superficially mapped the principles employed in the solved problem to the quiz problem without necessarily understanding the governing conditions underlying each principle and examining the applicability of the principle in the new situation in an in-depth manner. Findings suggest that more scaffolding is needed to help students in transferring from a two-step problem to a three-step problem and applying the physics principles appropriately. We outline a few

Using an isomorphic problem pair to learn introductory physics: Transferring from a two-step problem to a three-step problem

Science.gov (United States)

Lin, Shih-Yin; Singh, Chandralekha

2013-12-01

In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. 382 students from a calculus-based and an algebra-based introductory physics course were administered a quiz in the recitation in which they had to learn from a solved problem provided and take advantage of what they learned from it to solve another isomorphic problem (which we call the quiz problem). The solved problem provided has two subproblems while the quiz problem has three subproblems, which is known from previous research to be challenging for introductory students. In addition to the solved problem, students also received extra scaffolding supports that were intended to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. The data analysis suggests that students had great difficulty in transferring what they learned from a two-step problem to a three-step problem. Although most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem, they were not necessarily able to apply the principles correctly. We also conducted think-aloud interviews with six introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. The interviews suggest that students often superficially mapped the principles employed in the solved problem to the quiz problem without necessarily understanding the governing conditions underlying each principle and examining the applicability of the principle in the new situation in an in-depth manner. Findings suggest that more scaffolding is needed to help students in transferring from a two-step problem to a three-step problem and applying the physics principles appropriately. We outline a few possible strategies

Examining the Gender Gap in Introductory Physics

Science.gov (United States)

Kost, Lauren; Pollock, Steven; Finkelstein, Noah

2009-05-01

Our previous research[1] showed that despite the use of interactive engagement techniques in the introductory physics course, the gap in performance between males and females on a mechanics conceptual learning survey persisted from pre- to post-test, at our institution. Such findings were counter to previously published work[2]. Follow-up studies[3] identified correlations between student performance on the conceptual learning survey and students' prior physics and math knowledge and their incoming attitudes and beliefs about physics and learning physics. The results indicate that the gender gap at our institution is predominantly associated with differences in males' and females' previous physics and math knowledge, and attitudes and beliefs. Our current work extends these results in two ways: 1) we look at the gender gap in the second semester of the introductory sequence and find results similar to those in the first semester course and 2) we identify ways in which males and females differentially experience several aspects of the introductory course. [1] Pollock, et al, Phys Rev: ST: PER 3, 010107. [2] Lorenzo, et al, Am J Phys 74, 118. [3] Kost, et al, PERC Proceedings 2008.

Student Achievement in College Calculus, Louisiana State University 1967-1968.

Science.gov (United States)

Scannicchio, Thomas Henry

An investigation of freshmen achievement in an introductory calculus course was performed on the basis of high school mathematics background to find predictors of college calculus grades. Overall high school academic achievement, overall high school mathematics achievement, number of high school mathematics units, pattern of college preparatory…

Crossword Puzzles as Learning Tools in Introductory Soil Science

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Barbarick, K. A.

2010-01-01

Students in introductory courses generally respond favorably to novel approaches to learning. To this end, I developed and used three crossword puzzles in spring and fall 2009 semesters in Introductory Soil Science Laboratory at Colorado State University. The first hypothesis was that crossword puzzles would improve introductory soil science…

Technical calculus with analytic geometry

CERN Document Server

Gersting, Judith L

2010-01-01

This well-thought-out text, filled with many special features, is designed for a two-semester course in calculus for technology students with a background in college algebra and trigonometry. The author has taken special care to make the book appealing to students by providing motivating examples, facilitating an intuitive understanding of the underlying concepts involved, and by providing much opportunity to gain proficiency in techniques and skills.Initial chapters cover functions and graphs, straight lines and conic sections, new coordinate systems, the derivative, using the derivative, in

Introductory Anatomy and Physiology in an Undergraduate Nursing Curriculum

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Brown, S. J.; White, S.; Power, N.

2017-01-01

Using an educational data mining approach, first-year academic achievement of undergraduate nursing students, which included two compulsory courses in introductory human anatomy and physiology, was compared with achievement in a final semester course that transitioned students into the workplace. We hypothesized that students could be grouped…

The Pendulum and the Calculus.

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Sworder, Steven C.

A pair of experiments, appropriate for the lower division fourth semester calculus or differential equations course, are presented. The second order differential equation representing the equation of motion of a simple pendulum is derived. The period of oscillation for a particular pendulum can be predicted from the solution to this equation. As a…

Introductory real analysis

CERN Document Server

Kolmogorov, A N; Silverman, Richard A

1975-01-01

Self-contained and comprehensive, this elementary introduction to real and functional analysis is readily accessible to those with background in advanced calculus. It covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, and much more. 350 problems. 1970 edition.

The absolute differential calculus calculus of tensors

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Levi-Cività, Tullio

1926-01-01

Written by a towering figure of twentieth-century mathematics, this classic examines the mathematical background necessary for a grasp of relativity theory. Tullio Levi-Civita provides a thorough treatment of the introductory theories that form the basis for discussions of fundamental quadratic forms and absolute differential calculus, and he further explores physical applications.Part one opens with considerations of functional determinants and matrices, advancing to systems of total differential equations, linear partial differential equations, algebraic foundations, and a geometrical intro

Suggested Courseware for the Non-Calculus Physics Student: Measurement, Vectors, and One-Dimensional Motion.

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Mahoney, Joyce; And Others

1988-01-01

Evaluates 16 commercially available courseware packages covering topics for introductory physics. Discusses the price, sub-topics, program type, interaction, time, calculus required, graphics, and comments of each program. Recommends two packages in measurement and vectors, and one-dimensional motion respectively. (YP)

Encouraging Example Generation: A Teaching Experiment in First-Semester Calculus

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Wagner, Elaine Rumsey; Orme, Susan Marla; Turner, Heidi Jean; Yopp, David

2017-01-01

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article…

Teaching Electrostatics and Entropy in Introductory Physics

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Reeves, Mark

Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology courses is important contribution of the entropy in driving fundamental biological processes towards equilibrium. I will present material developed to teach electrostatic screening in solutions and the function of nerve cells where entropic effects act to counterbalance electrostatic attraction. These ideas are taught in an introductory, calculus-based physics course to biomedical engineers using SCALEUP pedagogy. Results of student mastering of complex problems that cross disciplinary boundaries between biology and physics, as well as the challenges that they face in learning this material will be presented.

Cognitive development in introductory physics: A research-based approach to curriculum reform

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Teodorescu, Raluca Elena

This project describes the research on a classification of physics problems in the context of introductory physics courses. This classification, called the Taxonomy of Introductory Physics Problems (TIPP), relates physics problems to the cognitive processes required to solve them. TIPP was created for designing and clarifying educational objectives, for developing assessments that can evaluate individual component processes of the problem-solving process, and for guiding curriculum design in introductory physics courses, specifically within the context of a "thinking-skills" curriculum. TIPP relies on the following resources: (1) cognitive research findings adopted by physics education research, (2) expert-novice research discoveries acknowledged by physics education research, (3) an educational psychology taxonomy for educational objectives, and (4) various collections of physics problems created by physics education researchers or developed by textbook authors. TIPP was used in the years 2006--2008 to reform the first semester of the introductory algebra-based physics course (called Phys 11) at The George Washington University. The reform sought to transform our curriculum into a "thinking-skills" curriculum that trades "breadth for depth" by focusing on fewer topics while targeting the students' cognitive development. We employed existing research on the physics problem-solving expert-novice behavior, cognitive science and behavioral science findings, and educational psychology recommendations. Our pedagogy relies on didactic constructs such as the GW-ACCESS problem-solving protocol, learning progressions and concept maps that we have developed and implemented in our introductory physics course. These tools were designed based on TIPP. Their purpose is: (1) to help students build local and global coherent knowledge structures, (2) to develop more context-independent problem-solving abilities, (3) to gain confidence in problem solving, and (4) to establish

Calculus of tensors and differential forms

CERN Document Server

Sinha, Rajnikant

2014-01-01

Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.

Preliminary Investigation of Instructor Effects on Gender Gap in Introductory Physics

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Kreutzer, Kimberley; Boudreaux, Andrew

2012-01-01

Gender differences in student learning in the introductory, calculus-based electricity and magnetism course were assessed by administering the Conceptual Survey of Electricity and Magnetism pre- and postcourse. As expected, male students outgained females in traditionally taught sections as well as sections that incorporated interactive engagement…

Evolution of Student Knowledge in a Traditional Introductory Classroom

Science.gov (United States)

Sayre, Eleanor C.; Heckler, Andrew F.

2008-10-01

In the physics education research community, a common format for evaluation is pre- and post-tests. In this study, we collect student test data many times throughout a course, allowing for the measurement of the changes of student knowledge with a time resolution on the order of a few days. The data cover the first two quarters (mechanics, E&M) of a calculus-based introductory sequence populated primarily by first- and second-year engineering majors. To avoid the possibility of test-retest effects, separate and quasi-random subpopulations of students are evaluated every week of the quarter on a variety of tasks. Unsurprisingly for a traditional introductory course, there is little change on many conceptual questions. However, the data suggest that some student ideas peak and decay rapidly during a quarter, a pattern consistent with memory research yet unmeasurable by pre-/post-testing.

Adding Resistances and Capacitances in Introductory Electricity

Science.gov (United States)

Efthimiou, C. J.; Llewellyn, R. A.

2005-09-01

All introductory physics textbooks, with or without calculus, cover the addition of both resistances and capacitances in series and in parallel as discrete summations. However, none includes problems that involve continuous versions of resistors in parallel or capacitors in series. This paper introduces a method for solving the continuous problems that is logical, straightforward, and within the mathematical preparation of students at the introductory level.

From Random Walks to Brownian Motion, from Diffusion to Entropy: Statistical Principles in Introductory Physics

Science.gov (United States)

Reeves, Mark

2014-03-01

Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is dominant contribution of the entropy in driving important biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy) that enable students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce seemingly complex biological processes and structures to be described by tractable models that include deterministic processes and simple probabilistic inference. The students test these models in simulations and in laboratory experiments that are biologically relevant. The students are challenged to bridge the gap between statistical parameterization of their data (mean and standard deviation) and simple model-building by inference. This allows the students to quantitatively describe realistic cellular processes such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront ``random'' forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk

Correlates of gender and achievement in introductory algebra based physics

Science.gov (United States)

Smith, Rachel Clara

The field of physics is heavily male dominated in America. Thus, half of the population of our country is underrepresented and underserved. The identification of factors that contribute to gender disparity in physics is necessary for educators to address the individual needs of students, and, in particular, the separate and specific needs of female students. In an effort to determine if any correlations could be established or strengthened between sex, gender identity, social network, algebra skill, scientific reasoning ability, and/or student attitude, a study was performed on a group of 82 students in an introductory algebra based physics course. The subjects each filled out a survey at the beginning of the semester of their first semester of algebra based physics. They filled out another survey at the end of that same semester. These surveys included physics content pretests and posttests, as well as questions about the students' habits, attitudes, and social networks. Correlates of posttest score were identified, in order of significance, as pretest score, emphasis on conceptual learning, preference for male friends, number of siblings (negatively correlated), motivation in physics, algebra score, and parents' combined education level. Number of siblings was also found to negatively correlate with, in order of significance, gender identity, preference for male friends, emphasis on conceptual learning, and motivation in physics. Preference for male friends was found to correlate with, in order of significance, emphasis on conceptual learning, gender identity, and algebra score. Also, gender identity was found to correlate with emphasis on conceptual learning, the strongest predictor of posttest score other than pretest score.

Social network analysis of a project-based introductory physics course

Science.gov (United States)

Oakley, Christopher

2016-03-01

Research suggests that students benefit from peer interaction and active engagement in the classroom. The quality, nature, effect of these interactions is currently being explored by Physics Education Researchers. Spelman College offers an introductory physics sequence that addresses content and research skills by engaging students in open-ended research projects, a form of Project-Based Learning. Students have been surveyed at regular intervals during the second semester of trigonometry-based course to determine the frequency of interactions in and out of class. These interactions can be with current or past students, tutors, and instructors. This line of inquiry focuses on metrics of Social Network analysis, such as centrality of participants as well as segmentation of groups. Further research will refine and highlight deeper questions regarding student performance in this pedagogy and course sequence.

Class Size and Academic Achievement in Introductory Political Science Courses

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Towner, Terri L.

2016-01-01

Research on the influence of class size on student academic achievement is important for university instructors, administrators, and students. The article examines the influence of class size--a small section versus a large section--in introductory political science courses on student grades in two comparable semesters. It is expected that…

Tablet PC: A Preliminary Report on a Tool for Teaching Calculus

Science.gov (United States)

Gorgievski, Nicholas; Stroud, Robert; Truxaw, Mary; DeFranco, Thomas

2005-01-01

This study examined students' perceptions of the Tablet PC as an instructional tool for teaching Calculus. A thirteen item survey was developed by the researchers and administered to 103 students in an introductory Calculus course at a large university in the Northeast of the United States. The purpose of this survey was to collect data regarding…

Analysis of the Impact of Introductory Physics on Engineering Students at Texas A&M University

Science.gov (United States)

Perry, Jonathan; Bassichis, William

Introductory physics forms a major part of the foundational knowledge of engineering majors, independent of discipline and institution. While the content of introductory physics courses is consistent from institution to institution, the manner in which it is taught can vary greatly due to professor, textbook, instructional method, and overall course design. This work attempts to examine variations in student success, as measured by overall academic performance in an engineering major, and matriculation rates, based on the type of introductory physics a student took while enrolled in an engineering degree at Texas A&M University. Specific options for introductory physics at Texas A&M University include two calculus based physics courses, one traditional (UP), and one more mathematically rigorous (DP), transfer credit, and high school (AP or dual) credit. In order to examine the impact of introductory physics on a student's degree progression, data mining analyses are performed on a data set of relatively comprehensive academic records for all students enrolled as an engineering major for a minimum of one academic term. Student data has been collected for years of entering freshman beginning in 1990 and ending in 2010. Correlations will be examined between freshman level courses, including introductory physics, and follow on engineering courses, matriculation rates, and time to graduation.

Tale of two curricula: The performance of 2000 students in introductory electromagnetism

Directory of Open Access Journals (Sweden)

Matthew A. Kohlmyer

2009-10-01

Full Text Available The performance of over 2000 students in introductory calculus-based electromagnetism (E&M courses at four large research universities was measured using the Brief Electricity and Magnetism Assessment (BEMA. Two different curricula were used at these universities: a traditional E&M curriculum and the Matter & Interactions (M&I curriculum. At each university, postinstruction BEMA test averages were significantly higher for the M&I curriculum than for the traditional curriculum. The differences in post-test averages cannot be explained by differences in variables such as preinstruction BEMA scores, grade point average, or SAT Reasoning Test (SAT scores. BEMA performance on categories of items organized by subtopic was also compared at one of the universities; M&I averages were significantly higher in each topic. The results suggest that the M&I curriculum is more effective than the traditional curriculum at teaching E&M concepts to students, possibly because the learning progression in M&I reorganizes and augments the traditional sequence of topics, for example, by increasing early emphasis on the vector field concept and by emphasizing the effects of fields on matter at the microscopic level.

A TENTATIVE GUIDE, DIFFERENTIAL AND INTEGRAL CALCULUS.

Science.gov (United States)

BRANT, VINCENT; GERARDI, WILLIAM

THE COURSE IS INTENDED TO GO BEYOND THE REQUIREMENTS OF THE ADVANCED PLACEMENT PROGRAM IN MATHEMATICS AS DESIGNED BY THE COLLEGE ENTRANCE EXAMINATION BOARD. THE ADVANCED PLACEMENT PROGRAM CONSISTS OF A 1-YEAR COURSE COMBINING ANALYTIC GEOMETRY AND CALCULUS. PRESUPPOSED HERE ARE--A SEMESTER COURSE IN ANALYTIC GEOMETRY AND A THOROUGH KNOWLEDGE OF…

Calculus introductory theory and applications in physical and life science

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Johnson, R M

1995-01-01

This lucid and balanced introduction for first year engineers and applied mathematicians conveys the clear understanding of the fundamentals and applications of calculus, as a prelude to studying more advanced functions. Short and fundamental diagnostic exercises at the end of each chapter test comprehension before moving to new material.Provides a clear understanding of the fundamentals and applications of calculus, as a prelude to studying more advanced functionsIncludes short, useful diagnostic exercises at the end of each chapter

The Association of Precollege Use of Calculators with Student Performance in College Calculus

Science.gov (United States)

Mao, Yi; White, Tyreke; Sadler, Philip M.; Sonnert, Gerhard

2017-01-01

This study investigates how the use of calculators during high school mathematics courses is associated with student performance in introductory college calculus courses in the USA. Data were drawn from a nationally representative sample of 7087 students enrolled in college calculus at 134 colleges and universities. They included information about…

Comparing the efficacy of multimedia modules with traditional textbooks for learning introductory physics content

Science.gov (United States)

Stelzer, Timothy; Gladding, Gary; Mestre, José P.; Brookes, David T.

2009-02-01

We compared the efficacy of multimedia learning modules with traditional textbooks for the first few topics of a calculus-based introductory electricity and magnetism course. Students were randomly assigned to three groups. One group received the multimedia learning module presentations, and the other two received the presentations via written text. All students were then tested on their learning immediately following the presentations as well as 2weeks later. The students receiving the multimedia learning modules performed significantly better on both tests than the students experiencing the text-based presentations.

Computer-Automated Approach for Scoring Short Essays in an Introductory Statistics Course

Science.gov (United States)

Zimmerman, Whitney Alicia; Kang, Hyun Bin; Kim, Kyung; Gao, Mengzhao; Johnson, Glenn; Clariana, Roy; Zhang, Fan

2018-01-01

Over two semesters short essay prompts were developed for use with the Graphical Interface for Knowledge Structure (GIKS), an automated essay scoring system. Participants were students in an undergraduate-level online introductory statistics course. The GIKS compares students' writing samples with an expert's to produce keyword occurrence and…

Assessing students' conceptual knowledge of electricity and magnetism

Science.gov (United States)

McColgan, Michele W.; Finn, Rose A.; Broder, Darren L.; Hassel, George E.

2017-12-01

We present the Electricity and Magnetism Conceptual Assessment (EMCA), a new assessment aligned with second-semester introductory physics courses. Topics covered include electrostatics, electric fields, circuits, magnetism, and induction. We have two motives for writing a new assessment. First, we find other assessments such as the Brief Electricity and Magnetism Assessment and the Conceptual Survey on Electricity and Magnetism not well aligned with the topics and content depth of our courses. We want to test introductory physics content at a level appropriate for our students. Second, we want the assessment to yield scores and gains comparable to the widely used Force Concept Inventory (FCI). After five testing and revision cycles, the assessment was finalized in early 2015 and is available online. We present performance results for a cohort of 225 students at Siena College who were enrolled in our algebra- and calculus-based physics courses during the spring 2015 and 2016 semesters. We provide pretest, post-test, and gain analyses, as well as individual question and whole test statistics to quantify difficulty and reliability. In addition, we compare EMCA and FCI scores and gains, and we find that students' FCI scores are strongly correlated with their performance on the EMCA. Finally, the assessment was piloted in an algebra-based physics course at George Washington University (GWU). We present performance results for a cohort of 130 GWU students and we find that their EMCA scores are comparable to the scores of students in our calculus-based physics course.

Internet computer coaches for introductory physics problem solving

Science.gov (United States)

Xu Ryan, Qing

The ability to solve problems in a variety of contexts is becoming increasingly important in our rapidly changing technological society. Problem-solving is a complex process that is important for everyday life and crucial for learning physics. Although there is a great deal of effort to improve student problem solving skills throughout the educational system, national studies have shown that the majority of students emerge from such courses having made little progress toward developing good problem-solving skills. The Physics Education Research Group at the University of Minnesota has been developing Internet computer coaches to help students become more expert-like problem solvers. During the Fall 2011 and Spring 2013 semesters, the coaches were introduced into large sections (200+ students) of the calculus based introductory mechanics course at the University of Minnesota. This dissertation, will address the research background of the project, including the pedagogical design of the coaches and the assessment of problem solving. The methodological framework of conducting experiments will be explained. The data collected from the large-scale experimental studies will be discussed from the following aspects: the usage and usability of these coaches; the usefulness perceived by students; and the usefulness measured by final exam and problem solving rubric. It will also address the implications drawn from this study, including using this data to direct future coach design and difficulties in conducting authentic assessment of problem-solving.

A MATLAB companion for multivariable calculus

CERN Document Server

Cooper, Jeffery

2001-01-01

Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, A MatLab Companion for Multivariable Calculus introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton''s method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http://www.harcourt-ap.com/matlab.html.* Computer-oriented material that complements the essential topics in multivariable calculus* Main ideas presented with examples of computations and graphics displays using MATLAB * Numerous examples of short code in the text, which can be modified for use with the exercises* MATLAB files are used to implem...

An ellipsoidal calculus based on propagation and fusion.

Science.gov (United States)

Ros, L; Sabater, A; Thomas, F

2002-01-01

Presents an ellipsoidal calculus based solely on two basic operations: propagation and fusion. Propagation refers to the problem of obtaining an ellipsoid that must satisfy an affine relation with another ellipsoid, and fusion to that of computing the ellipsoid that tightly bounds the intersection of two given ellipsoids. These two operations supersede the Minkowski sum and difference, affine transformation and intersection tight bounding of ellipsoids on which other ellipsoidal calculi are based. Actually, a Minkowski operation can be seen as a fusion followed by a propagation and an affine transformation as a particular case of propagation. Moreover, the presented formulation is numerically stable in the sense that it is immune to degeneracies of the involved ellipsoids and/or affine relations. Examples arising when manipulating uncertain geometric information in the context of the spatial interpretation of line drawings are extensively used as a testbed for the presented calculus.

Representations in Calculus: Two Contrasting Cases.

Science.gov (United States)

Aspinwall, Leslie; Shaw, Kenneth L.

2002-01-01

Illustrates the contrasting thinking processes of two beginning calculus students' geometric and analytic schemes for the derivative function. Suggests that teachers can enhance students' understanding by continuing to demonstrate how different representations of the same mathematical concept provide additional information. (KHR)

Beginning Introductory Physics with Two-Dimensional Motion

Science.gov (United States)

Huggins, Elisha

2009-01-01

During the session on "Introductory College Physics Textbooks" at the 2007 Summer Meeting of the AAPT, there was a brief discussion about whether introductory physics should begin with one-dimensional motion or two-dimensional motion. Here we present the case that by starting with two-dimensional motion, we are able to introduce a considerable…

Success in Introductory Calculus: The Role of High School and Pre-Calculus Preparation

Science.gov (United States)

Ayebo, Abraham; Ukkelberg, Sarah; Assuah, Charles

2017-01-01

Calculus at the college level has significant potential to serve as a pump for increasing the number of students majoring in STEM fields. It is a foundation course for all STEM majors and, if mastered well, should provide students with a positive and successful first-year experience and gateway into more advanced courses. Studies have shown that a…

Characterizing, modeling, and addressing gender disparities in introductory college physics

Science.gov (United States)

Kost-Smith, Lauren Elizabeth

2011-12-01

The underrepresentation and underperformance of females in physics has been well documented and has long concerned policy-makers, educators, and the physics community. In this thesis, we focus on gender disparities in the first- and second-semester introductory, calculus-based physics courses at the University of Colorado. Success in these courses is critical for future study and careers in physics (and other sciences). Using data gathered from roughly 10,000 undergraduate students, we identify and model gender differences in the introductory physics courses in three areas: student performance, retention, and psychological factors. We observe gender differences on several measures in the introductory physics courses: females are less likely to take a high school physics course than males and have lower standardized mathematics test scores; males outscore females on both pre- and post-course conceptual physics surveys and in-class exams; and males have more expert-like attitudes and beliefs about physics than females. These background differences of males and females account for 60% to 70% of the gender gap that we observe on a post-course survey of conceptual physics understanding. In analyzing underlying psychological factors of learning, we find that female students report lower self-confidence related to succeeding in the introductory courses (self-efficacy) and are less likely to report seeing themselves as a "physics person". Students' self-efficacy beliefs are significant predictors of their performance, even when measures of physics and mathematics background are controlled, and account for an additional 10% of the gender gap. Informed by results from these studies, we implemented and tested a psychological, self-affirmation intervention aimed at enhancing female students' performance in Physics 1. Self-affirmation reduced the gender gap in performance on both in-class exams and the post-course conceptual physics survey. Further, the benefit of the self

Student Selection of the Textbook for an Introductory Physics Course

Science.gov (United States)

Dake, L. S.

2007-01-01

Several years ago I had to select a new textbook for my calculus-based introductory physics class. I subscribe to Just-in-Time Teaching methods,1 which require students to read the book before the material is covered in class. Thus, the readability of the text by the students is critical. However, I did not feel that I was the best judge of this…

Patterns of Incorrect Responses on the FCI and Course Success

Science.gov (United States)

Wells, James; Mokaya, Fridah; Valente, Diego

The Force Concept Inventory (FCI) is often used to measure the effectiveness of instructional pedagogy in introductory physics courses both at the algebra- and calculus-based level. Scores on the FCI are correlated with the performance of students in a class, as measured by their final course grade. We have collected data from several semesters of first-semester introductory mechanics courses at a public 4-year university, taught in large-scale classrooms with pedagogy including elements of Just-in-Time Teaching pedagogy along with active learning course components. The data collected includes pre- and post-test FCI scores, midterm exam grades, and final course grades. We examine whether certain patterns of incorrect answers on the FCI post-test are predictive of course grades, indicating whether certain specific student preconceptions are more detrimental than others to the success of students in an introductory mechanics course. Funding from UConn - College of Liberal Arts and Sciences (CLAS).

Introductory life science mathematics and quantitative neuroscience courses.

Science.gov (United States)

Duffus, Dwight; Olifer, Andrei

2010-01-01

We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an upper-division course in computational neuroscience. We provide a description of each course, detailed syllabi, examples of content, and a brief discussion of the main issues encountered in developing and offering the courses.

Two cosmological solutions of Regge calculus

International Nuclear Information System (INIS)

Lewis, S.M.

1982-01-01

Two cosmological solutions of Regge calculus are presented which correspond to the flat Friedmann-Robertson-Walker and the Kasner solutions of general relativity. By taking advantage of the symmetries that are present, I am able to show explicitly that a limit of Regge calculus does yield Einstein's equations for these cases. The method of averaging these equations when taking limits is important, especially for the Kasner model. I display the leading error term that arises from keeping the Regge equations in discrete form rather than using their continuum limit. In particular, this work shows that for the ''Reggeized'' Friedmann model the minimum volume is a velocity-dominated singularity as in the continuum Friedmann model. However, unlike the latter, the Regge version has a nonzero minimum volume

Connecting Symbolic Integrals to Physical Meaning in Introductory Physics

Science.gov (United States)

Amos, Nathaniel R.

This dissertation presents a series of studies pertaining to introductory physics students' abilities to derive physical meaning from symbolic integrals (e.g., the integral of vdt) and their components, namely differentials and differential products (e.g., dt and vdt, respectively). Our studies focus on physical meaning in the form of interpretations (e.g., "the total displacement of an object") and units (e.g., "meters"). Our first pair of studies independently attempted to identify introductory-level mechanics students' common conceptual difficulties with and unproductive interpretations of physics integrals and their components, as well as to estimate the frequencies of these difficulties. Our results confirmed some previously-observed incorrect interpretations, such as the notion that differentials are physically meaningless; however, we also uncovered two new conceptualizations of differentials, the "rate" (differentials are "rates" or "derivatives") and "instantaneous value" (differentials are values of physical variables "at an instant") interpretations, which were exhibited by more than half of our participants at least once. Our next study used linear regression analysis to estimate the strengths of the inter-connections between the abilities to derive physical meaning from each of differentials, differential products, and integrals in both first- and second-semester, calculus-based introductory physics. As part of this study, we also developed a highly reliable, multiple choice assessment designed to measure students' abilities to connect symbolic differentials, differential products, and integrals with their physical interpretations and units. Findings from this study were consistent with statistical mediation via differential products. In particular, students' abilities to extract physical meaning from differentials were seen to be strongly related to their abilities to derive physical meaning from differential products, and similarly differential

Student Performance in Introductory Psychology Following Termination of the Programmed Achievement Contingency at Mid-Semester

Science.gov (United States)

Nation, Jack R.; And Others

1977-01-01

Discusses the Programmed Achievement learning system in an introductory psychology course. This system is based on an instructional system of motivation and reward in which a crucial ingredient is the testing procedure. (Author/JR)

Students' conceptions of evidence during a university introductory forensic science course

Science.gov (United States)

Yeshion, Theodore Elliot

Students' Conceptions of Science, Scientific Evidence, and Forensic Evidence during a University Introductory Forensic Science Course This study was designed to examine and understand what conceptions undergraduate students taking an introductory forensic science course had about scientific evidence. Because the relationships between the nature of science, the nature of evidence, and the nature of forensic evidence are not well understood in the science education literature, this study sought to understand how these concepts interact and affect students' understanding of scientific evidence. Four participants were purposefully selected for this study from among 89 students enrolled in two sections of an introductory forensic science course taught during the fall 2005 semester. Of the 89 students, 84 were criminal justice majors with minimal science background and five were chemistry majors with academic backgrounds in the natural and physical sciences. All 89 students completed a biographical data sheet and a pre-instruction Likert scale survey consisting of twenty questions relating to the nature of scientific evidence. An evaluation of these two documents resulted in a purposeful selection of four varied student participants, each of whom was interviewed three times throughout the semester about the nature of science, the nature of evidence, and the nature of forensic evidence. The same survey was administered to the participants again at the end of the semester-long course. This study examined students' assumptions, prior knowledge, their understanding of scientific inference, scientific theory, and methodology. Examination of the data found few differences with regard to how the criminal justice majors and the chemistry majors responded to interview questions about forensic evidence. There were qualitative differences, however, when the same participants answered interview questions relating to traditional scientific evidence. Furthermore, suggestions are

Research and Teaching: Reenvisioning the Introductory Science Course as a Cognitive Apprenticeship

Science.gov (United States)

Thompson, Meredith M.; Pastorino, Lucia; Lee, Star; Lipton, Paul

2016-01-01

Introductory science courses play a critical role in the recruitment and retention of undergraduate science majors. In particular, first-year courses are opportunities to engage students in scientific practices and motivate them to consider scientific careers. We developed an introductory course using a semester-long series of established…

Documenting the conversion from traditional to Studio Physics formats at the Colorado School of Mines: Process and early results

Science.gov (United States)

Kohl, Patrick B.; Kuo, H. Vincent; Ruskell, Todd G.

2008-10-01

The Colorado School of Mines (CSM) has taught its first-semester introductory physics course using a hybrid lecture/Studio Physics format for several years. Over the past year we have converted the second semester of our calculus-based introductory physics course (Physics II) to a Studio Physics format, starting from a traditional lecture-based format. In this paper, we document the early stages of this conversion in order to better understand which features succeed and which do not, and in order to develop a model for switching to Studio that keeps the time and resource investment manageable. We describe the recent history of the Physics II course and of Studio at Mines, discuss the PER-based improvements that we are implementing, and characterize our progress via several metrics, including pre/post Conceptual Survey of Electricity and Magnetism (CSEM) scores, Colorado Learning About Science Survey scores (CLASS), solicited student comments, failure rates, and exam scores.

Studio Physics at the Colorado School of Mines: A model for iterative development and assessment

Science.gov (United States)

Kohl, Patrick; Kuo, Vincent

2009-05-01

The Colorado School of Mines (CSM) has taught its first-semester introductory physics course using a hybrid lecture/Studio Physics format for several years. Based on this previous success, over the past 18 months we have converted the second semester of our traditional calculus-based introductory physics course (Physics II) to a Studio Physics format. In this talk, we describe the recent history of the Physics II course and of Studio at Mines, discuss the PER-based improvements that we are implementing, and characterize our progress via several metrics, including pre/post Conceptual Survey of Electricity and Magnetism (CSEM) scores, Colorado Learning About Science Survey scores (CLASS), failure rates, and exam scores. We also report on recent attempts to involve students in the department's Senior Design program with our course. Our ultimate goal is to construct one possible model for a practical and successful transition from a lecture course to a Studio (or Studio-like) course.

Impact of the second semester University Modeling Instruction course on students’ representation choices

Directory of Open Access Journals (Sweden)

Daryl McPadden

2017-11-01

Full Text Available Representation use is a critical skill for learning, problem solving, and communicating in science, especially in physics where multiple representations often scaffold the understanding of a phenomenon. University Modeling Instruction, which is an active-learning, research-based introductory physics curriculum centered on students’ use of scientific models, has made representation use a primary learning goal with explicit class time devoted to introducing and coordinating representations as part of the model building process. However, because of the semester break, the second semester course, Modeling Instruction-Electricity and Magnetism (MI-EM, contains a mixture of students who are returning from the Modeling Instruction-mechanics course (to whom we refer to as “returning students” and students who are new to Modeling Instruction with the MI-EM course (to whom we refer to as “new students”. In this study, we analyze the impact of MI-EM on students’ representation choices across the introductory physics content for these different groups of students by examining both what individual representations students choose and their average number of representations on a modified card-sort survey with a variety of mechanics and EM questions. Using Wilcoxon-signed-rank tests, Wilcoxon-Mann-Whitney tests, Cliff’s delta effect sizes, and box plots, we compare students’ representation choices from pre- to postsemester, from new and returning students, and from mechanics and EM content. We find that there is a significant difference between returning and new students’ representation choices, which serves as a baseline comparison between Modeling Instruction and traditional lecture-based physics classes. We also find that returning students maintain a high representation use across the MI-EM semester, while new students see significant growth in their representation use regardless of content.

Assessing students’ conceptual knowledge of electricity and magnetism

Directory of Open Access Journals (Sweden)

Michele W. McColgan

2017-10-01

Full Text Available We present the Electricity and Magnetism Conceptual Assessment (EMCA, a new assessment aligned with second-semester introductory physics courses. Topics covered include electrostatics, electric fields, circuits, magnetism, and induction. We have two motives for writing a new assessment. First, we find other assessments such as the Brief Electricity and Magnetism Assessment and the Conceptual Survey on Electricity and Magnetism not well aligned with the topics and content depth of our courses. We want to test introductory physics content at a level appropriate for our students. Second, we want the assessment to yield scores and gains comparable to the widely used Force Concept Inventory (FCI. After five testing and revision cycles, the assessment was finalized in early 2015 and is available online. We present performance results for a cohort of 225 students at Siena College who were enrolled in our algebra- and calculus-based physics courses during the spring 2015 and 2016 semesters. We provide pretest, post-test, and gain analyses, as well as individual question and whole test statistics to quantify difficulty and reliability. In addition, we compare EMCA and FCI scores and gains, and we find that students’ FCI scores are strongly correlated with their performance on the EMCA. Finally, the assessment was piloted in an algebra-based physics course at George Washington University (GWU. We present performance results for a cohort of 130 GWU students and we find that their EMCA scores are comparable to the scores of students in our calculus-based physics course.

A calculus for attribute-based communication

DEFF Research Database (Denmark)

Alrahman, Yehia Abd; De Nicola, Rocco; Loreti, Michele

2015-01-01

The notion of attribute-based communication seems promising to model and analyse systems with huge numbers of interacting components that dynamically adjust and combine their behaviour to achieve specific goals. A basic process calculus, named AbC, is introduced that has as primitive construct...... of how well-established process calculi could be encoded into AbC is given by considering the translation into AbC of a proto-typical π-calculus process....

Effect of scaffolding on helping introductory physics students solve quantitative problems involving strong alternative conceptions

Science.gov (United States)

Lin, Shih-Yin; Singh, Chandralekha

2015-12-01

It is well known that introductory physics students often have alternative conceptions that are inconsistent with established physical principles and concepts. Invoking alternative conceptions in the quantitative problem-solving process can derail the entire process. In order to help students solve quantitative problems involving strong alternative conceptions correctly, appropriate scaffolding support can be helpful. The goal of this study is to examine how different scaffolding supports involving analogical problem-solving influence introductory physics students' performance on a target quantitative problem in a situation where many students' solution process is derailed due to alternative conceptions. Three different scaffolding supports were designed and implemented in calculus-based and algebra-based introductory physics courses involving 410 students to evaluate the level of scaffolding needed to help students learn from an analogical problem that is similar in the underlying principles involved but for which the problem-solving process is not derailed by alternative conceptions. We found that for the quantitative problem involving strong alternative conceptions, simply guiding students to work through the solution of the analogical problem first was not enough to help most students discern the similarity between the two problems. However, if additional scaffolding supports that directly helped students examine and repair their knowledge elements involving alternative conceptions were provided, e.g., by guiding students to contemplate related issues and asking them to solve the targeted problem on their own first before learning from the analogical problem provided, students were more likely to discern the underlying similarities between the problems and avoid getting derailed by alternative conceptions when solving the targeted problem. We also found that some scaffolding supports were more effective in the calculus-based course than in the algebra-based

Two- and three-loop amplitudes in covariant loop calculus

International Nuclear Information System (INIS)

Roland, K.

1989-01-01

We study two- and three-loop vacuum amplitudes for the closed bosonic string. We compare two sets of expressions for the corresponding density on moduli space. One is based on the covariant reggeon loop calculus (where modular invariance is not manifest). The other is based on analytic geometry. We want to prove identity between the two sets of expressions. Quite apart from demonstrating modular invariance of the reggeon results, this would in itself be a remarkable mathematical feature. Identity is established to ''high'' order in some moduli and exactly in others. The expansions reveal an essentially number-theoretic structure. Agreement is found only by exploiting the connection between the four Jacobi θ-functions and number theory. (orig.)

From F = ma to flying squirrels: curricular change in an introductory physics course.

Science.gov (United States)

O'Shea, Brian; Terry, Laura; Benenson, Walter

2013-06-01

We present outcomes from curricular changes made to an introductory calculus-based physics course whose audience is primarily life sciences majors, the majority of whom plan to pursue postbaccalaureate studies in medical and scientific fields. During the 2011-2012 academic year, we implemented a Physics of the Life Sciences curriculum centered on a draft textbook that takes a novel approach to teaching physics to life sciences majors. In addition, substantial revisions were made to the homework and hands-on components of the course to emphasize the relationship between physics and the life sciences and to help the students learn to apply physical intuition to life sciences-oriented problems. Student learning and attitudinal outcomes were assessed both quantitatively, using standard physics education research instruments, and qualitatively, using student surveys and a series of postsemester interviews. Students experienced high conceptual learning gains, comparable to other active learning-based physics courses. Qualitatively, a substantial fraction of interviewed students reported an increased interest in physics relative to the beginning of the semester. Furthermore, more than half of students self-reported that they could now relate physics topics to their majors and future careers, with interviewed subjects demonstrating a high level of ability to come up with examples of how physics affects living organisms and how it helped them to better understand content presented in courses in their major.

A many-sorted calculus based on resolution and paramodulation

CERN Document Server

Walther, Christoph

1987-01-01

A Many-Sorted Calculus Based on Resolution and Paramodulation emphasizes the utilization of advantages and concepts of many-sorted logic for resolution and paramodulation based automated theorem proving.This book considers some first-order calculus that defines how theorems from given hypotheses by pure syntactic reasoning are obtained, shifting all the semantic and implicit argumentation to the syntactic and explicit level of formal first-order reasoning. This text discusses the efficiency of many-sorted reasoning, formal preliminaries for the RP- and ?RP-calculus, and many-sorted term rewrit

Comparing the Attitudes of Pre-Health Professional and Engineering Students in Introductory Physics Courses

Science.gov (United States)

McKinney, Meghan

2015-04-01

This talk will discuss using the Colorado Learning Attitudes about Science Survey (CLASS) to compare student attitudes towards the study of physics of two different groups. Northern Illinois University has two levels of introductory mechanics courses, one geared towards biology majors and pre-health professionals, and one for engineering and physics majors. The course for pre-health professionals is an algebra based course, while the course for engineering and physics majors is a calculus based course. We've adapted the CLASS into a twenty question survey that measures student attitudes towards the practice of and conceptions about physics. The survey is administered as a pre and post assessment to look at student attitudes before and after their first course in physics.

Two- and three-loop amplitudes in covariant loop calculus

International Nuclear Information System (INIS)

Roland, K.

1988-04-01

We study 2- and 3-loop vacuum-amplitudes for the closed bosonic string. We compare two sets of expressions for the corresponding density on moduli space: One, based on the covariant Reggeon loop calculus (where modular invariance is not manifest). The other, based on analytic geometry. We want to prove identity between the two sets of expressions. Quite apart from demonstrating modular invariance of the Reggeon results, this would in itself be a remarkable mathematical feature. Identity is established to 'high' order in some moduli and exactly in others. The expansions reveal an essentially number-theoretical structure. Agreement is found only by exploiting the connection between the 4 Jacobi θ-functions and number theory. (orig.)

Can Earth Materials BE Adequately Covered in a - or Two-Semester Course?

Science.gov (United States)

Hefferan, K. P.; O'Brien, J.

2007-12-01

Traditional geology programs offer courses in mineralogy, optical mineralogy, igneous petrology, metamorphic petrology, sedimentology and economic geology. At many universities this suite of mineralogy/petrology courses has been supplanted by a one-semester or two-semester Earth Materials course. This interactive poster poses five questions to faculty and students related to the means by which Earth Materials can be delivered: 1) Available online syllabi demonstrate a wide variation in the topics addressed in Earth Materials courses; is there a standard core of key topics that must be covered and in what level of detail? 2) Can a one-semester or two- semester Earth Materials course adequately cover these topics? 3) Excellent textbooks exist in both mineralogy and in petrology; what textbooks, if any, adequately encompass Earth Materials? 4) How has the online environment changed the way in which we use textbooks in the classroom? 5) Given the evolution of geology programs, higher education and the global economy in the past twenty years, what additional changes can be anticipated with respect to delivery and demand of Earth Materials topics? Answers-- or at least related discussions-- to these questions are encouraged via verbal dialogue among participants and/or by comments written on the poster. Our goal is to solicit faculty, student and industry feedback to create a textbook, curricula and online materials that support an Earth Materials course.

Student effort expectations and their learning in first-year introductory physics: A case study in Thailand

Directory of Open Access Journals (Sweden)

N. Emarat

2011-06-01

Full Text Available The Maryland Physics Expectations (MPEX survey was designed to probe students’ expectations about their understanding of the process of learning physics and the structure of physics knowledge—cognitive expectations. This survey was administered to first-year university students in Thailand in the first semester of an introductory calculus-based physics course during academic years 2007 and 2008, to assess their expectations at the beginning of the course. The precourse MPEX results were compared and correlated with two separate measures of student learning: (1 individual students’ normalized gains from pre and post Force and Motion Conceptual Evaluation (FMCE results, which measure students’ conceptual understanding, and (2 student’s scores on the final exam, which measure their more general problem-solving ability. The results showed a significant positive correlation between their overall MPEX score and five of the six MPEX cluster scores, with their normalized learning gains on the FMCE for both academic years. The results also showed significant positive correlations between student MPEX scores and their final exam scores for the overall MPEX score and all MPEX cluster scores except for the effort cluster. We interviewed two groups of five students each, one group with small favorable scores on the precourse MPEX effort cluster and one with high favorable scores on the precourse MPEX effort cluster, to see how the students’ learning efforts compared with their MPEX results. We concluded from the interviews that what the students think or expect about the MPEX effort involved in learning physics does not match what they actually do.

Student effort expectations and their learning in first-year introductory physics: A case study in Thailand

Directory of Open Access Journals (Sweden)

U. Wutchana

2011-06-01

Full Text Available The Maryland Physics Expectations (MPEX survey was designed to probe students’ expectations about their understanding of the process of learning physics and the structure of physics knowledge—cognitive expectations. This survey was administered to first-year university students in Thailand in the first semester of an introductory calculus-based physics course during academic years 2007 and 2008, to assess their expectations at the beginning of the course. The precourse MPEX results were compared and correlated with two separate measures of student learning: (1 individual students’ normalized gains from pre and post Force and Motion Conceptual Evaluation (FMCE results, which measure students’ conceptual understanding, and (2 student’s scores on the final exam, which measure their more general problem-solving ability. The results showed a significant positive correlation between their overall MPEX score and five of the six MPEX cluster scores, with their normalized learning gains on the FMCE for both academic years. The results also showed significant positive correlations between student MPEX scores and their final exam scores for the overall MPEX score and all MPEX cluster scores except for the effort cluster. We interviewed two groups of five students each, one group with small favorable scores on the precourse MPEX effort cluster and one with high favorable scores on the precourse MPEX effort cluster, to see how the students’ learning efforts compared with their MPEX results. We concluded from the interviews that what the students think or expect about the MPEX effort involved in learning physics does not match what they actually do.

Student effort expectations and their learning in first-year introductory physics: A case study in Thailand

Science.gov (United States)

Wutchana, U.; Emarat, N.

2011-06-01

The Maryland Physics Expectations (MPEX) survey was designed to probe students’ expectations about their understanding of the process of learning physics and the structure of physics knowledge—cognitive expectations. This survey was administered to first-year university students in Thailand in the first semester of an introductory calculus-based physics course during academic years 2007 and 2008, to assess their expectations at the beginning of the course. The precourse MPEX results were compared and correlated with two separate measures of student learning: (1) individual students’ normalized gains from pre and post Force and Motion Conceptual Evaluation (FMCE) results, which measure students’ conceptual understanding, and (2) student’s scores on the final exam, which measure their more general problem-solving ability. The results showed a significant positive correlation between their overall MPEX score and five of the six MPEX cluster scores, with their normalized learning gains on the FMCE for both academic years. The results also showed significant positive correlations between student MPEX scores and their final exam scores for the overall MPEX score and all MPEX cluster scores except for the effort cluster. We interviewed two groups of five students each, one group with small favorable scores on the precourse MPEX effort cluster and one with high favorable scores on the precourse MPEX effort cluster, to see how the students’ learning efforts compared with their MPEX results. We concluded from the interviews that what the students think or expect about the MPEX effort involved in learning physics does not match what they actually do.

Improving student performance in an introductory biology majors course: A social action project in the scholarship of teaching

Science.gov (United States)

Chambers, Sara Lang Ketchum

This social action study followed an introductory biology course for a three-year period to determine whether changes in teaching personnel, instructional techniques and reorientation to student-centered learning would impact student performance. The course was redirected from a traditional lecture-laboratory format to one emphasizing active learning inquiry methods. Student retention, achievement, and failure were observed for three years in addition to one year prior, and one year following, the study. The study examined the two semester introductory biology course required of all biology majors and those intending a career in science, medicine or dentistry. During the first semester of the study, the dropout rate decreased from 46% to 21%. Prior to the study, 39% of the students completing the course received a grade of D or F while only 4% received a grade of B or above. During the first semester of the study 14% of the students received a grade of D or F while 46% received a B, B+ or A grade. Similar results were seen in other semesters of the study. A statistical comparison of student retention and performance was carried out using grade data for classes taught by the original faculty, the action study faculty and the post-study faculty. The differences between the original faculty and the action study faculty were statistically significant. Effect size calculations indicated large differences between the action study faculty and the two other faculty groups in terms of student retention, achievement and failure. The results are attributed to both the personnel change and, more significantly, the change in teaching methods and emphasis on student-active learning. Comparison between the pre- and post-study teams showed less dramatic effect sizes than when the action study data were compared with the data from either other team. Nevertheless, the post-study results showed that although the retention rate dropped during the year after the study, the improvement

Chronicling a successful secondary implementation of Studio Physics

Science.gov (United States)

Kohl, Patrick B.; Vincent Kuo, H.

2012-09-01

The Colorado School of Mines (CSM) has taught its first-semester calculus-based introductory physics course (Physics I) using a hybrid lecture/Studio Physics format since the spring of 1997. Starting in the fall of 2007, we have been converting the second semester of our calculus-based introductory physics course (Physics II) to a hybrid lecture/Studio Physics format, beginning from a traditional lecture/lab/recitation course. In this paper, we document the stages of this transformation, highlighting what has worked and what has not, and the challenges and benefits associated with the switch to Studio Physics. A major goal in this study is to develop a method for secondary implementations of Studio physics that keeps the time and resource investments manageable. We describe the history of Studio at CSM and characterize our progress via several metrics, including pre/post Conceptual Survey of Electricity and Magnetism (CSEM) scores, Colorado Learning About Science Survey scores (CLASS), exam scores, failure rates, and a variety of qualitative observations. Results suggest that Studio has increased student performance and satisfaction despite an aggressive expansion of class sizes in the past few years. Gains have been concentrated mostly in problem-solving skills and exam performance (as opposed to conceptual survey gains), in contrast to what has sometimes been seen in other studies.

Assessment of Factors that Influence the Recruitment of Majors from Introductory Geology Classes

Science.gov (United States)

Hoisch, T. D.; Bowie, J. I.

2009-12-01

In order to guide the formulation of strategies for recruiting undergraduates taking introductory geology courses into the geology program at Northern Arizona University, we surveyed 783 students in introductory geology classes and 23 geology majors in their junior and senior years. Our introductory courses (GLG100, Introduction to Geology; GLG101, Physical Geology; and GLG112, Geologic Disasters) typically enroll ~600 students each semester. The majority of students in these classes are non-majors who take them in order to satisfy a university general education requirement (called “Liberal Studies requirements” at NAU). A large proportion of these students are freshmen (51%) and sophomores (30%), and many have not yet decided on a major or are uncertain about the major they have chosen. Our analysis shows that ~7% of students in the introductory classes are possible candidates for recruitment. Although a small percentage, it represents a large number of individuals, in fact more than could be accommodated were they all to decide to major in geology. Influential factors that weigh in favor of majoring in geology include good employability, good salary potential, and opportunities for working outdoors, field work, observing nature, travel, and environmentally friendly employment. In addition, students view a career as a geologist as potentially the most fulfilling of the different science occupations (biologist, chemist, geologist, environmental scientist, physicist) and among the more environmentally friendly. However, students perceive geology to be the least difficult of the sciences, and geology occupations to be low-paying and low in prestige relative to the other sciences. These negative perceptions could be countered by providing data to introductory students showing the starting salaries of geologists in comparison to other science occupations, and by communicating the rigorous nature of the more advanced classes in the geology degree program. A

Calculus in Your Career: Putting the "Relate" Back in Related Rates

Science.gov (United States)

Lommatsch, Christina W.

2017-01-01

"Find the extreme values of the function." "At what rate is the distance between A and B increasing after 12 seconds?" Prompts like these can be heard in most first-semester calculus courses. Unfortunately, these cues also tend to prompt students' eyes to glaze over with thoughts of "When will I ever use this?" This…

Exterior calculus and two-dimensional supersymmetric models

International Nuclear Information System (INIS)

Sciuto, S.

1980-01-01

An important property of the calculus of differential forms on superspace is pointed out, and an economical way to treat the linear problem associated with certain supersymmetric two-dimensional models is discussed. A generalization of the super sine-Gordon model is proposed; its bosonic limit is a new model whose associate linear set has an SU(3) structure. (orig.)

Evaluating multiple-choice exams in large introductory physics courses

Directory of Open Access Journals (Sweden)

Gary Gladding

2006-07-01

Full Text Available The reliability and validity of professionally written multiple-choice exams have been extensively studied for exams such as the SAT, graduate record examination, and the force concept inventory. Much of the success of these multiple-choice exams is attributed to the careful construction of each question, as well as each response. In this study, the reliability and validity of scores from multiple-choice exams written for and administered in the large introductory physics courses at the University of Illinois, Urbana-Champaign were investigated. The reliability of exam scores over the course of a semester results in approximately a 3% uncertainty in students’ total semester exam score. This semester test score uncertainty yields an uncertainty in the students’ assigned letter grade that is less than 1 / 3 of a letter grade. To study the validity of exam scores, a subset of students were ranked independently based on their multiple-choice score, graded explanations, and student interviews. The ranking of these students based on their multiple-choice score was found to be consistent with the ranking assigned by physics instructors based on the students’ written explanations ( r>0.94 at the 95% confidence level and oral interviews (r=0.94−0.09+0.06 .

Calculus of variations and optimal control theory a concise introduction

CERN Document Server

Liberzon, Daniel

2011-01-01

This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the h...

Modern calculus and analytic geometry

CERN Document Server

Silverman, Richard A

2012-01-01

A self-contained text for an introductory course, this volume places strong emphasis on physical applications. Key elements of differential equations and linear algebra are introduced early and are consistently referenced, all theorems are proved using elementary methods, and numerous worked-out examples appear throughout. The highly readable text approaches calculus from the student's viewpoint and points out potential stumbling blocks before they develop. A collection of more than 1,600 problems ranges from exercise material to exploration of new points of theory - many of the answers are fo

Implementing Recommendations for Introductory Biology by Writing a New Textbook

Science.gov (United States)

Barsoum, Mark J.; Sellers, Patrick J.; Campbell, A. Malcolm; Heyer, Laurie J.; Paradise, Christopher J.

2013-01-01

We redesigned the undergraduate introductory biology course by writing a new textbook (Integrating Concepts in Biology [ICB]) that follows first principles of learning. Our approach emphasizes primary data interpretation and the utility of mathematics in biology, while de-emphasizing memorization. This redesign divides biology into five big ideas (information, evolution, cells, emergent properties, homeostasis), addressing each at five levels of organization (molecules, cells, organisms, populations, ecological systems). We compared our course outcomes with two sections that used a traditional textbook and were taught by different instructors. On data interpretation assessments administered periodically during the semester, our students performed better than students in the traditional sections (p = 0.046) and exhibited greater improvement over the course of the semester (p = 0.015). On factual content assessments, our students performed similarly to students in the other sections (p = 0.737). Pre- and postsemester assessment of disciplinary perceptions and self-appraisal indicate that our students acquired a more accurate perception of biology as a discipline and may have developed a more realistic evaluation of their scientific abilities than did the control students (p < 0.05). We conclude that ICB improves critical thinking, metacognition, and disciplinary perceptions without compromising content knowledge in introductory biology. PMID:23463233

A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

Science.gov (United States)

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

Gender Disparities in Second-Semester College Physics: The Incremental Effects of a "Smog of Bias"

Science.gov (United States)

Kost-Smith, Lauren E.; Pollock, Steven J.; Finkelstein, Noah D.

2010-01-01

Our previous research [Kost et al., Phys. Rev. ST Phys. Educ. Res. 5, 010101 (2009)] examined gender differences in the first-semester, introductory physics class at the University of Colorado at Boulder. We found that: (1) there were gender differences in several aspects of the course, including conceptual survey performance, (2) these…

Go Figure: Calculus Students' Use of Figures and Graphs in Technical Report Writing

Directory of Open Access Journals (Sweden)

Thomas J. Pfaff

2011-01-01

Full Text Available Understanding how to read and use graphs to communicate scientific and mathematical information is critical for STEM majors, as well as an important part of quantitative literacy. Our study suggests that first-semester calculus students do not know how to use graphs in a technical report without explicit instruction. Although not a surprising result, it leaves us wondering about when such skills are developed, and if calculus I is a place to start. Our work is now exploring the potential benefit on students' use of graphs by having them formally evaluate other students' reports.

Tensor Calculus: Unlearning Vector Calculus

Science.gov (United States)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Fluorescence-based calculus detection using a 405-nm excitation wavelength

Science.gov (United States)

Brede, O.; Schelle, F.; Krueger, S.; Oehme, B.; Dehn, C.; Frentzen, M.; Braun, A.

2011-03-01

The aim of this study was to assess the difference of fluorescence signals of cement and calculus using a 405 nm excitation wavelength. A total number of 20 freshly extracted teeth was used. The light source used for this study was a blue LED with a wavelength of 405nm. For each tooth the spectra of calculus and cementum were measured separately. Fluorescence light was collimated into an optical fibre and spectrally analyzed using an echelle spectrometer (aryelle 200, Lasertechnik Berlin, Germany) with an additionally bandpass (fgb 67, Edmund Industrial Optics, Karlsruhe, Germany). From these 40 measurements the median values were calculated over the whole spectrum, leading to two different median spectra, one for calculus and one for cementum. For further statistical analysis we defined 8 areas of interest (AOI) in wavelength regions, showing remarkable differences in signal strength. In 7 AOIs the intensity of the calculus spectrum differed statistically significant from the intensity of the cementum spectrum (p calculus and cement between 600nm and 700nm. Thus, we can conclude that fluorescence of calculus shows a significant difference to the fluorescence of cement. A differentiation over the intensity is possible as well as over the spectrum. Using a wavelength of 405nm, it is possible to distinguish between calculus and cement. These results could be used for further devices to develop a method for feedback controlled calculus removal.

Calculus in physics classes at UFRGS: an exploratory study

Directory of Open Access Journals (Sweden)

Maria Cecilia Pereira Santarosa

2011-11-01

Full Text Available This study is part f a larger one whose general objective is to investigate and to develop a new strategy for teaching Differential and Integral Calculus I, specifically for physics majors, through a possible integration with the teaching of General and Experimental Physics I. With the specific objective of identifying physics problem-situations that may help in making sense of the mathematical concepts used in Calculus I, and languages and notations that might be used in the teaching of Calculus to favor physics learning, it was investigates, through an ethnographic study, the may mathematics is transposed to classes of General and Experimental Physics I, in classes of physics courses at the Federal University of Rio Grande do Sul (UFRGS. Some findings of this study confirmed those reported in the literature regarding the teaching and learning process in introductory college physics courses. These findings will subsidize the preparation of potentially meaningful instructional materials that will be used in a second stage of the research designed to investigate the learning of declarative and procedural knowledge in basic college physics under an approach that integrates problem-situation in physics and calculus mathematical concepts.

The Effectiveness of Guided Discovery Learning to Teach Integral Calculus for the Mathematics Students of Mathematics Education Widya Dharma University

OpenAIRE

Yuliana, Yuliana; Tasari, Tasari; Wijayanti, Septiana

2017-01-01

The objectives of this research are (1) to develop Guided Discovery Learning in integral calculus subject; (2) to identify the effectiveness of Guided Discovery Learning in improving the students' understanding toward integral calculus subject. This research was quasy experimental research with the students of even semester in Mathematics Education Widya Dharma University as the sample. Cluster Random sampling was conducted to determine control group that was taught using Conventional model a...

Calculus domains modelled using an original bool algebra based on polygons

Science.gov (United States)

Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.

2016-08-01

Analytical and numerical computer based models require analytical definitions of the calculus domains. The paper presents a method to model a calculus domain based on a bool algebra which uses solid and hollow polygons. The general calculus relations of the geometrical characteristics that are widely used in mechanical engineering are tested using several shapes of the calculus domain in order to draw conclusions regarding the most effective methods to discretize the domain. The paper also tests the results of several CAD commercial software applications which are able to compute the geometrical characteristics, being drawn interesting conclusions. The tests were also targeting the accuracy of the results vs. the number of nodes on the curved boundary of the cross section. The study required the development of an original software consisting of more than 1700 computer code lines. In comparison with other calculus methods, the discretization using convex polygons is a simpler approach. Moreover, this method doesn't lead to large numbers as the spline approximation did, in that case being required special software packages in order to offer multiple, arbitrary precision. The knowledge resulted from this study may be used to develop complex computer based models in engineering.

Developing and validating a conceptual survey to assess introductory physics students’ understanding of magnetism

Science.gov (United States)

Li, Jing; Singh, Chandralekha

2017-03-01

Development of validated physics surveys on various topics is important for investigating the extent to which students master those concepts after traditional instruction and for assessing innovative curricula and pedagogies that can improve student understanding significantly. Here, we discuss the development and validation of a conceptual multiple-choice survey related to magnetism suitable for introductory physics courses. The survey was developed taking into account common students’ difficulties with magnetism concepts covered in introductory physics courses found in our investigation and the incorrect choices to the multiple-choice questions were designed based upon those common student difficulties. After the development and validation of the survey, it was administered to introductory physics students in various classes in paper-pencil format before and after traditional lecture-based instruction in relevant concepts. We compared the performance of students on the survey in the algebra-based and calculus-based introductory physics courses before and after traditional lecture-based instruction in relevant magnetism concepts. We discuss the common difficulties of introductory physics students with magnetism concepts we found via the survey. We also administered the survey to upper-level undergraduates majoring in physics and PhD students to benchmark the survey and compared their performance with those of traditionally taught introductory physics students for whom the survey is intended. A comparison with the base line data on the validated magnetism survey from traditionally taught introductory physics courses and upper-level undergraduate and PhD students discussed in this paper can help instructors assess the effectiveness of curricula and pedagogies which is especially designed to help students integrate conceptual and quantitative understanding and develop a good grasp of the concepts. In particular, if introductory physics students’ average

Developing and validating a conceptual survey to assess introductory physics students’ understanding of magnetism

International Nuclear Information System (INIS)

Li, Jing; Singh, Chandralekha

2017-01-01

Development of validated physics surveys on various topics is important for investigating the extent to which students master those concepts after traditional instruction and for assessing innovative curricula and pedagogies that can improve student understanding significantly. Here, we discuss the development and validation of a conceptual multiple-choice survey related to magnetism suitable for introductory physics courses. The survey was developed taking into account common students’ difficulties with magnetism concepts covered in introductory physics courses found in our investigation and the incorrect choices to the multiple-choice questions were designed based upon those common student difficulties. After the development and validation of the survey, it was administered to introductory physics students in various classes in paper–pencil format before and after traditional lecture-based instruction in relevant concepts. We compared the performance of students on the survey in the algebra-based and calculus-based introductory physics courses before and after traditional lecture-based instruction in relevant magnetism concepts. We discuss the common difficulties of introductory physics students with magnetism concepts we found via the survey. We also administered the survey to upper-level undergraduates majoring in physics and PhD students to benchmark the survey and compared their performance with those of traditionally taught introductory physics students for whom the survey is intended. A comparison with the base line data on the validated magnetism survey from traditionally taught introductory physics courses and upper-level undergraduate and PhD students discussed in this paper can help instructors assess the effectiveness of curricula and pedagogies which is especially designed to help students integrate conceptual and quantitative understanding and develop a good grasp of the concepts. In particular, if introductory physics students’ average

An Excel-Aided Method for Teaching Calculus-Based Business Mathematics

Science.gov (United States)

Liang, Jiajuan; Martin, Linda

2008-01-01

Calculus-based business mathematics is a required quantitative course for undergraduate business students in most AACSB accredited schools or colleges of business. Many business students, however, have relatively weak mathematical background or even display math-phobia when presented with calculus problems. Because of the popularity of Excel, its…

Basic Math Skills and Performance in an Introductory Economics Class

Science.gov (United States)

Ballard, Charles L.; Johnson, Marianne F.

2004-01-01

The authors measure math skills with a broader set of explanatory variables than have been used in previous studies. To identify what math skills are important for student success in introductory microeconomics, they examine (1) the student's score on the mathematics portion of the ACT Assessment Test, (2) whether the student has taken calculus,…

Using Facebook Data to Turn Introductory Statistics Students into Consultants

Science.gov (United States)

Childers, Adam F.

2017-01-01

Facebook provides businesses and organizations with copious data that describe how users are interacting with their page. This data affords an excellent opportunity to turn introductory statistics students into consultants to analyze the Facebook data using descriptive and inferential statistics. This paper details a semester-long project that…

Noncausal stochastic calculus

CERN Document Server

Ogawa, Shigeyoshi

2017-01-01

This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...

Preliminary investigation of instructor effects on gender gap in introductory physics

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Kimberley Kreutzer1

2012-05-01

Full Text Available Gender differences in student learning in the introductory, calculus-based electricity and magnetism course were assessed by administering the Conceptual Survey of Electricity and Magnetism pre- and postcourse. As expected, male students outgained females in traditionally taught sections as well as sections that incorporated interactive engagement (IE techniques. In two of the IE course sections, however, the gains of female students were comparable to those of male students. Classroom observations of the course sections involved were made over an extended period. In this paper, we characterize the observed instructor-student interactions using a framework from educational psychology referred to as wise schooling. Results suggest that instructor practices affect differential learning, and that wise schooling techniques may constitute an effective strategy for promoting gender equity in the physics classroom.

Preliminary investigation of instructor effects on gender gap in introductory physics

Science.gov (United States)

Kreutzer, Kimberley; Boudreaux, Andrew

2012-06-01

Gender differences in student learning in the introductory, calculus-based electricity and magnetism course were assessed by administering the Conceptual Survey of Electricity and Magnetism pre- and postcourse. As expected, male students outgained females in traditionally taught sections as well as sections that incorporated interactive engagement (IE) techniques. In two of the IE course sections, however, the gains of female students were comparable to those of male students. Classroom observations of the course sections involved were made over an extended period. In this paper, we characterize the observed instructor-student interactions using a framework from educational psychology referred to as wise schooling. Results suggest that instructor practices affect differential learning, and that wise schooling techniques may constitute an effective strategy for promoting gender equity in the physics classroom.

Exploring the Relationship between Self-Efficacy and Retention in Introductory Physics

Science.gov (United States)

Sawtelle, Vashti; Brewe, Eric; Kramer, Laird H.

2012-01-01

The quantitative results of Sources of Self-Efficacy in Science Courses-Physics (SOSESC-P) are presented as a logistic regression predicting the passing of students in introductory Physics with Calculus I, overall as well as disaggregated by gender. Self-efficacy as a theory to explain human behavior change [Bandura [1977] "Psychological…

Incorporating Code-Based Software in an Introductory Statistics Course

Science.gov (United States)

Doehler, Kirsten; Taylor, Laura

2015-01-01

This article is based on the experiences of two statistics professors who have taught students to write and effectively utilize code-based software in a college-level introductory statistics course. Advantages of using software and code-based software in this context are discussed. Suggestions are made on how to ease students into using code with…

Noninvasive control of dental calculus removal: qualification of two fluorescence methods

Science.gov (United States)

Gonchukov, S.; Sukhinina, A.; Bakhmutov, D.; Biryukova, T.

2013-02-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.

Noninvasive control of dental calculus removal: qualification of two fluorescence methods

International Nuclear Information System (INIS)

Gonchukov, S; Sukhinina, A; Bakhmutov, D; Biryukova, T

2013-01-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise noninvasive detection of calculus-tooth interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing.

The impact of taking a college pre-calculus course on students' college calculus performance

Science.gov (United States)

Sonnert, Gerhard; Sadler, Philip M.

2014-11-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and four-year colleges continues to grow, and these courses are well-populated with students who already took pre-calculus in high school. We examine student performance in college calculus, using regression discontinuity to estimate the effects of taking college pre-calculus or not, in a national US sample of 5507 students at 132 institutions. We find that students who take college pre-calculus do not earn higher calculus grades.

Two-Language, Two-Paradigm Introductory Computing Curriculum Model and its Implementation

OpenAIRE

Zanev, Vladimir; Radenski, Atanas

2011-01-01

This paper analyzes difficulties with the introduction of object-oriented concepts in introductory computing education and then proposes a two-language, two-paradigm curriculum model that alleviates such difficulties. Our two-language, two-paradigm curriculum model begins with teaching imperative programming using Python programming language, continues with teaching object-oriented computing using Java, and concludes with teaching object-oriented data structures with Java.

Introduction to stochastic analysis and Malliavin calculus

CERN Document Server

Prato, Giuseppe

2014-01-01

This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown out of a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several years of teaching experience in the subject. The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Itô's formula. The second part deals with differential stochastic equations and their connection with parabolic problems. The third part provides an introduction to the Malliavin calculus. Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems. In this third edition several small improvements are added and a new section devo...

Calculus

CERN Document Server

Jones, Patrick

2014-01-01

Practice makes perfect-and helps deepen your understanding of calculus 1001 Calculus Practice Problems For Dummies takes you beyond the instruction and guidance offered in Calculus For Dummies, giving you 1001 opportunities to practice solving problems from the major topics in your calculus course. Plus, an online component provides you with a collection of calculus problems presented in multiple-choice format to further help you test your skills as you go. Gives you a chance to practice and reinforce the skills you learn in your calculus courseHelps you refine your understanding of calculusP

A Fixpoint-Based Calculus for Graph-Shaped Computational Fields

DEFF Research Database (Denmark)

Lluch Lafuente, Alberto; Loreti, Michele; Montanari, Ugo

2015-01-01

topology is represented by a graph-shaped field, namely a network with attributes on both nodes and arcs, where arcs represent interaction capabilities between nodes. We propose a calculus where computation is strictly synchronous and corresponds to sequential computations of fixpoints in the graph......-shaped field. Under some conditions, those fixpoints can be computed by synchronised iterations, where in each iteration the attributes of a node is updated based on the attributes of the neighbours in the previous iteration. Basic constructs are reminiscent of the semiring μ-calculus, a semiring......-valued generalisation of the modal μ-calculus, which provides a flexible mechanism to specify the neighbourhood range (according to path formulae) and the way attributes should be combined (through semiring operators). Additional control-How constructs allow one to conveniently structure the fixpoint computations. We...

Biotechnology by Design: An Introductory Level, Project-Based, Synthetic Biology Laboratory Program for Undergraduate Students.

Science.gov (United States)

Beach, Dale L; Alvarez, Consuelo J

2015-12-01

Synthetic biology offers an ideal opportunity to promote undergraduate laboratory courses with research-style projects, immersing students in an inquiry-based program that enhances the experience of the scientific process. We designed a semester-long, project-based laboratory curriculum using synthetic biology principles to develop a novel sensory device. Students develop subject matter knowledge of molecular genetics and practical skills relevant to molecular biology, recombinant DNA techniques, and information literacy. During the spring semesters of 2014 and 2015, the Synthetic Biology Laboratory Project was delivered to sophomore genetics courses. Using a cloning strategy based on standardized BioBrick genetic "parts," students construct a "reporter plasmid" expressing a reporter gene (GFP) controlled by a hybrid promoter regulated by the lac-repressor protein (lacI). In combination with a "sensor plasmid," the production of the reporter phenotype is inhibited in the presence of a target environmental agent, arabinose. When arabinose is absent, constitutive GFP expression makes cells glow green. But the presence of arabinose activates a second promoter (pBAD) to produce a lac-repressor protein that will inhibit GFP production. Student learning was assessed relative to five learning objectives, using a student survey administered at the beginning (pre-survey) and end (post-survey) of the course, and an additional 15 open-ended questions from five graded Progress Report assignments collected throughout the course. Students demonstrated significant learning gains (p Biology Laboratory Project enhanced their understanding of molecular genetics. The laboratory project is highly adaptable for both introductory and advanced courses.

The Impact of Taking a College Pre-Calculus Course on Students' College Calculus Performance

Science.gov (United States)

Sonnert, Gerhard; Sadler, Philip M.

2014-01-01

Poor performance on placement exams keeps many US students who pursue a STEM (science, technology, engineering, mathematics) career from enrolling directly in college calculus. Instead, they must take a pre-calculus course that aims to better prepare them for later calculus coursework. In the USA, enrollment in pre-calculus courses in two- and…

Dental calculus image based on optical coherence tomography

Science.gov (United States)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-03-01

In this study, the dental calculus was characterized and imaged by means of swept-source optical coherence tomography (SSOCT). The refractive indices of enamel, dentin, cementum and calculus were measured as 1.625+/-0.024, 1.534+/-0.029, 1.570+/-0.021 and 1.896+/-0.085, respectively. The dental calculus lead strong scattering property and thus the region can be identified under enamel with SSOCT imaging. An extracted human tooth with calculus was covered by gingiva tissue as in vitro sample for SSOCT imaging.

Sequent Calculus and Equational Programming

Directory of Open Access Journals (Sweden)

Nicolas Guenot

2015-07-01

Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.

Study Modules for Calculus-Based General Physics. [Includes Modules 1 and 2: Dimensions and Vector Addition; Rectilinear Motion; plus a Trigonometry and Calculus Review].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Initialized Fractional Calculus

Science.gov (United States)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

This paper demonstrates the need for a nonconstant initialization for the fractional calculus and establishes a basic definition set for the initialized fractional differintegral. This definition set allows the formalization of an initialized fractional calculus. Two basis calculi are considered; the Riemann-Liouville and the Grunwald fractional calculi. Two forms of initialization, terminal and side are developed.

Student Selection of the Textbook for an Introductory Physics Course

Science.gov (United States)

Dake, L. S.

2007-10-01

Several years ago I had to select a new textbook for my calculus-based introductory physics class. I subscribe to Just-in-Time Teaching methods, which require students to read the book before the material is covered in class. Thus, the readability of the text by the students is critical. However, I did not feel that I was the best judge of this factor, so I turned the textbook selection into a class project. The students unanimously chose one textbook, which I have now successfully used for three years. The project was decidedly worthwhile, and I gained considerable insight into what students prefer in a textbook.

Student Responses to a Flipped Introductory Physics Class with built-in Post-Video Feedback Quizzes

Science.gov (United States)

Ramos, Roberto

We present and analyze student responses to multiple Introductory physics classes in a university setting, taught in a ''flipped'' class format. The classes included algebra- and calculus-based introductory physics. Outside class, students viewed over 100 online video lectures on Classical Mechanics, Electricity and Magnetism, and Modern Physics prepared by this author and in some cases, by a third-party lecture package available over YouTube. Inside the class, students solved and discussed problems and conceptual issues in greater detail. A pre-class online quiz was deployed as an important source of feedback. I will report on the student reactions to the feedback mechanism, student responses using data based on anonymous surveys, as well as on learning gains from pre-/post- physics diagnostic tests. The results indicate a broad mixture of responses to different lecture video packages that depend on learning styles and perceptions. Students preferred the online quizzes as a mechanism to validate their understanding. The learning gains based on FCI and CSEM surveys were significant.

Mediating relationship of differential products in understanding integration in introductory physics

Science.gov (United States)

Amos, Nathaniel; Heckler, Andrew F.

2018-01-01

In the context of introductory physics, we study student conceptual understanding of differentials, differential products, and integrals and possible pathways to understanding these quantities. We developed a multiple choice conceptual assessment employing a variety of physical contexts probing physical understanding of these three quantities and administered the instrument to over 1000 students in first and second semester introductory physics courses. Using a regression-based mediation analysis with conceptual understanding of integration as the dependent variable, we found evidence consistent with a simple mediation model: the relationship between differentials scores and integral scores may be mediated by the understanding of differential products. The indirect effect (a quantifiable metric of mediation) was estimated as a b =0.29 , 95% CI [0.25, 0.33] for N =1102 Physics 1 students, and a b =0.27 , 95% CI [0.14, 0.48] for N =65 Physics 2 students. We also find evidence that the physical context of the questions can be an important factor. These results imply that for introductory physics courses, instructional emphasis first on differentials then on differential products in a variety of contexts may in turn promote better integral understanding.

Optimal Strategy in the "Price Is Right" Showcase Showdown: A Module for Students of Calculus and Probability

Science.gov (United States)

Swenson, Daniel

2015-01-01

We walk through a module intended for undergraduates in mathematics, with the focus of finding the best strategies for competing in the Showcase Showdown on the game show "The Price Is Right." Students should have completed one semester of calculus, as well as some probability. We also give numerous suggestions for further questions that…

Laboratory Sequence in Computational Methods for Introductory Chemistry

Science.gov (United States)

Cody, Jason A.; Wiser, Dawn C.

2003-07-01

A four-exercise laboratory sequence for introductory chemistry integrating hands-on, student-centered experience with computer modeling has been designed and implemented. The progression builds from exploration of molecular shapes to intermolecular forces and the impact of those forces on chemical separations made with gas chromatography and distillation. The sequence ends with an exploration of molecular orbitals. The students use the computers as a tool; they build the molecules, submit the calculations, and interpret the results. Because of the construction of the sequence and its placement spanning the semester break, good laboratory notebook practices are reinforced and the continuity of course content and methods between semesters is emphasized. The inclusion of these techniques in the first year of chemistry has had a positive impact on student perceptions and student learning.

Assessing critical thinking in medical sciences students in two sequential semesters: Does it improve?

Science.gov (United States)

Athari, Zeinab-Sadat; Sharif, Sayyed-Mostafa; Nasr, Ahmad Reza; Nematbakhsh, Mehdi

2013-01-01

Critical thinking is an important outcome criterion of higher education in any discipline. Medical and paramedical students always encounter with many new problems in clinical settings and medicinal laboratory, and critical thinking is an essential skill in obtaining a better approach for problem solving. We performed a pre-and post-test to evaluate the change of critical thinking skills in medical sciences students who enrolled in Isfahan University of Medical Sciences in Iran during the academic years 2008-2010. In a longitudinal design study, the critical thinking skills were compared in medical sciences students in two sequential semesters using the California Critical Thinking Skills Test. The test is divided into two parts (parts 1 and 2), including 17 items in each part. Based on proportional stratified sampling, a groups of students (group 1, n=159) were selected from the university population, who enrolled in medicine, pharmacy, nursing, and rehabilitation colleges. The students in group 1 were asked to complete the part 1 of the test (phase I). After one semester, another group (group 2, n=138) from the same population was randomly selected, and they were asked to complete the part two (phase II). The students' demographic data also were recorded. The California critical thinking skills test was translated and it validity and reliability were approved before. No significant difference was observed between the two groups in the demographic data. The students critical thinking scores in phase II significantly reduced in comparison with phase 1 (pstudents' critical thinking.

Introductory modern algebra a historical approach

CERN Document Server

Stahl, Saul

2013-01-01

Praise for the First Edition ""Stahl offers the solvability of equations from the historical point of view...one of the best books available to support a one-semester introduction to abstract algebra.""-CHOICE Introductory Modern Algebra: A Historical Approach, Second Edition presents the evolution of algebra and provides readers with the opportunity to view modern algebra as a consistent movement from concrete problems to abstract principles. With a few pertinent excerpts from the writings of some of the greatest mathematicians, the Second Edition uniquely facilitates the understanding of pi

Exploring Factors Related to Completion of an Online Undergraduate-Level Introductory Statistics Course

Science.gov (United States)

Zimmerman, Whitney Alicia; Johnson, Glenn

2017-01-01

Data were collected from 353 online undergraduate introductory statistics students at the beginning of a semester using the Goals and Outcomes Associated with Learning Statistics (GOALS) instrument and an abbreviated form of the Statistics Anxiety Rating Scale (STARS). Data included a survey of expected grade, expected time commitment, and the…

Evaluating an Active Learning Approach to Teaching Introductory Statistics: A Classroom Workbook Approach

Science.gov (United States)

Carlson, Kieth A.; Winquist, Jennifer R.

2011-01-01

The study evaluates a semester-long workbook curriculum approach to teaching a college level introductory statistics course. The workbook curriculum required students to read content before and during class and then work in groups to complete problems and answer conceptual questions pertaining to the material they read. Instructors spent class…

Calculus

CERN Document Server

Grossman, Stanley I

1984-01-01

Calculus, Third Edition emphasizes the techniques and theorems of calculus, including many applied examples and exercises in both drill and applied-type problems.This book discusses shifting the graphs of functions, derivative as a rate of change, derivative of a power function, and theory of maxima and minima. The area between two curves, differential equations of exponential growth and decay, inverse hyperbolic functions, and integration of rational functions are also elaborated. This text likewise covers the fluid pressure, ellipse and translation of axes, graphing in polar coordinates, pro

Implementing recommendations for introductory biology by writing a new textbook.

Science.gov (United States)

Barsoum, Mark J; Sellers, Patrick J; Campbell, A Malcolm; Heyer, Laurie J; Paradise, Christopher J

2013-01-01

We redesigned the undergraduate introductory biology course by writing a new textbook (Integrating Concepts in Biology [ICB]) that follows first principles of learning. Our approach emphasizes primary data interpretation and the utility of mathematics in biology, while de-emphasizing memorization. This redesign divides biology into five big ideas (information, evolution, cells, emergent properties, homeostasis), addressing each at five levels of organization (molecules, cells, organisms, populations, ecological systems). We compared our course outcomes with two sections that used a traditional textbook and were taught by different instructors. On data interpretation assessments administered periodically during the semester, our students performed better than students in the traditional sections (p = 0.046) and exhibited greater improvement over the course of the semester (p = 0.015). On factual content assessments, our students performed similarly to students in the other sections (p = 0.737). Pre- and postsemester assessment of disciplinary perceptions and self-appraisal indicate that our students acquired a more accurate perception of biology as a discipline and may have developed a more realistic evaluation of their scientific abilities than did the control students (p biology.

Measuring Student Engagement, Knowledge, and Perceptions of Climate Change in an Introductory Environmental Geology Course

Science.gov (United States)

McNeal, Karen S.; Spry, Jacob M.; Mitra, Ritayan; Tipton, Jamie L.

2014-01-01

This research examines a semester-long introductory environmental geology course, which emphasized climate science using an Earth systems approach and employed a multipronged teaching strategy comprising lecture, movie viewing, class dialogues, and journaling. Evidence of student engagement during various pedagogical approaches (e.g., movie…

Web-Based Alcohol Intervention in First-Year College Students: Efficacy of Full-Program Administration Prior to Second Semester.

Science.gov (United States)

Gilbertson, Rebecca J; Norton, Tina R; Beery, Susan H; Lee, Kassandra R

2018-05-12

Commercially available, web-based interventions for the prevention of alcohol use are being adopted for universal use with first-year college students, yet few have received empirical evaluation. This randomized controlled trial investigated the effectiveness of a novel, commercially available, personalized web-based alcohol intervention, Alcohol-Wise (version 4.0, 3 rd Millennium Classrooms), on multiple measures of alcohol consumption, alcohol consequences, alcohol expectancies, academic achievement, and adaptation to college in first-year students. Participants received Alcohol-Wise either prior to first semester or were waitlisted and received the intervention second semester. As longitudinal effectiveness was of interest, follow-up surveys were conducted 10 weeks (n = 76) and 24 weeks (n = 64) following the web-based alcohol intervention. Completion of Alcohol-Wise had effects on academic achievement. Specifically, at the 24 week follow-up, academic achievement was higher in participants who received the intervention first semester of their freshman year as compared to the waitlist control. The incremental rise in heavy episodic drinking during the first semester of college was also reduced in waitlisted participants by Alcohol-Wise administration prior to second semester. Conclusion/Importance: Implications for the timing of web-based alcohol interventions to include administration prior to both first and second semesters of the freshman year are discussed.

The Influence of Collaborative Learning on Student Attitudes and Performance in an Introductory Chemistry Laboratory

Science.gov (United States)

Shibley, Ivan A., Jr.; Zimmaro, Dawn M.

2002-06-01

This study was designed to determine the effect of collaborative learning on student attitudes and performance in an introductory chemistry laboratory. Two sections per semester for three semesters were randomly designated as either a control section or an experimental section. Students in the control section performed most labs individually, while those in the experimental section performed all labs in groups of four. Both quantitative and qualitative measures were used to evaluate the impact of collaborative learning on student achievement and attitudes. Grades did not differ between the two sections, indicating that collaborative learning did not affect short-term student achievement. Students seemed to develop a more positive attitude about the laboratory and about chemistry in the collaborative learning sections as judged from their classroom evaluations of the teacher, the course, and the collaborative learning experience. The use of collaborative learning in the laboratory as described in this paper therefore may provide a means of improving student attitudes toward chemistry.

University mathematics teachers' views on the required reasoning in calculus exams

OpenAIRE

Bergqvist, Ewa

2012-01-01

Students often use imitative reasoning, i.e. copy algorithms or recall facts, when solving mathematical tasks. Research show that this type of imitative reasoning might weaken the students' understanding of the underlying mathematical concepts. In a previous study, the author classified tasks from 16 final exams from introductory calculus courses at Swedish universities. The results showed that it was possible to pass 15 of the exams, and solve most of the tasks, using imitative reasoning. Th...

Dissociative conceptual and quantitative problem solving outcomes across interactive engagement and traditional format introductory physics

Directory of Open Access Journals (Sweden)

Mark A. McDaniel

2016-11-01

Full Text Available The existing literature indicates that interactive-engagement (IE based general physics classes improve conceptual learning relative to more traditional lecture-oriented classrooms. Very little research, however, has examined quantitative problem-solving outcomes from IE based relative to traditional lecture-based physics classes. The present study included both pre- and post-course conceptual-learning assessments and a new quantitative physics problem-solving assessment that included three representative conservation of energy problems from a first-semester calculus-based college physics course. Scores for problem translation, plan coherence, solution execution, and evaluation of solution plausibility were extracted for each problem. Over 450 students in three IE-based sections and two traditional lecture sections taught at the same university during the same semester participated. As expected, the IE-based course produced more robust gains on a Force Concept Inventory than did the lecture course. By contrast, when the full sample was considered, gains in quantitative problem solving were significantly greater for lecture than IE-based physics; when students were matched on pre-test scores, there was still no advantage for IE-based physics on gains in quantitative problem solving. Further, the association between performance on the concept inventory and quantitative problem solving was minimal. These results highlight that improved conceptual understanding does not necessarily support improved quantitative physics problem solving, and that the instructional method appears to have less bearing on gains in quantitative problem solving than does the kinds of problems emphasized in the courses and homework and the overlap of these problems to those on the assessment.

The effects of students' reasoning abilities on conceptual understandings and problem-solving skills in introductory mechanics

International Nuclear Information System (INIS)

Ates, S; Cataloglu, E

2007-01-01

The purpose of this study was to determine if there are relationships among freshmen/first year students' reasoning abilities, conceptual understandings and problem-solving skills in introductory mechanics. The sample consisted of 165 freshmen science education prospective teachers (female = 86, male = 79; age range 17-21) who were enrolled in an introductory physics course. Data collection was done during the fall semesters in two successive years. At the beginning of each semester, the force concept inventory (FCI) and the classroom test of scientific reasoning (CTSR) were administered to assess students' initial understanding of basic concepts in mechanics and reasoning levels. After completing the course, the FCI and the mechanics baseline test (MBT) were administered. The results indicated that there was a significant difference in problem-solving skill test mean scores, as measured by the MBT, among concrete, formal and postformal reasoners. There were no significant differences in conceptual understanding levels of pre- and post-test mean scores, as measured by FCI, among the groups. The Benferroni post hoc comparison test revealed which set of reasoning levels showed significant difference for the MBT scores. No statistical difference between formal and postformal reasoners' mean scores was observed, while the mean scores between concrete and formal reasoners and concrete and postformal reasoners were statistically significantly different

Investigating and improving introductory physics students’ understanding of symmetry and Gauss’s law

Science.gov (United States)

Li, Jing; Singh, Chandralekha

2018-01-01

We discuss an investigation of student difficulties with symmetry and Gauss’s law and how the research on students’ difficulties was used as a guide to develop a tutorial related to these topics to help students in the calculus-based introductory physics courses learn these concepts. During the development of the tutorial, we interviewed students individually at various stages of development and administered written tests in the free-response and multiple-choice formats on these concepts to learn about common student difficulties. We also obtained feedback from physics instructors who teach introductory physics courses regularly in which these concepts were covered. The students in several ‘equivalent’ sections worked on the tutorial after traditional lecture-based instruction. We discuss the performance of students on the written pre-test (administered after lecture-based instruction in relevant concepts) and post-test given after students worked on the tutorial. We find that on the pre-test, all sections of the course performed comparably regardless of the instructor. Also, on average, student performance on the post-test after working on the tutorial is significantly better than on the pre-test after lecture-based instruction. We also compare the post-test performance of introductory students in sections of the course in which the tutorial was used versus not used and find that sections in which students engaged with the tutorial outperformed those in which students did not engage with it.

Generalized vector calculus on convex domain

Science.gov (United States)

Agrawal, Om P.; Xu, Yufeng

2015-06-01

In this paper, we apply recently proposed generalized integral and differential operators to develop generalized vector calculus and generalized variational calculus for problems defined over a convex domain. In particular, we present some generalization of Green's and Gauss divergence theorems involving some new operators, and apply these theorems to generalized variational calculus. For fractional power kernels, the formulation leads to fractional vector calculus and fractional variational calculus for problems defined over a convex domain. In special cases, when certain parameters take integer values, we obtain formulations for integer order problems. Two examples are presented to demonstrate applications of the generalized variational calculus which utilize the generalized vector calculus developed in the paper. The first example leads to a generalized partial differential equation and the second example leads to a generalized eigenvalue problem, both in two dimensional convex domains. We solve the generalized partial differential equation by using polynomial approximation. A special case of the second example is a generalized isoperimetric problem. We find an approximate solution to this problem. Many physical problems containing integer order integrals and derivatives are defined over arbitrary domains. We speculate that future problems containing fractional and generalized integrals and derivatives in fractional mechanics will be defined over arbitrary domains, and therefore, a general variational calculus incorporating a general vector calculus will be needed for these problems. This research is our first attempt in that direction.

Dental Hygiene Faculty Calibration Using Two Accepted Standards for Calculus Detection: A Pilot Study.

Science.gov (United States)

Santiago, Lisa J; Freudenthal, Jacqueline J; Peterson, Teri; Bowen, Denise M

2016-08-01

Faculty calibration studies for calculus detection use two different standards for examiner evaluation, yet the only therapeutic modality that can be used for nonsurgical periodontal treatment is scaling/root debridement or planing. In this study, a pretest-posttest design was used to assess the feasibility of faculty calibration for calculus detection using two accepted standards: that established by the Central Regional Dental Testing Service, Inc. (CRDTS; readily detectible calculus) and the gold standard for scaling/root debridement (root roughness). Four clinical dental hygiene faculty members out of five possible participants at Halifax Community College agreed to participate. The participants explored calculus on the 16 assigned teeth (64 surfaces) of four patients. Calculus detection scores were calculated before and after training. Kappa averages using CRDTS criteria were 0.561 at pretest and 0.631 at posttest. Kappa scores using the scaling/root debridement or planing standard were 0.152 at pretest and 0.271 at posttest. The scores indicated improvement from moderate (Kappa=0.41-0.60) to substantial agreement (Kappa=0.61-0.80) following training using the CRDTS standard. Although this result differed qualitatively and Kappas were significantly different from 0, the differences for pre- to post-Kappas for patient-rater dyads using CRDTS were not statistically significant (p=0.778). There was no difference (p=0.913) in Kappa scores pre- to post-training using the scaling/root debridement standard. Despite the small number of participants in this study, the results indicated that training to improve interrater reliability to substantial agreement was feasible using the CRDTS standard but not using the gold standard. The difference may have been due to greater difficulty in attaining agreement regarding root roughness. Future studies should include multiple training sessions with patients using the same standard for scaling/root debridement used for

Consideration of learning orientations as an application of achievement goals in evaluating life science majors in introductory physics

Science.gov (United States)

Mason, Andrew J.; Bertram, Charles A.

2018-06-01

When considering performing an Introductory Physics for Life Sciences course transformation for one's own institution, life science majors' achievement goals are a necessary consideration to ensure the pedagogical transformation will be effective. However, achievement goals are rarely an explicit consideration in physics education research topics such as metacognition. We investigate a sample population of 218 students in a first-semester introductory algebra-based physics course, drawn from 14 laboratory sections within six semesters of course sections, to determine the influence of achievement goals on life science majors' attitudes towards physics. Learning orientations that, respectively, pertain to mastery goals and performance goals, in addition to a learning orientation that does not report a performance goal, were recorded from students in the specific context of learning a problem-solving framework during an in-class exercise. Students' learning orientations, defined within the context of students' self-reported statements in the specific context of a problem-solving-related research-based course implementation, are compared to pre-post results on physics problem-solving items in a well-established attitudinal survey instrument, in order to establish the categories' validity. In addition, mastery-related and performance-related orientations appear to extend to overall pre-post attitudinal shifts, but not to force and motion concepts or to overall course grade, within the scope of an introductory physics course. There also appears to be differentiation regarding overall course performance within health science majors, but not within biology majors, in terms of learning orientations; however, health science majors generally appear to fare less well on all measurements in the study than do biology majors, regardless of learning orientations.

Differential Calculus on Quantum Spheres

OpenAIRE

Welk, Martin

1998-01-01

We study covariant differential calculus on the quantum spheres S_q^2N-1. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including a particular first order calculus obtained by factorization, higher order calculi and a symmetry concept.

Research as a guide for curriculum development: An example from introductory spectroscopy. II. Addressing student difficulties with atomic emission spectra

Science.gov (United States)

Ivanjek, L.; Shaffer, P. S.; McDermott, L. C.; Planinic, M.; Veza, D.

2015-02-01

This is the second of two closely related articles (Paper I and Paper II) that together illustrate how research in physics education has helped guide the design of instruction that has proved effective in improving student understanding of atomic spectroscopy. Most of the more than 1000 students who participated in this four-year investigation were science majors enrolled in the introductory calculus-based physics course at the University of Washington (UW) in Seattle, WA, USA. The others included graduate and undergraduate teaching assistants at UW and physics majors in introductory and advanced physics courses at the University of Zagreb, Zagreb, Croatia. About half of the latter group were preservice high school physics teachers. Paper I describes how several conceptual and reasoning difficulties were identified among university students as they tried to relate a discrete line spectrum to the energy levels of atoms in a light source. This second article (Paper II) illustrates how findings from this research informed the development of a tutorial that led to improvement in student understanding of atomic emission spectra.

Relationships between undergraduates' argumentation skills, conceptual quality of problem solutions, and problem solving strategies in introductory physics

Science.gov (United States)

Rebello, Carina M.

This study explored the effects of alternative forms of argumentation on undergraduates' physics solutions in introductory calculus-based physics. A two-phase concurrent mixed methods design was employed to investigate relationships between undergraduates' written argumentation abilities, conceptual quality of problem solutions, as well as approaches and strategies for solving argumentative physics problems across multiple physics topics. Participants were assigned via stratified sampling to one of three conditions (control, guided construct, or guided evaluate) based on gender and pre-test scores on a conceptual instrument. The guided construct and guided evaluate groups received tasks and prompts drawn from literature to facilitate argument construction or evaluation. Using a multiple case study design, with each condition serving as a case, interviews were conducted consisting of a think-aloud problem solving session paired with a semi-structured interview. The analysis of problem solving strategies was guided by the theoretical framework on epistemic games adapted by Tuminaro and Redish (2007). This study provides empirical evidence that integration of written argumentation into physics problems can potentially improve the conceptual quality of solutions, expand their repertoire of problem solving strategies and show promise for addressing the gender gap in physics. The study suggests further avenues for research in this area and implications for designing and implementing argumentation tasks in introductory college physics.

Subgingival calculus imaging based on swept-source optical coherence tomography

Science.gov (United States)

Hsieh, Yao-Sheng; Ho, Yi-Ching; Lee, Shyh-Yuan; Lu, Chih-Wei; Jiang, Cho-Pei; Chuang, Ching-Cheng; Wang, Chun-Yang; Sun, Chia-Wei

2011-07-01

We characterized and imaged dental calculus using swept-source optical coherence tomography (SS-OCT). The refractive indices of enamel, dentin, cementum, and calculus were measured as 1.625 +/- 0.024, 1.534 +/- 0.029, 1.570 +/- 0.021, and 2.097 +/- 0.094, respectively. Dental calculus leads strong scattering properties, and thus, the region can be identified from enamel with SS-OCT imaging. An extracted human tooth with calculus is covered with gingiva tissue as an in vitro sample for tomographic imaging.

Effect of written presentation on performance in introductory physics

Directory of Open Access Journals (Sweden)

Shawn Ballard

2010-10-01

Full Text Available This study examined the written work of students in the introductory calculus-based electricity and magnetism course at the University of Arkansas. The students’ solutions to hourly exams were divided into a small set of countable features organized into three major categories, mathematics, language, and graphics. Each category was further divided into subfeatures. The total number of features alone explained more than 30% of the variance in exam scores and from 9% to 15% of the variance in conceptual posttest scores. If all features and subfeatures are used, between 44% and 49% of the variance in exam scores is explained and between 22% and 28% of the variance in conceptual posttest scores. The use of language is consistently positively correlated with both exam performance and conceptual understanding.

An analysis of science content and representations in introductory college physics textbooks and multimodal learning resources

Science.gov (United States)

Donnelly, Suzanne M.

This study features a comparative descriptive analysis of the physics content and representations surrounding the first law of thermodynamics as presented in four widely used introductory college physics textbooks representing each of four physics textbook categories (calculus-based, algebra/trigonometry-based, conceptual, and technical/applied). Introducing and employing a newly developed theoretical framework, multimodal generative learning theory (MGLT), an analysis of the multimodal characteristics of textbook and multimedia representations of physics principles was conducted. The modal affordances of textbook representations were identified, characterized, and compared across the four physics textbook categories in the context of their support of problem-solving. Keywords: college science, science textbooks, multimodal learning theory, thermodynamics, representations

Factors Associated with Success in College Calculus II

Science.gov (United States)

Rosasco, Margaret E.

2013-01-01

Students are entering college having earned credit for college Calculus 1 based on their scores on the College Board's Advanced Placement (AP) Calculus AB exam. Despite being granted credit for college Calculus 1, it is unclear whether these students are adequately prepared for college Calculus 2. College calculus classes are often taught from a…

Quantum variational calculus

CERN Document Server

Malinowska, Agnieszka B

2014-01-01

This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations fo...

Jet-calculus approach including coherence effects

International Nuclear Information System (INIS)

Jones, L.M.; Migneron, R.; Narayanan, K.S.S.

1987-01-01

We show how integrodifferential equations typical of jet calculus can be combined with an averaging procedure to obtain jet-calculus-based results including the Mueller interference graphs. Results in longitudinal-momentum fraction x for physical quantities are higher at intermediate x and lower at large x than with the conventional ''incoherent'' jet calculus. These results resemble those of Marchesini and Webber, who used a Monte Carlo approach based on the same dynamics

On the Presentation of Pre-Calculus and Calculus Topics: An Alternate View

Science.gov (United States)

Davydov, Aleksandr; Sturm-Beiss, Rachel

2008-01-01

The orders of presentation of pre-calculus and calculus topics, and the notation used, deserve careful study as they affect clarity and ultimately students' level of understanding. We introduce an alternate approach to some of the topics included in this sequence. The suggested alternative is based on years of teaching in colleges within and…

Quantum Variational Calculus

OpenAIRE

Malinowska , Agnieszka B.; Torres , Delfim

2014-01-01

International audience; Introduces readers to the treatment of the calculus of variations with q-differences and Hahn difference operators Provides the reader with the first extended treatment of quantum variational calculus Shows how the techniques described can be applied to economic models as well as other mathematical systems This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of it...

Calculus of bivariant function

OpenAIRE

PTÁČNÍK, Jan

2011-01-01

This thesis deals with the introduction of function of two variables and differential calculus of this function. This work should serve as a textbook for students of elementary school's teacher. Each chapter contains a summary of basic concepts and explanations of relationships, then solved model exercises of the topic and finally the exercises, which should solve the student himself. Thesis have transmit to students basic knowledges of differential calculus of functions of two variables, inc...

Examining students' views about validity of experiments: From introductory to Ph.D. students

Science.gov (United States)

Hu, Dehui; Zwickl, Benjamin M.

2018-06-01

We investigated physics students' epistemological views on measurements and validity of experimental results. The roles of experiments in physics have been underemphasized in previous research on students' personal epistemology, and there is a need for a broader view of personal epistemology that incorporates experiments. An epistemological framework incorporating the structure, methodology, and validity of scientific knowledge guided the development of an open-ended survey. The survey was administered to students in algebra-based and calculus-based introductory physics courses, upper-division physics labs, and physics Ph.D. students. Within our sample, we identified several differences in students' ideas about validity and uncertainty in measurement. The majority of introductory students justified the validity of results through agreement with theory or with results from others. Alternatively, Ph.D. students frequently justified the validity of results based on the quality of the experimental process and repeatability of results. When asked about the role of uncertainty analysis, introductory students tended to focus on the representational roles (e.g., describing imperfections, data variability, and human mistakes). However, advanced students focused on the inferential roles of uncertainty analysis (e.g., quantifying reliability, making comparisons, and guiding refinements). The findings suggest that lab courses could emphasize a variety of approaches to establish validity, such as by valuing documentation of the experimental process when evaluating the quality of student work. In order to emphasize the role of uncertainty in an authentic way, labs could provide opportunities to iterate, make repeated comparisons, and make decisions based on those comparisons.

Backpropagation and ordered derivatives in the time scales calculus.

Science.gov (United States)

Seiffertt, John; Wunsch, Donald C

2010-08-01

Backpropagation is the most widely used neural network learning technique. It is based on the mathematical notion of an ordered derivative. In this paper, we present a formulation of ordered derivatives and the backpropagation training algorithm using the important emerging area of mathematics known as the time scales calculus. This calculus, with its potential for application to a wide variety of inter-disciplinary problems, is becoming a key area of mathematics. It is capable of unifying continuous and discrete analysis within one coherent theoretical framework. Using this calculus, we present here a generalization of backpropagation which is appropriate for cases beyond the specifically continuous or discrete. We develop a new multivariate chain rule of this calculus, define ordered derivatives on time scales, prove a key theorem about them, and derive the backpropagation weight update equations for a feedforward multilayer neural network architecture. By drawing together the time scales calculus and the area of neural network learning, we present the first connection of two major fields of research.

Characterizing the changes in teaching practice during first semester implementation of an argument-based inquiry approach in a middle school science classroom

Science.gov (United States)

Pinney, Brian Robert John

The purpose of this study was to characterize ways in which teaching practice in classroom undergoing first semester implementation of an argument-based inquiry approach changes in whole-class discussion. Being that argument is explicitly called for in the Next Generation Science Standards and is currently a rare practice in teaching, many teachers will have to transform their teaching practice for inclusion of this feature. Most studies on Argument-Based Inquiry (ABI) agree that development of argument does not come easily and is only acquired through practice. Few studies have examined the ways in which teaching practice changes in relation to the big idea or disciplinary core idea (NGSS), the development of dialogue, and/or the development of argument during first semester implementation of an argument-based inquiry approach. To explore these areas, this study posed three primary research questions: (1) How does a teacher in his first semester of Science Writing Heuristic professional development make use of the "big idea"?, (1a) Is the indicated big idea consistent with NGSS core concepts?, (2) How did the dialogue in whole-class discussion change during the first semester of argument-based inquiry professional development?, (3) How did the argument in whole-class discussion change during the first semester of argument-based inquiry professional development? This semester-long study that took place in a middle school in a rural Midwestern city was grounded in interactive constructivism, and utilized a qualitative design to identify the ways in which the teacher utilized big ideas and how dialogue and argumentative dialogue developed over time. The purposefully selected teacher in this study provided a unique situation where he was in his first semester of professional development using the Science Writing Heuristic Approach to argument-based inquiry with 19 students who had two prior years' experience in ABI. Multiple sources of data were collected, including

Strengthening introductory psychology: A new model for teaching the introductory course.

Science.gov (United States)

Gurung, Regan A R; Hackathorn, Jana; Enns, Carolyn; Frantz, Susan; Cacioppo, John T; Loop, Trudy; Freeman, James E

2016-01-01

Introductory psychology (Intro Psych) is one of the most popular and frequently taught courses on college campuses, yet educators in psychology have limited knowledge about what is covered in classes around the nation or the extent to which class content reflects the current scope of the discipline. There is no explicit model to guide course content selection for the intro course, which poses substantial challenges for instructors. This article proposes a new model for teaching the intro course that integrates (a) scientific foundations, (b) 5 major domains or pillars of knowledge (biological, cognitive, developmental, social and personality, and mental and physical health), and (c) cross-cutting themes relevant to all domains (cultural and social diversity, ethics, variations in human functioning, and applications; American Psychological Association, 2014). We advocate for national assessment of the course, a similar introductory course for majors and nonmajors, the inclusion of experiential or laboratory components, and additional training resources for instructors of the intro course. Given the exponential growth of psychological knowledge and applications during the past decades, we caution against attempting to provide exhaustive coverage of all topic areas of psychology in a one-semester course. We conclude by discussing the challenges that lie ahead for the discipline of psychology as it launches this new model for Intro Psych. (c) 2016 APA, all rights reserved).

Assessment of burnout in veterinary medical students using the Maslach Burnout Inventory-Educational Survey: a survey during two semesters.

Science.gov (United States)

Chigerwe, Munashe; Boudreaux, Karen A; Ilkiw, Jan E

2014-11-28

Burnout among veterinary students can result from known stressors in the absence of a support system. The objectives of this study were to evaluate use of the Maslach Burnout Inventory-Educator Survey (MBI-ES) to assess burnout in veterinary students and evaluate the factors that predict the MBI-ES scores. The MBI-ES was administered to first (Class of 2016) and second year (Class of 2015) veterinary medical students during the 2012-2013 academic year in the fall and spring semesters. Factor analysis and test reliability for the survey were determined. Mean scores for the subscales determining burnout namely emotional exhaustion (EE), depersonalization (DP) and lack of personal accomplishment (PA) were calculated for both classes in the 2 semesters. Multiple regression analysis was performed to evaluate other factors that predict the MBI-ES scores. A non-probability sampling method was implemented consisting of a voluntary sample of 170 and 123 students in the fall and spring semesters, respectively. Scores for EE, DP and PA were not different between the 2 classes within the same semester. Mean ± SD scores for EE, DP and PA for the fall semester were 22.9 ± 9.6, 5.0 ± 4.8 and 32.3 ± 6.7, respectively. Mean ± SD scores for EE, DP and PA the spring semester were 27.8 ± 10.7, 6.5 ± 6.1and 31.7 ± 6.8, respectively. The EE score was higher in spring compared to fall while DP and PA scores were not different between the 2 semesters. Living arrangements specifically as to whether or not a student lived with another veterinary medical students was the only variable significantly associated with the MBI-ES scores. Students in this study had moderate levels of burnout based on the MBI-ES scores. The MBI-ES was an acceptable instrument for assessing burnout in veterinary medical students. The EE scores were higher in the spring semester as compared to the fall semester. Thus students in the first and second years of veterinary school under the current curriculum

Calculus

CERN Document Server

Larson, Ron

2014-01-01

The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

Calculus, Biology and Medicine: A Case Study in Quantitative Literacy for Science Students

Directory of Open Access Journals (Sweden)

Kim Rheinlander

2011-01-01

Full Text Available This paper describes a course designed to enhance the numeracy of biology and pre-medical students. The course introduces students with the background of one semester of calculus to systems of nonlinear ordinary differential equations as they appear in the mathematical biology literature. Evaluation of the course showed increased enjoyment and confidence in doing mathematics, and an increased appreciation of the utility of mathematics to science. Students who complete this course are better able to read the research literature in mathematical biology and carry out research problems of their own.

Continuation calculus

NARCIS (Netherlands)

Geron, B.; Geuvers, J.H.; de'Liguoro, U.; Saurin, A.

2013-01-01

Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head

Making Politics "Click": The Costs and Benefits of Using Clickers in an Introductory Political Science Course

Science.gov (United States)

Evans, Heather K.

2012-01-01

In this article, the author addresses both the costs and benefits of implementing clickers into an introductory political science course. Comparing student responses to a mid-semester survey in both a clicker and non-clicker course, the results show that students have higher satisfaction of the course and instructor, higher exam scores, and feel…

Understanding the gender gap: Social cognitive changes during an introductory stem course.

Science.gov (United States)

Hardin, Erin E; Longhurst, Melanie O

2016-03-01

Despite robust support for the basic theoretical model of social cognitive career theory (Lent, Brown, & Hackett, 1994) and predictions that, for example, increases (or declines) in self-efficacy would lead to subsequent increases (or declines) in interest, there has been surprisingly little longitudinal research that has directly examined the extent to which members of different groups (e.g., women and men) actually do experience changes in critical social-cognitive variables over time early in their curricula in the fields of science, technology, engineering, and mathematics (STEM). Knowing the extent to which such changes occur in typical introductory undergraduate courses is important for targeting interventions to increase persistence of underrepresented groups in STEM. We measured social-cognitive-career-theory-relevant variables near the middle and at the end of the 1st semester of a gateway introductory chemistry course and found that women had lower STEM self-efficacy, coping self-efficacy, and STEM interest than did men, even after controlling for actual course performance. Although there were no detrimental changes across the semester for women or men, men experienced a small but significant increase in their perceived support for pursuing a STEM degree, whereas women did not. (c) 2016 APA, all rights reserved).

The efficacy of selective calculus ablation at 400 nm: comparison to conventional calculus removal methods

Science.gov (United States)

Schoenly, Joshua E.; Seka, Wolf; Romanos, Georgios; Rechmann, Peter

A desired outcome of scaling and root planing is the complete removal of calculus and infected root tissue and preservation of healthy cementum for rapid healing of periodontal tissues. Conventional periodontal treatments for calculus removal, such as hand instrument scaling and ultrasonic scaling, often deeply scrape the surface of the underlying hard tissue and may leave behind a smear layer. Pulsed lasers emitting at violet wavelengths (specifically, 380 to 400 nm) are a potential alternative treatment since they can selectively ablate dental calculus without ablating pristine hard tissue (i.e., enamel, cementum, and dentin). In this study, light and scanning electron microscopy are used to compare and contrast the efficacy of in vitro calculus removal for several conventional periodontal treatments (hand instruments, ultrasonic scaler, and Er:YAG laser) to calculus removal with a frequency-doubled Ti:sapphire (λ = 400 nm). After calculus removal, enamel and cementum surfaces are investigated for calculus debris and damage to the underlying hard tissue surface. Compared to the smear layer, grooves, and unintentional hard tissue removal typically found using these conventional treatments, calculus removal using the 400-nm laser is complete and selective without any removal of pristine dental hard tissue. Based on these results, selective ablation from the 400-nm laser appears to produce a root surface that would be more suitable for successful healing of periodontal tissues.

An Empirical Evaluation of Puzzle-Based Learning as an Interest Approach for Teaching Introductory Computer Science

Science.gov (United States)

Merrick, K. E.

2010-01-01

This correspondence describes an adaptation of puzzle-based learning to teaching an introductory computer programming course. Students from two offerings of the course--with and without the puzzle-based learning--were surveyed over a two-year period. Empirical results show that the synthesis of puzzle-based learning concepts with existing course…

A Case-Based Curriculum for Introductory Geology

Science.gov (United States)

Goldsmith, David W.

2011-01-01

For the past 5 years I have been teaching my introductory geology class using a case-based method that promotes student engagement and inquiry. This article presents an explanation of how a case-based curriculum differs from a more traditional approach to the material. It also presents a statistical analysis of several years' worth of student…

Impact of Calculus Reform in a Liberal Arts Calculus Course.

Science.gov (United States)

Brosnan, Patricia A.; Ralley, Thomas G.

This report describes the changes in a freshman-level calculus course that occurred as a consequence of adopting the Harvard Consortium Calculus text. The perspective is that of the lecturer. The course is intended as an introduction to calculus for liberal arts students, that is, students who will not be expected to use calculus as a mathematical…

Engineering electromagnetics

CERN Document Server

Ida, Nathan

2015-01-01

This book provides students with a thorough theoretical understanding of electromagnetic field equations and it also treats a large number of applications. The text is a comprehensive two-semester textbook. The work treats most topics in two steps – a short, introductory chapter followed by a second chapter with in-depth extensive treatment; between 10 to 30 applications per topic; examples and exercises throughout the book; experiments, problems  and summaries.   The new edition includes: updated end of chapter problems; a new introduction to electromagnetics based on behavior of charges; a new section on units; MATLAB tools for solution of problems and demonstration of subjects; most chapters include a summary. The book is an undergraduate textbook at the Junior level, intended for required classes in electromagnetics. It is written in simple terms with all details of derivations included and all steps in solutions listed. It requires little beyond basic calculus and can be used for self-study. The weal...

Calculus

CERN Document Server

Grossman, Stanley I

1981-01-01

Calculus, Second Edition discusses the techniques and theorems of calculus. This edition introduces the sine and cosine functions, distributes ?-? material over several chapters, and includes a detailed account of analytic geometry and vector analysis.This book also discusses the equation of a straight line, trigonometric limit, derivative of a power function, mean value theorem, and fundamental theorems of calculus. The exponential and logarithmic functions, inverse trigonometric functions, linear and quadratic denominators, and centroid of a plane region are likewise elaborated. Other topics

Series expansion in fractional calculus and fractional differential equations

OpenAIRE

Li, Ming-Fan; Ren, Ji-Rong; Zhu, Tao

2009-01-01

Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this theorem, in this paper we introduce fractional series expansion method to fractional calculus. We define a kind of fractional Taylor series of an infinitely fractionally-differentiable function. Further, based on our definition we generalize hypergeometric functio...

Ups and downs of using ``kitchen sink'' experiments in an introductory fluid mechanics class

Science.gov (United States)

Kaye, Nigel

2015-11-01

Both positive and negative experiences from two semesters of using take home ``kitchen sink'' experiments in an introductory civil engineering fluid mechanics class are reported. Four different experimental assignments were given each semester to groups of four students. The students were tasked with using common household equipment to measure various properties of fluids or fluid flows. These included the density of cooking oil, the exit velocity from a garden hose, and the mass flux of air from a compressed air can. Students were given minimal guidance on how to do the measurements and each measurement had to be done in at least two different ways. The labs were used to relate their course work to everyday situations and was also used as a platform for discussing experimental uncertainty and error propagation in calculations. In general the students successfully completed each task using at least one method. Finding a second method sometimes proved problematic. The presentation will discuss the logistics of running the program and the positive and negative aspects from the instructor viewpoint. A summary of student feedback on the labs will also be presented. Links to resources for those interested in implementing such a program will be provided.

Reasoning about objects using process calculus techniques

DEFF Research Database (Denmark)

Kleist, Josva

This thesis investigates the applicability of techniques known from the world of process calculi to reason about properties of object-oriented programs. The investigation is performed upon a small object-oriented language - The Sigma-calculus of Abadi and Cardelli. The investigation is twofold: We......-calculus turns out to be insufficient. Based on our experiences, we present a translation of a typed imperative Sigma-calculus, which looks promising. We are able to provide simple proofs of the equivalence of different Sigma-calculus objects using this translation. We use a labelled transition system adapted...... to the Sigma-calculus to investigate the use of process calculi techniques directly on the Sigma-calculus. The results obtained are of a fairly theoretical nature. We investigate the connection between the operational and denotaional semantics for a typed functional Sigma-calculus. The result is that Abadi...

Complex variables

CERN Document Server

Fisher, Stephen D

1999-01-01

The most important topics in the theory and application of complex variables receive a thorough, coherent treatment in this introductory text. Intended for undergraduates or graduate students in science, mathematics, and engineering, this volume features hundreds of solved examples, exercises, and applications designed to foster a complete understanding of complex variables as well as an appreciation of their mathematical beauty and elegance. Prerequisites are minimal; a three-semester course in calculus will suffice to prepare students for discussions of these topics: the complex plane, basic

Data Quality Indicators Composition and Calculus: Engineering and Information Systems Approaches

Directory of Open Access Journals (Sweden)

Leon REZNIK

2015-02-01

Full Text Available Big Data phenomenon is a result of novel technological developments in sensor, computer and communication technologies. Nowadays more and more data are produced by nanoscale photonic, optoelectronic and electronic devices. However, their quality characteristics could be very low. The paper proposes new methods of the data management with huge data amounts that is based on associating of data quality indicators with each data entity. To achieve this goal, one needs to define the composition of the data quality indicators and to develop their integration calculus. As data quality evaluation involves multi-disciplinary research, various metrics have been investigated. The paper describes two major approaches in assigning the data quality indicators and developing their integration calculus. The information systems approach employs traditional high-level metrics like data accuracy, consistency and completeness. The engineering approach utilizes signal characteristics processed with the probability based calculus. The data quality metrics composition and calculus are discussed. The tools developed to automate the metrics selection and calculus procedures are presented. The user- friendly interface examples are provided.

Operational calculus

CERN Document Server

Boehme, Thomas K

1987-01-01

Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included.Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and non-ho

Framework and implementation for improving physics essential skills via computer-based practice: Vector math

Science.gov (United States)

Mikula, Brendon D.; Heckler, Andrew F.

2017-06-01

We propose a framework for improving accuracy, fluency, and retention of basic skills essential for solving problems relevant to STEM introductory courses, and implement the framework for the case of basic vector math skills over several semesters in an introductory physics course. Using an iterative development process, the framework begins with a careful identification of target skills and the study of specific student difficulties with these skills. It then employs computer-based instruction, immediate feedback, mastery grading, and well-researched principles from cognitive psychology such as interleaved training sequences and distributed practice. We implemented this with more than 1500 students over 2 semesters. Students completed the mastery practice for an average of about 13 min /week , for a total of about 2-3 h for the whole semester. Results reveal large (>1 SD ) pretest to post-test gains in accuracy in vector skills, even compared to a control group, and these gains were retained at least 2 months after practice. We also find evidence of improved fluency, student satisfaction, and that awarding regular course credit results in higher participation and higher learning gains than awarding extra credit. In all, we find that simple computer-based mastery practice is an effective and efficient way to improve a set of basic and essential skills for introductory physics.

Classroom Research: Assessment of Student Understanding of Sampling Distributions of Means and the Central Limit Theorem in Post-Calculus Probability and Statistics Classes

Science.gov (United States)

Lunsford, M. Leigh; Rowell, Ginger Holmes; Goodson-Espy, Tracy

2006-01-01

We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we…

Study Modules for Calculus-Based General Physics. [Includes Modules 24-26: Electric Potential; Ohm's Law; and Capacitors].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

A collaborative learning approach for service-oriented introductory physics

Science.gov (United States)

Smith, Michael R.

1997-03-01

I have taught algebra-based introductory physics for six years to liberal arts students. It was primarily a service course for students majoring in Athletic Training, Physical Therapy, Geology, Biology, and Pre-Med. The typical student was characterized by having a minimal math and problem-solving proficiency. There also was a pattern of students being predisposed to memorizing facts and formulas, and attempting to solve problems by finding the correct formula and "plugging in" numbers to get an answer. The students seemed to have a minimal ability in deductive reasoning and problem solving, starting from basic principles. It is no wonder that they entered the introductory physics service course with extreme trepidation, based upon a strongly perceived physics phobia. A standard lecture format was used for the class size of approximately 25-30 students; and an attempt was always made to engage the students through the Socratic approach, by asking leading questions during the course of the lecture. The students were relatively unprepared and couldn't participate in the class, and often responded antagonistically. They indicated they didn't want to be asked to think about an issue, but would rather just be told the facts so they could take specific notes for subsequent memorization. It was clear from the results of the open book exams given during the semester that the majority of students could not approach problem solving using deductive reasoning based on basic principles, but relied on attempting to force-fit the problem into a worked example in the text (often out of context, with illogical results). The absentee rate in the classroom was usually around 30-40%. The academic administration of my liberal arts university has the policy of formal course evaluations by the students at the end of each semester. The evaluation questionnaire appears to be primarily a measurement of the stress level of the student during the course, and the evaluation score I received

Geometric calculus: a new computational tool for Riemannian geometry

International Nuclear Information System (INIS)

Moussiaux, A.; Tombal, P.

1988-01-01

We compare geometric calculus applied to Riemannian geometry with Cartan's exterior calculus method. The correspondence between the two methods is clearly established. The results obtained by a package written in an algebraic language and doing general manipulations on multivectors are compared. We see that the geometric calculus is as powerful as exterior calculus

A Higher-Order Calculus for Categories

DEFF Research Database (Denmark)

Cáccamo, Mario José; Winskel, Glynn

2001-01-01

A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic...... in their free variables. There are special binders for limits and more general ends. The rules for limits and ends support an algebraic manipulation of universal constructions as opposed to a more traditional diagrammatic approach. Duality within the calculus and applications in proving continuity are discussed...... with examples. The calculus gives a basis for mechanising a theory of categories in a generic theorem prover like Isabelle....

Fundamentals of calculus

CERN Document Server

Morris, Carla C

2015-01-01

Fundamentals of Calculus encourages students to use power, quotient, and product rules for solutions as well as stresses the importance of modeling skills.  In addition to core integral and differential calculus coverage, the book features finite calculus, which lends itself to modeling and spreadsheets.  Specifically, finite calculus is applied to marginal economic analysis, finance, growth, and decay.  Includes: Linear Equations and FunctionsThe DerivativeUsing the Derivative Exponential and Logarithmic Functions Techniques of DifferentiationIntegral CalculusIntegration TechniquesFunctions

The two-parameter deformation of GL(2), its differential calculus, and Lie algebra

International Nuclear Information System (INIS)

Schirrmacher, A.; Wess, J.

1991-01-01

The Yang-Baxter equation is solved in two dimensions giving rise to a two-parameter deformation of GL(2). The transformation properties of quantum planes are briefly discussed. Non-central determinant and inverse are constructed. A right-invariant differential calculus is presented and the role of the different deformation parameters investigated. While the corresponding Lie algebra relations are simply deformed, the comultiplication exhibits both quantization parameters. (orig.)

On the fractional calculus of Besicovitch function

International Nuclear Information System (INIS)

Liang Yongshun

2009-01-01

Relationship between fractional calculus and fractal functions has been explored. Based on prior investigations dealing with certain fractal functions, fractal dimensions including Hausdorff dimension, Box dimension, K-dimension and Packing dimension is shown to be a linear function of order of fractional calculus. Both Riemann-Liouville fractional calculus and Weyl-Marchaud fractional derivative of Besicovitch function have been discussed.

Team-Based Learning Reduces Attrition in a First-Semester General Chemistry Course

Science.gov (United States)

Comeford, Lorrie

2016-01-01

Team-based learning (TBL) is an instructional method that has been shown to reduce attrition and increase student learning in a number of disciplines. TBL was implemented in a first-semester general chemistry course, and its effect on attrition was assessed. Attrition from sections before implementing TBL (fall 2008 to fall 2009) was compared with…

Workshop Physics Activity Guide, Module 4: Electricity and Magnetism

Science.gov (United States)

Laws, Priscilla W.

2004-05-01

The Workshop Physics Activity Guide is a set of student workbooks designed to serve as the foundation for a two-semester calculus-based introductory physics course. It consists of 28 units that interweave text materials with activities that include prediction, qualitative observation, explanation, equation derivation, mathematical modeling, quantitative experiments, and problem solving. Students use a powerful set of computer tools to record, display, and analyze data, as well as to develop mathematical models of physical phenomena. The design of many of the activities is based on the outcomes of physics education research. The Workshop Physics Activity Guide is supported by an Instructor's Website that: (1) describes the history and philosophy of the Workshop Physics Project; (2) provides advice on how to integrate the Guide into a variety of educational settings; (3) provides information on computer tools (hardware and software) and apparatus; and (4) includes suggested homework assignments for each unit. Log on to the Workshop Physics Project website at http://physics.dickinson.edu/ Workshop Physics is a component of the Physics Suite--a collection of materials created by a group of educational reformers known as the Activity Based Physics Group. The Physics Suite contains a broad array of curricular materials that are based on physics education research, including: Understanding Physics, by Cummings, Laws, Redish and Cooney (an introductory textbook based on the best-selling text by Halliday/Resnick/Walker) RealTime Physics Laboratory Modules Physics by Inquiry (intended for use in a workshop setting) Interactive Lecture Demonstration Tutorials in Introductory Physics Activity Based Tutorials (designed primarily for use in recitations)

A calculus for quality

DEFF Research Database (Denmark)

Nielson, Hanne Riis; Nielson, Flemming; Vigo, Roberto

2013-01-01

for default behaviour in case the ideal behaviour fails due to unreliable communication and thereby to increase the quality of service offered by the systems. The development is facilitated by a SAT-based robustness analysis to determine whether or not the code is vulnerable to unreliable communication......A main challenge of programming component-based software is to ensure that the components continue to behave in a reasonable manner even when communication becomes unreliable. We propose a process calculus, the Quality Calculus, for programming software components where it becomes natural to plan...

A Formal Calculus for Categories

DEFF Research Database (Denmark)

Cáccamo, Mario José

This dissertation studies the logic underlying category theory. In particular we present a formal calculus for reasoning about universal properties. The aim is to systematise judgements about functoriality and naturality central to categorical reasoning. The calculus is based on a language which...... extends the typed lambda calculus with new binders to represent universal constructions. The types of the languages are interpreted as locally small categories and the expressions represent functors. The logic supports a syntactic treatment of universality and duality. Contravariance requires a definition...... of universality generous enough to deal with functors of mixed variance. Ends generalise limits to cover these kinds of functors and moreover provide the basis for a very convenient algebraic manipulation of expressions. The equational theory of the lambda calculus is extended with new rules for the definitions...

Toward equity through participation in Modeling Instruction in introductory university physics

Science.gov (United States)

Brewe, Eric; Sawtelle, Vashti; Kramer, Laird H.; O'Brien, George E.; Rodriguez, Idaykis; Pamelá, Priscilla

2010-06-01

We report the results of a five year evaluation of the reform of introductory calculus-based physics by implementation of Modeling Instruction (MI) at Florida International University (FIU), a Hispanic-serving institution. MI is described in the context of FIU’s overall effort to enhance student participation in physics and science broadly. Our analysis of MI from a “participationist” perspective on learning identifies aspects of MI including conceptually based instruction, culturally sensitive instruction, and cooperative group learning, which are consistent with research on supporting equitable learning and participation by students historically under-represented in physics (i.e., Black, Hispanic, women). This study uses markers of conceptual understanding as measured by the Force Concept Inventory (FCI) and odds of success as measured by the ratio of students completing introductory physics and earning a passing grade (i.e., C- or better) by students historically under-represented in physics to reflect equity and participation in introductory physics. FCI pre and post scores for students in MI are compared with lecture-format taught students. Modeling Instruction students outperform students taught in lecture-format classes on post instruction FCI (61.9% vs 47.9%, p<0.001 ), where these benefits are seen across both ethnic and gender comparisons. In addition, we report that the odds of success in MI are 6.73 times greater than in lecture instruction. Both odds of success and FCI scores within Modeling Instruction are further disaggregated by ethnicity and by gender to address the question of equity within the treatment. The results of this disaggregation indicate that although ethnically under-represented students enter with lower overall conceptual understanding scores, the gap is not widened during introductory physics but instead is maintained, and the odds of success for under-represented students is not different from majority students. Women

Toward equity through participation in Modeling Instruction in introductory university physics

Directory of Open Access Journals (Sweden)

Eric Brewe

2010-05-01

Full Text Available We report the results of a five year evaluation of the reform of introductory calculus-based physics by implementation of Modeling Instruction (MI at Florida International University (FIU, a Hispanic-serving institution. MI is described in the context of FIU’s overall effort to enhance student participation in physics and science broadly. Our analysis of MI from a “participationist” perspective on learning identifies aspects of MI including conceptually based instruction, culturally sensitive instruction, and cooperative group learning, which are consistent with research on supporting equitable learning and participation by students historically under-represented in physics (i.e., Black, Hispanic, women. This study uses markers of conceptual understanding as measured by the Force Concept Inventory (FCI and odds of success as measured by the ratio of students completing introductory physics and earning a passing grade (i.e., C− or better by students historically under-represented in physics to reflect equity and participation in introductory physics. FCI pre and post scores for students in MI are compared with lecture-format taught students. Modeling Instruction students outperform students taught in lecture-format classes on post instruction FCI (61.9% vs 47.9%, p<0.001, where these benefits are seen across both ethnic and gender comparisons. In addition, we report that the odds of success in MI are 6.73 times greater than in lecture instruction. Both odds of success and FCI scores within Modeling Instruction are further disaggregated by ethnicity and by gender to address the question of equity within the treatment. The results of this disaggregation indicate that although ethnically under-represented students enter with lower overall conceptual understanding scores, the gap is not widened during introductory physics but instead is maintained, and the odds of success for under-represented students is not different from majority students

Students' network integration as a predictor of persistence in introductory physics courses

Science.gov (United States)

Zwolak, Justyna P.; Dou, Remy; Williams, Eric A.; Brewe, Eric

2017-06-01

Increasing student retention (successfully finishing a particular course) and persistence (continuing through a sequence of courses or the major area of study) is currently a major challenge for universities. While students' academic and social integration into an institution seems to be vital for student retention, research into the effect of interpersonal interactions is rare. We use network analysis as an approach to investigate academic and social experiences of students in the classroom. In particular, centrality measures identify patterns of interaction that contribute to integration into the university. Using these measures, we analyze how position within a social network in a Modeling Instruction (MI) course—an introductory physics course that strongly emphasizes interactive learning—predicts their persistence in taking a subsequent physics course. Students with higher centrality at the end of the first semester of MI are more likely to enroll in a second semester of MI. Moreover, we found that chances of successfully predicting individual student's persistence based on centrality measures are fairly high—up to 75%, making the centrality a good predictor of persistence. These findings suggest that increasing student social integration may help in improving persistence in science, technology, engineering, and mathematics fields.

Active learning and student-centered pedagogy improve student attitudes and performance in introductory biology.

Science.gov (United States)

Armbruster, Peter; Patel, Maya; Johnson, Erika; Weiss, Martha

2009-01-01

We describe the development and implementation of an instructional design that focused on bringing multiple forms of active learning and student-centered pedagogies to a one-semester, undergraduate introductory biology course for both majors and nonmajors. Our course redesign consisted of three major elements: 1) reordering the presentation of the course content in an attempt to teach specific content within the context of broad conceptual themes, 2) incorporating active and problem-based learning into every lecture, and 3) adopting strategies to create a more student-centered learning environment. Assessment of our instructional design consisted of a student survey and comparison of final exam performance across 3 years-1 year before our course redesign was implemented (2006) and during two successive years of implementation (2007 and 2008). The course restructuring led to significant improvement of self-reported student engagement and satisfaction and increased academic performance. We discuss the successes and ongoing challenges of our course restructuring and consider issues relevant to institutional change.

Regularization of positive definite matrix fields based on multiplicative calculus

NARCIS (Netherlands)

Florack, L.M.J.; Bruckstein, A.M.; Haar Romeny, ter B.M.; Bronstein, A.M.; Bronstein, M.M.

2012-01-01

Multiplicative calculus provides a natural framework in problems involving positive images and positivity preserving operators. In increasingly important, complex imaging frameworks, such as diffusion tensor imaging, it complements standard calculus in a nontrivial way. The purpose of this article

Mathematics for physics with calculus

CERN Document Server

Das, Biman

2005-01-01

Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful-and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.

q-fractional calculus and equations

CERN Document Server

Annaby, Mahmoud H

2012-01-01

This nine-chapter monograph introduces a rigorous investigation of q-difference operators in standard and fractional settings. It starts with elementary calculus of q-differences and integration of Jackson’s type before turning to q-difference equations. The existence and uniqueness theorems are derived using successive approximations, leading to systems of equations with retarded arguments. Regular  q-Sturm–Liouville theory is also introduced; Green’s function is constructed and the eigenfunction expansion theorem is given. The monograph also discusses some integral equations of Volterra and Abel type, as introductory material for the study of fractional q-calculi. Hence fractional q-calculi of the types Riemann–Liouville; Grünwald–Letnikov;  Caputo;  Erdélyi–Kober and Weyl are defined analytically. Fractional q-Leibniz rules with applications  in q-series are  also obtained with rigorous proofs of the formal  results of  Al-Salam-Verma, which remained unproved for decades. In working ...

Association between chronic kidney disease and urinary calculus by stone location: a population-based study.

Science.gov (United States)

Keller, Joseph J; Chen, Yi-Kuang; Lin, Herng-Ching

2012-12-01

Study Type--Disease prevalence study (cohort design) Level of Evidence 2a. What's known on the subject? and What does the study add? Several studies have estimated the potential association of urinary calculus (UC) with chronic kidney disease (CKD). However, previous literature focusing on this issue tended to evaluate the impact of kidney stones alone on incident CKD, with no studies having been conducted investigating the association between CKD and stone formation in other portions of the urological system. We found that patients with CKD were consistently more likely than comparison subjects to have been previously diagnosed with kidney calculus (odds ratio [OR] 2.10, 95% confidence interval [CI] 1.95-2.27), ureter calculus (OR 1.68, 95% CI 1.51-1.85), bladder calculus (OR 1.49, 95% CI 1.13-1.98), and unspecified calculus (OR 1.89, 95% CI 1.74-2.06). We concluded that there was an association between CKD and UC regardless of stone location. • To explore the association of chronic kidney disease (CKD) with prior kidney calculus, ureter calculus, and bladder calculus using a population-based dataset in Taiwan. Several studies have estimated the potential association of urinary calculus (UC) with CKD. However, previous literature focusing on this issue tended to evaluate the impact of kidney stones alone on incident CKD, with no studies having been conducted investigating the association between CKD and stone formation in other portions of the urological system. • We identified 21,474 patients who received their first-time diagnosis of CKD between 2001 and 2009. • The 21,474 controls were frequency-matched with cases for sex, age group, and index year. • We used conditional logistic regression analyses to compute the odds ratio (OR) and corresponding 95% confidence interval (CI) as an estimation of association between CKD and having been previously diagnosed with UC. • The results show that compared with controls, the OR of prior UC for cases was 1

General quantum variational calculus

Directory of Open Access Journals (Sweden)

Artur M. C. Brito da Cruz

2018-02-01

Full Text Available We develop a new variational calculus based in the general quantum difference operator recently introduced by Hamza et al. In particular, we obtain optimality conditions for generalized variational problems where the Lagrangian may depend on the endpoints conditions and a real parameter, for the basic and isoperimetric problems, with and without fixed boundary conditions. Our results provide a generalization to previous results obtained for the $q$- and Hahn-calculus.

Study Modules for Calculus-Based General Physics. [Includes Modules 38-40: Optical Instruments; Diffraction; and Alternating Current Circuits].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Study Modules for Calculus-Based General Physics. [Includes Modules 41 and 42: Lenses and Mirrors; Relativity; and Appendix].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Study Modules for Calculus-Based General Physics. [Includes Modules 3-5: Planar Motion; Newton's Laws; and Vector Multiplication].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Association between osteoporosis and urinary calculus: evidence from a population-based study.

Science.gov (United States)

Keller, J J; Lin, C-C; Kang, J-H; Lin, H-C

2013-02-01

This population-based case-control analysis investigated the association between osteoporosis and prior urinary calculus (UC) in Taiwan. We succeeded in detecting an association between osteoporosis and prior UC (adjusted odds ratio = 1.66). This association was consistent and significant regardless of stone location. UC has been demonstrated to be a risk factor for osteoporotic fractures, but no studies to date have directly investigated the association between UC and osteoporosis. This case-control analysis aimed to investigate the association of osteoporosis with prior UC using a population-based dataset in Taiwan. We first identified 39,840 cases ≥40 years who received their first-time diagnosis of osteoporosis between 2002 and 2009 and then randomly selected 79,680 controls. We used conditional logistic regression analyses to compute the odds ratio (OR) and the corresponding 95 % confidence interval (CI) for having been previously diagnosed with UC between cases and controls. The OR of having been previously diagnosed with UC for patients with osteoporosis was 1.66 (95 % CI = 1.59-1.73) when compared to controls after adjusting for geographic location, urbanization level, type I diabetes mellitus, coronary heart disease, hyperlipidemia, rheumatoid arthritis, stroke, renal disease, Parkinson's disease, hyperthyroidism, chronic hepatopathy, Cushing's syndrome, malabsorption, gastrectomy, obesity, and alcohol abuse/alcohol dependence syndrome. The results consistently showed that osteoporosis was significantly associated with a previous diagnosis of UC regardless of stone location; the adjusted ORs of prior kidney calculus, ureter calculus, bladder calculus, and unspecified calculus when compared to controls were 1.71 (95 % CI = 1.61-1.81), 1.60 (95 % CI = 1.47-1.74), 1.59 (95 % CI = 1.23-2.04), and 1.69 (95 % CI = 1.59-1.80), respectively. This study succeeded in detecting an association between osteoporosis and prior UC. In addition

Vector Differential Calculus

OpenAIRE

HITZER, Eckhard MS

2002-01-01

This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. In order to make the treatment self-contained, I first compile all important geometric algebra relationships,which are necesssary for vector differential calculus. Then differentiation by vectors is introduced and a host of major ve...

Association of bladder pain syndrome/interstitial cystitis with urinary calculus: a nationwide population-based study.

Science.gov (United States)

Keller, Joseph; Chen, Yi-Kuang; Lin, Herng-Ching

2013-04-01

Although one prior study reported an association between bladder pain syndrome/interstitial cystitis (BPS/IC) and urinary calculi (UC), no population-based study to date has been conducted to explore this relationship. Therefore, using a population-based data set in Taiwan, this study set out to investigate the association between BPS/IC and a prior diagnosis of UC. This study included 9,269 cases who had received their first-time diagnosis of BPS/IC between 2006 and 2007 and 46,345 randomly selected controls. We used conditional logistic regression analysis to compute the odds ratio (OR) and its corresponding 95 % confidence interval (CI) for having been previously diagnosed with UC between cases and controls. There was a significant difference in the prevalence of prior UC between cases and controls (8.1 vs 4.3 %, p calculus, ureter calculus, bladder calculus, and unspecified calculus when compared to controls were 1.58 (95 % CI = 1.38-1.81), 1.73 (95 % CI = 1.45-2.05), 3.80 (95 % CI = 2.18-6.62), and 1.83 (95 % CI = 1.59-2.11), respectively. This work generates the hypothesis that UC may be associated with BPS/IC.

Calculus and analysis in Euclidean space

CERN Document Server

Shurman, Jerry

2016-01-01

The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skil...

Study on bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis.

Science.gov (United States)

Wan, Tien-Chun; Cheng, Fu-Yuan; Liu, Yu-Tse; Lin, Liang-Chuan; Sakata, Ryoichi

2009-12-01

The purpose of the study was to investigate bioactive compounds of in vitro cultured Calculus Suis and natural Calculus Bovis obtained as valuable by-products from animals used for meat production. The results showed that the components of natural Calculus Bovis were rich in bilirubin and biliverdin and had higher content of essential amino acids. The major amino acids of in vitro cultured Calculus Suis were identified as glycine, alanine, glutamic acid and aspartic acid, and those for natural Calculus Bovis were found to be glutamic acid, aspartic acid, proline, and arginine. The methionine and cysteine contents of precursors for glutathione in natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The mineral contents of zinc, iron and manganese of natural Calculus Bovis were significantly higher than those of in vitro cultured Calculus Suis. The major bile acids in both products were cholic acid and dehydrocholic acid, respectively. The chenodeoxycholic and ursodeoxycholic acid content of in vitro cultured Calculus Suis was significantly higher than that of natural Calculus Bovis.

Synthesis of NMP, a Fluoxetine (Prozac) Precursor, in the Introductory Organic Laboratory

Science.gov (United States)

Perrine, Daniel M.; Sabanayagam, Nathan R.; Reynolds, Kristy J.

1998-10-01

A synthesis of the immediate precursor of the widely used antidepressant fluoxetine (Prozac) is described. The procedure is short, safe, and simple enough to serve as a laboratory exercise for undergraduate students in the second semester of introductory organic chemistry and is one which will be particularly interesting to those planning a career in the health sciences. The compound synthesized is (°)-N,N-dimethyl-3-(p-trifluoromethylphenoxy)-3-phenylpropylamine, or "N-methyl Prozac" (NMP). The synthesis of NMP requires one two-hour period and a second three-hour period. In the first period, a common Mannich base, 3-dimethylaminopropiophenone, is reduced with sodium borohydride to form (°)-3-dimethylamino-1-phenylpropanol. In the second period, potassium t-butoxide is used to couple (°)-3-dimethylamino-1-phenylpropanol with p-chlorotrifluoromethylbenzene to form NMP, which is isolated as its oxalate salt. All processes use equipment and materials that are inexpensive and readily available in most undergraduate laboratories. Detailed physical data are given on NMP, including high-field DEPT 13C NMR.

Gender Differences in Both Force Concept Inventory and Introductory Physics Performance

Science.gov (United States)

Docktor, Jennifer; Heller, Kenneth

2008-10-01

We present data from a decade of introductory calculus-based physics courses for science and engineering students at the University of Minnesota taught using cooperative group problem solving. The data include 40 classes with more than 5500 students taught by 22 different professors. The average normalized gain for males is 0.4 for these large classes that emphasized problem solving. Female students made up approximately 20% of these classes. We present relationships between pre and post Force Concept Inventory (FCI) scores, course grades, and final exam scores for females and males. We compare our results with previous studies from Harvard [2] and the University of Colorado [3,4]. Our data show there is a significant gender gap in pre-test FCI scores that persists post-instruction although there is essentially no gender difference in course performance as determined by course grade.

Improving student learning in calculus through applications

Science.gov (United States)

Young, C. Y.; Georgiopoulos, M.; Hagen, S. C.; Geiger, C. L.; Dagley-Falls, M. A.; Islas, A. L.; Ramsey, P. J.; Lancey, P. M.; Straney, R. A.; Forde, D. S.; Bradbury, E. E.

2011-07-01

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.

Imagine Yourself in This Calculus Classroom

Science.gov (United States)

Bryan, Luajean

2007-01-01

The efforts to attract students to precalculus, trigonometry, and calculus classes became more successful at the author's school when projects-based classes were offered. Data collection from an untethered hot air balloon flight for calculus students was planned to maximize enrollment. The data were analyzed numerically, graphically, and…

Optimizing Introductory Physics for the Life Sciences: Placing Physics in Biological Context

Science.gov (United States)

Crouch, Catherine

2014-03-01

Physics is a critical foundation for today's life sciences and medicine. However, the physics content and ways of thinking identified by life scientists as most important for their fields are often not taught, or underemphasized, in traditional introductory physics courses. Furthermore, such courses rarely give students practice using physics to understand living systems in a substantial way. Consequently, students are unlikely to recognize the value of physics to their chosen fields, or to develop facility in applying physics to biological systems. At Swarthmore, as at several other institutions engaged in reforming this course, we have reorganized the introductory course for life science students around touchstone biological examples, in which fundamental physics contributes significantly to understanding biological phenomena or research techniques, in order to make explicit the value of physics to the life sciences. We have also focused on the physics topics and approaches most relevant to biology while seeking to develop rigorous qualitative reasoning and quantitative problem solving skills, using established pedagogical best practices. Each unit is motivated by and culminates with students analyzing one or more touchstone examples. For example, in the second semester we emphasize electric potential and potential difference more than electric field, and start from students' typically superficial understanding of the cell membrane potential and of electrical interactions in biochemistry to help them develop a more sophisticated understanding of electric forces, field, and potential, including in the salt water environment of life. Other second semester touchstones include optics of vision and microscopes, circuit models for neural signaling, and magnetotactic bacteria. When possible, we have adapted existing research-based curricular materials to support these examples. This talk will describe the design and development process for this course, give examples of

Using Case Studies in Calculus-based Physics

Science.gov (United States)

Katz, Debora M.

2006-12-01

Do your students believe that the physics only works in your classroom or laboratory? Or do they see that physics underlies their everyday experience? Case studies in physics help students connect physics principles to their everyday experience. For decades, case studies have been used to teach law, medicine and biology, but they are rarely used in physics. I am working on a calculus-based physics textbook for scientists and engineers. Case studies are woven into each chapter. Stop by and get a case study to test out in your classroom. I would love to get your feedback.

Propositional Calculus in Coq

OpenAIRE

van Doorn, Floris

2015-01-01

I formalize important theorems about classical propositional logic in the proof assistant Coq. The main theorems I prove are (1) the soundness and completeness of natural deduction calculus, (2) the equivalence between natural deduction calculus, Hilbert systems and sequent calculus and (3) cut elimination for sequent calculus.

Creation and Assessment of an Active e-Learning Introductory Geology Course

Science.gov (United States)

Sit, Stefany M.; Brudzinski, Michael R.

2017-12-01

The recent emphasis in higher education on both student engagement and online learning encouraged the authors to develop an active e-learning environment for an introductory geohazards course, which enrolls 70+ undergraduate students per semester. Instructors focused on replicating the achievements and addressing the challenges within an already established face-to-face student-centered class (Brudzinski and Sikorski 2010; Sit 2013). Through the use of a learning management system (LMS) and other available technologies, a wide range of course components were developed including online homework assignments with automatic grading and tailored feedback, video tutorials of software programs like Google Earth and Microsoft Excel, and more realistic scientific investigations using authentic and freely available data downloaded from the internet. The different course components designed to engage students and improve overall student learning and development were evaluated using student surveys and instructor reflection. Each component can be used independently and intertwined into a face-to-face course. Results suggest that significant opportunities are available in an online environment including the potential for improved student performance and new datasets for educational research. Specifically, results from pre and post-semester Geoscience Concept Inventory (GCI) testing in an active e-learning course show enhanced student learning gains compared to face-to-face lecture-based and student-centered courses.

Dental calculus detection using the VistaCam.

Science.gov (United States)

Shakibaie, Fardad; Walsh, Laurence J

2016-12-01

The VistaCam® intra-oral camera system (Dürr Dental, Bietigheim-Bissingen, Germany) is a fluorescence system using light emitting diodes that produce a 405-nm violet light. This wavelength has potential application for detection of dental calculus based on red emissions from porphyrin molecules. This study assessed the digital scores obtained for both supragingival and subgingival calculus on 60 extracted teeth and compared these with lesions of dental caries. It has also examined the effect of saliva and blood on the fluorescence readings for dental calculus. VistaCam fluorescence scores for both supragingival (1.7-3.3) and subgingival calculus (1.3-2.4) were higher than those for sound root surfaces (0.9-1.1) and dental caries (0.9-2.2) ( p  calculus samples were not affected by the presence of saliva or blood. These results suggest that the use of violet light fluorescence could be a possible adjunct to clinical examination for deposits of dental calculus.

Tuplix Calculus

OpenAIRE

Bergstra, J. A.; Ponse, A.; van der Zwaag, M. B.

2007-01-01

We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive composition. We define a standard model and prove that CTC is relatively complete with respect to it. The core calculus is extended with operators for choice, information hiding, scalar multiplicatio...

Effectiveness of a Low-Cost, Graduate Student-Led Intervention on Study Habits and Performance in Introductory Biology.

Science.gov (United States)

Hoskins, Tyler D; Gantz, J D; Chaffee, Blake R; Arlinghaus, Kel; Wiebler, James; Hughes, Michael; Fernandes, Joyce J

2017-01-01

Institutions have developed diverse approaches that vary in effectiveness and cost to improve student performance in introductory science, technology, engineering, and mathematics courses. We developed a low-cost, graduate student-led, metacognition-based study skills course taught in conjunction with the introductory biology series at Miami University. Our approach aimed to improve performance for underachieving students by combining an existing framework for the process of learning (the study cycle) with concrete tools (outlines and concept maps) that have been shown to encourage deep understanding. To assess the effectiveness of our efforts, we asked 1) how effective our voluntary recruitment model was at enrolling the target cohort, 2) how the course impacted performance on lecture exams, 3) how the course impacted study habits and techniques, and 4) whether there are particular study habits or techniques that are associated with large improvements on exam scores. Voluntary recruitment attracted only 11-17% of our target cohort. While focal students improved on lecture exams relative to their peers who did not enroll, gains were relatively modest, and not all students improved. Further, although students across both semesters of our study reported improved study habits (based on pre and post surveys) and on outlines and concept maps (based on retrospectively scored assignments), gains were more dramatic in the Fall semester. Multivariate models revealed that, while changes in study habits and in the quality of outlines and concept maps were weakly associated with change in performance on lecture exams, relationships were only significant in the Fall semester and were sometimes counterintuitive. Although benefits of the course were offset somewhat by the inefficiency of voluntary recruitment, we demonstrate the effectiveness our course, which is inexpensive to implement and has advantage of providing pedagogical experience to future educators. © 2017 T. D

Computer-Tailored Student Support in Introductory Physics

Science.gov (United States)

Huberth, Madeline; Chen, Patricia; Tritz, Jared; McKay, Timothy A.

2015-01-01

Large introductory courses are at a disadvantage in providing personalized guidance and advice for students during the semester. We introduce E2Coach (an Expert Electronic Coaching system), which allows instructors to personalize their communication with thousands of students. We describe the E2Coach system, the nature of the personalized support it provides, and the features of the students who did (and did not) opt-in to using it during the first three terms of its use in four introductory physics courses at the University of Michigan. Defining a ‘better-than-expected’ measure of performance, we compare outcomes for students who used E2Coach to those who did not. We found that moderate and high E2Coach usage was associated with improved performance. This performance boost was prominent among high users, who improved by 0.18 letter grades on average when compared to nonusers with similar incoming GPAs. This improvement in performance was comparable across both genders. E2Coach represents one way to use technology to personalize education at scale, contributing to the move towards individualized learning that is becoming more attainable in the 21st century. PMID:26352403

Computer-Tailored Student Support in Introductory Physics.

Science.gov (United States)

Huberth, Madeline; Chen, Patricia; Tritz, Jared; McKay, Timothy A

2015-01-01

Large introductory courses are at a disadvantage in providing personalized guidance and advice for students during the semester. We introduce E2Coach (an Expert Electronic Coaching system), which allows instructors to personalize their communication with thousands of students. We describe the E2Coach system, the nature of the personalized support it provides, and the features of the students who did (and did not) opt-in to using it during the first three terms of its use in four introductory physics courses at the University of Michigan. Defining a 'better-than-expected' measure of performance, we compare outcomes for students who used E2Coach to those who did not. We found that moderate and high E2Coach usage was associated with improved performance. This performance boost was prominent among high users, who improved by 0.18 letter grades on average when compared to nonusers with similar incoming GPAs. This improvement in performance was comparable across both genders. E2Coach represents one way to use technology to personalize education at scale, contributing to the move towards individualized learning that is becoming more attainable in the 21st century.

Fluorescence detection of dental calculus

International Nuclear Information System (INIS)

Gonchukov, S; Sukhinina, A; Vdovin, Yu; Biryukova, T

2010-01-01

This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 – 645 nm and 340 – 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy

Fluorescence detection of dental calculus

Science.gov (United States)

Gonchukov, S.; Biryukova, T.; Sukhinina, A.; Vdovin, Yu

2010-11-01

This work is devoted to the optimization of fluorescence dental calculus diagnostics in optical spectrum. The optimal wavelengths for fluorescence excitation and registration are determined. Two spectral ranges 620 - 645 nm and 340 - 370 nm are the most convenient for supra- and subgingival calculus determination. The simple implementation of differential method free from the necessity of spectrometer using was investigated. Calculus detection reliability in the case of simple implementation is higher than in the case of spectra analysis at optimal wavelengths. The use of modulated excitation light and narrowband detection of informative signal allows us to decrease essentially its diagnostic intensity even in comparison with intensity of the low level laser dental therapy.

Essential AOP: The A Calculus

DEFF Research Database (Denmark)

De Fraine, Bruno; Ernst, Erik; Südholt, Mario

2012-01-01

Aspect-oriented programming (AOP) has produced interesting language designs, but also ad hoc semantics that needs clarification. We contribute to this clarification with a calculus that models essential AOP, both simpler and more general than existing formalizations. In AOP, advice may intercept......-oriented code. Two well-known pointcut categories, call and execution, are commonly considered similar.We formally expose their differences, and resolve the associated soundness problem. Our calculus includes type ranges, an intuitive and concise alternative to explicit type variables that allows advice...... to be polymorphic over intercepted methods. We use calculus parameters to cover type safety for a wide design space of other features. Type soundness is verified in Coq....

Can multiple-choice questions simulate free-response questions?

OpenAIRE

Lin, Shih-Yin; Singh, Chandralekha

2016-01-01

We discuss a study to evaluate the extent to which free-response questions could be approximated by multiple-choice equivalents. Two carefully designed research-based multiple-choice questions were transformed into a free-response format and administered on the final exam in a calculus-based introductory physics course. The original multiple-choice questions were administered in another similar introductory physics course on final exam. Findings suggest that carefully designed multiple-choice...

Efficient model checking for duration calculus based on branching-time approximations

DEFF Research Database (Denmark)

Fränzle, Martin; Hansen, Michael Reichhardt

2008-01-01

Duration Calculus (abbreviated to DC) is an interval-based, metric-time temporal logic designed for reasoning about embedded real-time systems at a high level of abstraction. But the complexity of model checking any decidable fragment featuring both negation and chop, DC's only modality, is non...

The Case for Infusing Quantitative Literacy into Introductory Geoscience Courses

Directory of Open Access Journals (Sweden)

Jennifer M. Wenner

2009-01-01

Full Text Available We present the case for introductory geoscience courses as model venues for increasing the quantitative literacy (QL of large numbers of the college-educated population. The geosciences provide meaningful context for a number of fundamental mathematical concepts that are revisited several times in a single course. Using some best practices from the mathematics education community surrounding problem solving, calculus reform, pre-college mathematics and five geoscience/math workshops, geoscience and mathematics faculty have identified five pedagogical ideas to increase the QL of the students who populate introductory geoscience courses. These five ideas include techniques such as: place mathematical concepts in context, use multiple representations, use technology appropriately, work in groups, and do multiple-day, in-depth problems that place quantitative skills in multiple contexts. We discuss the pedagogical underpinnings of these five ideas and illustrate some ways that the geosciences represent ideal places to use these techniques. However, the inclusion of QL in introductory courses is often met with resistance at all levels. Faculty who wish to include quantitative content must use creative means to break down barriers of public perception of geoscience as qualitative, administrative worry that enrollments will drop and faculty resistance to change. Novel ways to infuse QL into geoscience classrooms include use of web-based resources, shadow courses, setting clear expectations, and promoting quantitative geoscience to the general public. In order to help faculty increase the QL of geoscience students, a community-built faculty-centered web resource (Teaching Quantitative Skills in the Geosciences houses multiple examples that implement the five best practices of QL throughout the geoscience curriculum. We direct faculty to three portions of the web resource: Teaching Quantitative Literacy, QL activities, and the 2006 workshop website

Study Modules for Calculus-Based General Physics. [Includes Modules 6 and 7: Work and Energy; Applications of Newton's Laws].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Continuation calculus

Directory of Open Access Journals (Sweden)

Bram Geron

2013-09-01

Full Text Available Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic model of computation that is evaluated using only head reduction, and argue that it is suitable for modeling programs with control. It is demonstrated how to define programs, specify them, and prove them correct. This is shown in detail by presenting in CC a list multiplication program that prematurely returns when it encounters a zero. The correctness proof includes termination of the program. In continuation calculus we can model both call-by-name and call-by-value. In addition, call-by-name functions can be applied to call-by-value results, and conversely.

Life science students' attitudes, interest, and performance in introductory physics for life sciences: An exploratory study

Science.gov (United States)

Crouch, Catherine H.; Wisittanawat, Panchompoo; Cai, Ming; Renninger, K. Ann

2018-06-01

In response to national calls for improved physical sciences education for students pursuing careers in the life sciences and medicine, reformed introductory physics for life sciences (IPLS) courses are being developed. This exploratory study is among the first to assess the effect of an IPLS course on students' attitudes, interest, and performance. The IPLS course studied was the second semester of introductory physics, following a standard first semester course, allowing the outcomes of the same students in a standard course and in an IPLS course to be compared. In the IPLS course, each physics topic was introduced and elaborated in the context of a life science example, and developing students' skills in applying physics to life science situations was an explicitly stated course goal. Items from the Colorado Learning about Science Survey were used to assess change in students' attitudes toward and their interest in physics. Whereas the same students' attitudes declined during the standard first semester course, we found that students' attitudes toward physics hold steady or improve in the IPLS course. In particular, students with low initial interest in physics displayed greater increases in both attitudes and interest during the IPLS course than in the preceding standard course. We also find that in the IPLS course, students' interest in the life science examples is a better predictor of their performance than their pre-IPLS interest in physics. Our work suggests that the life science examples in the IPLS course can support the development of student interest in physics and positively influence their performance.

Life science students’ attitudes, interest, and performance in introductory physics for life sciences: An exploratory study

Directory of Open Access Journals (Sweden)

Catherine H. Crouch

2018-03-01

Full Text Available In response to national calls for improved physical sciences education for students pursuing careers in the life sciences and medicine, reformed introductory physics for life sciences (IPLS courses are being developed. This exploratory study is among the first to assess the effect of an IPLS course on students’ attitudes, interest, and performance. The IPLS course studied was the second semester of introductory physics, following a standard first semester course, allowing the outcomes of the same students in a standard course and in an IPLS course to be compared. In the IPLS course, each physics topic was introduced and elaborated in the context of a life science example, and developing students’ skills in applying physics to life science situations was an explicitly stated course goal. Items from the Colorado Learning about Science Survey were used to assess change in students’ attitudes toward and their interest in physics. Whereas the same students’ attitudes declined during the standard first semester course, we found that students’ attitudes toward physics hold steady or improve in the IPLS course. In particular, students with low initial interest in physics displayed greater increases in both attitudes and interest during the IPLS course than in the preceding standard course. We also find that in the IPLS course, students’ interest in the life science examples is a better predictor of their performance than their pre-IPLS interest in physics. Our work suggests that the life science examples in the IPLS course can support the development of student interest in physics and positively influence their performance.

Learning by doing at the Colorado School of Mines

Science.gov (United States)

Furtak, Thomas E.; Ruskell, Todd G.

2013-03-01

With over 260 majors, the undergraduate physics program at CSM is among the largest in the country. An underlying theme in this success is experiential learning, starting with a studio teaching method in the introductory calculus-based physics courses. After their second year students complete a 6-week full-time summer course devoted to hands-on practical knowledge and skills, including machine shop techniques, high-vacuum technology, applied optics, electronic control systems, and computational tools. This precedes a two-semester laboratory sequence that can be taught at an advanced level because of the students' experience. The required capstone senior course is a year-long open-ended challenge in which students partner with members of the faculty to work on authentic research projects, teaming with grad students or post-docs as contributing members to the department's externally funded scholarship. All of these features are important components of our B.S. degree, Engineering Physics, which is officially accredited by ABET.

Physics of the Life Sciences

CERN Document Server

Newman, Jay

2008-01-01

Originally developed for the author's course at Union College, this text is designed for life science students who need to understand the connections of fundamental physics to modern biology and medicine. Almost all areas of modern life sciences integrally involve physics in both experimental techniques and in basic understanding of structure and function. Physics of the Life Sciences is not a watered-down, algebra-based engineering physics book with sections on relevant biomedical topics added as an afterthought. This authoritative and engaging text, which is designed to be covered in a two-semester course, was written with a thoroughgoing commitment to the needs and interests of life science students. Although covering most of the standard topics in introductory physics in a more or less traditional sequence, the author gives added weight and space to concepts and applications of greater relevance to the life sciences. Students benefit from occasional sidebars using calculus to derive fundamental relations,...

THE EFFECTIVENESS OF GUIDED DISCOVERY LEARNING TO TEACH INTEGRAL CALCULUS FOR THE MATHEMATICS STUDENTS OF MATHEMATICS EDUCATION WIDYA DHARMA UNIVERSITY

Directory of Open Access Journals (Sweden)

Yuliana Yuliana

2017-01-01

Full Text Available The objectives of this research are (1 to develop Guided Discovery Learning in integral calculus subject; (2 to identify the effectiveness of Guided Discovery Learning in improving the students’ understanding toward integral calculus subject. This research was quasy experimental research with the students of even semester in Mathematics Education Widya Dharma University as the sample. Cluster Random sampling was conducted to determine control group that was taught using Conventional model and experimental group that was taught using Guided Discovery Learning model. The instruments of this research included pre-test, post-test, and student’s response questionnaire. The data of post-test was analyzed using T-test. The result was H0 was rejected for the level of significance The result of this data analysis found out that Guide Discovery Learning was more effective than Conventional Model. It was supported by the result questionnaire. The result of questionnaire that  more than 75% questionnaire items got 67.65% positive response. It means Guided Discovery Learning can increase students’ interest in joining integral calculus class.

Prepare, Do, Review: A Model Used to Reduce the Negative Feelings towards Laboratory Classes in an Introductory Chemistry Undergraduate Unit

Science.gov (United States)

Spagnoli, Dino; Wong, Lawrence; Maisey, Shannan; Clemons, Tristan D.

2017-01-01

Student feelings towards the laboratory component of an introductory chemistry unit were evaluated in an action research study, over a three-year period at the University of Western Australia. In 2013 we found that the percentage of students with negative feelings towards the laboratory increased over the duration of a semester. In 2014 we…

The Science Semester: Cross-Disciplinary Inquiry for Prospective Elementary Teachers

Science.gov (United States)

Ford, Danielle J.; Fifield, Steve; Madsen, John; Qian, Xiaoyu

2013-10-01

We describe the Science Semester, a semester-long course block that integrates three science courses and a science education methods course for elementary teacher education majors, and examine prospective elementary teachers’ developing conceptions about inquiry, science teaching efficacy, and reflections on learning through inquiry. The Science Semester was designed to provide inquiry-oriented and problem-based learning experiences, opportunities to examine socially relevant issues through cross-disciplinary perspectives, and align with content found in elementary curricula and standards. By the end of the semester, prospective elementary teachers moved from naïve to intermediate understandings of inquiry and significantly increased self-efficacy for science teaching as measured on one subscore of the STEBI-B. Reflecting on the semester, prospective teachers understood and appreciated the goals of the course and the PBL format, but struggled with the open-ended and student-directed elements of the course.

Development and Assessment of Modules to Integrate Quantitative Skills in Introductory Biology Courses.

Science.gov (United States)

Hoffman, Kathleen; Leupen, Sarah; Dowell, Kathy; Kephart, Kerrie; Leips, Jeff

2016-01-01

Redesigning undergraduate biology courses to integrate quantitative reasoning and skill development is critical to prepare students for careers in modern medicine and scientific research. In this paper, we report on the development, implementation, and assessment of stand-alone modules that integrate quantitative reasoning into introductory biology courses. Modules are designed to improve skills in quantitative numeracy, interpreting data sets using visual tools, and making inferences about biological phenomena using mathematical/statistical models. We also examine demographic/background data that predict student improvement in these skills through exposure to these modules. We carried out pre/postassessment tests across four semesters and used student interviews in one semester to examine how students at different levels approached quantitative problems. We found that students improved in all skills in most semesters, although there was variation in the degree of improvement among skills from semester to semester. One demographic variable, transfer status, stood out as a major predictor of the degree to which students improved (transfer students achieved much lower gains every semester, despite the fact that pretest scores in each focus area were similar between transfer and nontransfer students). We propose that increased exposure to quantitative skill development in biology courses is effective at building competency in quantitative reasoning. © 2016 K. Hoffman, S. Leupen, et al. CBE—Life Sciences Education © 2016 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

Measuring and Advancing Experimental Design Ability in an Introductory Course without Altering Existing Lab Curriculum

Directory of Open Access Journals (Sweden)

Ryan A. Shanks

2017-05-01

Full Text Available Introductory biology courses provide an important opportunity to prepare students for future courses, yet existing cookbook labs, although important in their own way, fail to provide many of the advantages of semester-long research experiences. Engaging, authentic research experiences aid biology students in meeting many learning goals. Therefore, overlaying a research experience onto the existing lab structure allows faculty to overcome barriers involving curricular change. Here we propose a working model for this overlay design in an introductory biology course and detail a means to conduct this lab with minimal increases in student and faculty workloads. Furthermore, we conducted exploratory factor analysis of the Experimental Design Ability Test (EDAT and uncovered two latent factors which provide valid means to assess this overlay model’s ability to increase advanced experimental design abilities. In a pre-test/post-test design, we demonstrate significant increases in both basic and advanced experimental design abilities in an experimental and comparison group. We measured significantly higher gains in advanced experimental design understanding in students in the experimental group. We believe this overlay model and EDAT factor analysis contribute a novel means to conduct and assess the effectiveness of authentic research experiences in an introductory course without major changes to the course curriculum and with minimal increases in faculty and student workloads.

Predicting Student Success in a Major's Introductory Biology Course via Logistic Regression Analysis of Scientific Reasoning Ability and Mathematics Scores

Science.gov (United States)

Thompson, E. David; Bowling, Bethany V.; Markle, Ross E.

2018-02-01

Studies over the last 30 years have considered various factors related to student success in introductory biology courses. While much of the available literature suggests that the best predictors of success in a college course are prior college grade point average (GPA) and class attendance, faculty often require a valuable predictor of success in those courses wherein the majority of students are in the first semester and have no previous record of college GPA or attendance. In this study, we evaluated the efficacy of the ACT Mathematics subject exam and Lawson's Classroom Test of Scientific Reasoning in predicting success in a major's introductory biology course. A logistic regression was utilized to determine the effectiveness of a combination of scientific reasoning (SR) scores and ACT math (ACT-M) scores to predict student success. In summary, we found that the model—with both SR and ACT-M as significant predictors—could be an effective predictor of student success and thus could potentially be useful in practical decision making for the course, such as directing students to support services at an early point in the semester.

Analysis of Errors and Misconceptions in the Learning of Calculus by Undergraduate Students

Science.gov (United States)

Muzangwa, Jonatan; Chifamba, Peter

2012-01-01

This paper is going to analyse errors and misconceptions in an undergraduate course in Calculus. The study will be based on a group of 10 BEd. Mathematics students at Great Zimbabwe University. Data is gathered through use of two exercises on Calculus 1&2.The analysis of the results from the tests showed that a majority of the errors were due…

Dental hygiene faculty calibration in the evaluation of calculus detection.

Science.gov (United States)

Garland, Kandis V; Newell, Kathleen J

2009-03-01

The purpose of this pilot study was to explore the impact of faculty calibration training on intra- and interrater reliability regarding calculus detection. After IRB approval, twelve dental hygiene faculty members were recruited from a pool of twenty-two for voluntary participation and randomized into two groups. All subjects provided two pre- and two posttest scorings of calculus deposits on each of three typodonts by recording yes or no indicating if they detected calculus. Accuracy and consistency of calculus detection were evaluated using an answer key. The experimental group received three two-hour training sessions to practice a prescribed exploring sequence and technique for calculus detection. Participants immediately corrected their answers, received feedback from the trainer, and reconciled missed areas. Intra- and interrater reliability (pre- and posttest) was determined using Cohen's Kappa and compared between groups using repeated measures (split-plot) ANOVA. The groups did not differ from pre- to posttraining (intrarater reliability p=0.64; interrater reliability p=0.20). Training had no effect on reliability levels for simulated calculus detection in this study. Recommendations for future studies of faculty calibration when evaluating students include using patients for assessing rater reliability, employing larger samples at multiple sites, and assessing the impact on students' attitudes and learning outcomes.

Miniature endoscopic optical coherence tomography for calculus detection.

Science.gov (United States)

Kao, Meng-Chun; Lin, Chun-Li; Kung, Che-Yen; Huang, Yi-Fung; Kuo, Wen-Chuan

2015-08-20

The effective treatment of periodontitis involves the detection and removal of subgingival dental calculus. However, subgingival calculus is more difficult to detect than supragingival calculus because it is firmly attached to root surfaces within periodontal pockets. To achieve a smooth root surface, clinicians often remove excessive amounts of root structure because of decreased visibility. In addition, enamel pearl, a rare type of ectopic enamel formation on the root surface, can easily be confused with dental calculus in the subgingival environment. In this study, we developed a fiber-probe swept-source optical coherence tomography (SSOCT) technique and combined it with the quantitative measurement of an optical parameter [standard deviation (SD) of the optical coherence tomography (OCT) intensity] to differentiate subgingival calculus from sound enamel, including enamel pearl. Two-dimensional circumferential images were constructed by rotating the miniprobe (0.9 mm diameter) while acquiring image lines, and the adjacent lines in each rotation were stacked to generate a three-dimensional volume. In OCT images, compared to sound enamel and enamel pearls, dental calculus showed significant differences (Pdental calculus.

The Enriched Effect Calculus: Syntax and Semantics

DEFF Research Database (Denmark)

Møgelberg, Rasmus Ejlers; Simpson, Alex; Egger, Jeff

2014-01-01

This article introduces the enriched effect calculus, which extends established type theories for computational effects with primitives from linear logic. The new calculus provides a formalism for expressing linear aspects of computational effects; e.g. the linear usage of imperative features....... The second half of the article investigates models for the enriched effect calculus, based on enriched category theory. We give several examples of such models, relating them to models of standard effect calculi (such as those based on monads), and to models of intuitionistic linear logic. We also prove...

A SAT-Based Analysis of a Calculus for Wireless Sensor Networks

DEFF Research Database (Denmark)

Wu, Xi; Nielson, Hanne Riis; Zhu, Huibiao

2015-01-01

In viewing the common unreliability problem in wireless communications, the CWQ calculus (a Calculus for Wireless sensor networks from Quality perspective) was recently proposed for modeling and reasoning about WSNs(Wireless Sensor Networks) and their applications from a quality perspective...

The BFKL pomeron calculus in the dipole approach

International Nuclear Information System (INIS)

Kozlov, M.; Levin, E.; Prygarin, A.

2007-01-01

In this paper we continue to pursue a goal of finding an effective theory for high energy interaction in QCD based on the colour dipole approach, for which the BFKL pomeron calculus gives a low energy limit. The key problem, that we try to solve in this paper is the probabilistic interpretation of the BFKL pomeron calculus in terms of the colourless dipoles and their interactions. We demonstrate that the BFKL pomeron calculus has two equivalent descriptions: (i) one is the generating functional which gives a clear probabilistic interpretation of the processes of high energy scattering and also provides a Hamiltonian-like description of the system of interacting dipoles; (ii) the second is the Langevin equation with a specific noise term which is rather complicated. We found that at high energies this Langevin equation can be reduced to the Langevin equation for directed percolation in the momentum space if the impact parameter is large, namely, b1/k, where k is the transverse momentum of a dipole. Unfortunately, this simplified form of Langevin equation is not applicable for summation of pomeron loops, where one integrates over all possible values of impact parameter. We show that the BFKL pomeron calculus with two vertices (splitting P->P+P and merging P+P->P of pomerons) can be interpreted as a system of colourless dipoles with two processes: the decay of one dipole into two and the merging of two dipoles into one dipole. However, a number of assumptions we have to make on the way to simplify the noise term in the Langevin equation and/or to apply the probabilistic interpretation, therefore, we can consider both of these approaches in the present form only as the QCD motivated models

A Transition Course from Advanced Placement to College Calculus

Science.gov (United States)

Lucas, Timothy A.; Spivey, Joseph

2011-01-01

In the Spring of 2007, a group of highly motivated mathematics graduate students conducted a review of Duke's Calculus curriculum. They focused on two main problems. The first problem is the result of a very positive trend: a growing number of students are earning AP credit for Calculus I in high school. However, this results in Calculus II…

Early Vector Calculus: A Path through Multivariable Calculus

Science.gov (United States)

Robertson, Robert L.

2013-01-01

The divergence theorem, Stokes' theorem, and Green's theorem appear near the end of calculus texts. These are important results, but many instructors struggle to reach them. We describe a pathway through a standard calculus text that allows instructors to emphasize these theorems. (Contains 2 figures.)

Enhancing the Teaching of Introductory Economics with a Team-Based, Multi-Section Competition

Science.gov (United States)

Beaudin, Laura; Berdiev, Aziz N.; Kaminaga, Allison Shwachman; Mirmirani, Sam; Tebaldi, Edinaldo

2017-01-01

The authors describe a unique approach to enhancing student learning at the introductory economics level that utilizes a multi-section, team-based competition. The competition is structured to supplement learning throughout the entire introductory course. Student teams are presented with current economic issues, trends, or events, and use economic…

Calculus detection technologies: where do we stand now?

Science.gov (United States)

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data.

Calculus detection technologies: where do we stand now?

Science.gov (United States)

Archana, V

2014-01-01

Epidemiological studies have implicated dental calculus as an ideal substrate for subgingival microbial colonization. Therefore, the main objective of periodontal therapy is to eliminate the microbial biofilm along with the calculus deposits from the root surface by root surface debridement. Over the past years, a large number of clinical and laboratory studies have been conducted to evaluate the efficacy of calculus removal by various methods. None of these conventional methods or devices was effective in completely eliminating all the calculus from the diseased root surfaces. In this context, a number of newer technologies have been developed to identify and selectively remove the dental calculus. Regarding this fact, the present article highlights a critical review of these devices based on published clinical and experimental data. PMID:25870667

Calculus

CERN Document Server

Spivak, Michael

2006-01-01

Spivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.

A fully-abstract semantics of lambda-mu in the pi-calculus

Directory of Open Access Journals (Sweden)

Steffen van Bakel

2014-09-01

Full Text Available We study the lambda-mu-calculus, extended with explicit substitution, and define a compositional output-based interpretation into a variant of the pi-calculus with pairing that preserves single-step explicit head reduction with respect to weak bisimilarity. We define four notions of weak equivalence for lambda-mu – one based on weak reduction, two modelling weak head-reduction and weak explicit head reduction (all considering terms without weak head-normal form equivalent as well, and one based on weak approximation – and show they all coincide. We will then show full abstraction results for our interpretation for the weak equivalences with respect to weak bisimilarity on processes.

Curricular Activities that Promote Metacognitive Skills Impact Lower-Performing Students in an Introductory Biology Course†

Science.gov (United States)

Dang, Nathan V.; Chiang, Jacob C.; Brown, Heather M.

2018-01-01

This study explores the impacts of repeated curricular activities designed to promote metacognitive skills development and academic achievement on students in an introductory biology course. Prior to this study, the course curriculum was enhanced with pre-assignments containing comprehension monitoring and self-evaluation questions, exam review assignments with reflective questions related to study habits, and an optional opportunity for students to explore metacognition and deep versus surface learning. We used a mixed-methods study design and collected data over two semesters. Self-evaluation, a component of metacognition, was measured via exam score postdictions, in which students estimated their exam scores after completing their exam. Metacognitive awareness was assessed using the Metacognitive Awareness Inventory (MAI) and a reflective essay designed to gauge students’ perceptions of their metacognitive skills and study habits. In both semesters, more students over-predicted their Exam 1 scores than under-predicted, and statistical tests revealed significantly lower mean exam scores for the over-predictors. By Exam 3, under-predictors still scored significantly higher on the exam, but they outnumbered the over-predictors. Lower-performing students also displayed a significant increase in exam postdiction accuracy by Exam 3. While there was no significant difference in students’ MAI scores from the beginning to the end of the semester, qualitative analysis of reflective essays indicated that students benefitted from the assignments and could articulate clear action plans to improve their learning and performance. Our findings suggest that assignments designed to promote metacognition can have an impact on students over the course of one semester and may provide the greatest benefits to lower-performing students. PMID:29904551

Curricular Activities that Promote Metacognitive Skills Impact Lower-Performing Students in an Introductory Biology Course.

Science.gov (United States)

Dang, Nathan V; Chiang, Jacob C; Brown, Heather M; McDonald, Kelly K

2018-01-01

This study explores the impacts of repeated curricular activities designed to promote metacognitive skills development and academic achievement on students in an introductory biology course. Prior to this study, the course curriculum was enhanced with pre-assignments containing comprehension monitoring and self-evaluation questions, exam review assignments with reflective questions related to study habits, and an optional opportunity for students to explore metacognition and deep versus surface learning. We used a mixed-methods study design and collected data over two semesters. Self-evaluation, a component of metacognition, was measured via exam score postdictions, in which students estimated their exam scores after completing their exam. Metacognitive awareness was assessed using the Metacognitive Awareness Inventory (MAI) and a reflective essay designed to gauge students' perceptions of their metacognitive skills and study habits. In both semesters, more students over-predicted their Exam 1 scores than under-predicted, and statistical tests revealed significantly lower mean exam scores for the over-predictors. By Exam 3, under-predictors still scored significantly higher on the exam, but they outnumbered the over-predictors. Lower-performing students also displayed a significant increase in exam postdiction accuracy by Exam 3. While there was no significant difference in students' MAI scores from the beginning to the end of the semester, qualitative analysis of reflective essays indicated that students benefitted from the assignments and could articulate clear action plans to improve their learning and performance. Our findings suggest that assignments designed to promote metacognition can have an impact on students over the course of one semester and may provide the greatest benefits to lower-performing students.

Can Free-Response Questions Be Approximated by Multiple-Choice Equivalents?

OpenAIRE

Lin, Shih-Yin; Singh, Chandralekha

2016-01-01

We discuss a study to evaluate the extent to which free-response questions can be approximated by multiple-choice equivalents. Two carefully designed research-based multiple-choice questions were transformed into a free-response format and administered on the final exam in a calculus-based introductory physics course. The original multiple-choice questions were administered in another, similar introductory physics course on the final exam. Our findings suggest that carefully designed multiple...

Towards Model Checking a Spi-Calculus Dialect

NARCIS (Netherlands)

Gnesi, S.; Latella, D.; Lenzini, Gabriele

We present a model checking framework for a spi-calculus dialect which uses a linear time temporal logic for expressing security properties. We have provided our spi-calculus dialect, called SPID, with a semantics based on labeled transition systems (LTS), where the intruder is modeled in the

A Cost-Effective Two-Part Experiment for Teaching Introductory Organic Chemistry Techniques

Science.gov (United States)

Sadek, Christopher M.; Brown, Brenna A.; Wan, Hayley

2011-01-01

This two-part laboratory experiment is designed to be a cost-effective method for teaching basic organic laboratory techniques (recrystallization, thin-layer chromatography, column chromatography, vacuum filtration, and melting point determination) to large classes of introductory organic chemistry students. Students are exposed to different…

Motivation of first semester undergraduate students

DEFF Research Database (Denmark)

Schlichter, Bjarne; Sigvardsen, Kari; Jonsson, Sofia

in the curriculum. Method - The study is based on interpretative research (Walsham, 2006; Yin, 2003) and the method chosen was a qualitative case study (Myers, 2009). The data for this study was collected through fieldwork and semi-structured interviews. The fieldwork was conducted during the autumn semester 2010...... of first semester undergraduate students. Keywords -Motivation; first year undergraduate students; Management Information Systems; teaching assistants. Paper type - Research paper....... to the processes in a company. 2) Methods for formal modeling of processes, data and occurrences. 3) An introduction to a company's information systems and the relationship of these to business strategies. In addition to the lectures and tutorials, the students have to hand in a prescribed group assignment...

Study Modules for Calculus-Based General Physics. [Includes Modules 8-10: Conservation of Energy; Impulse and Momentum; and Rotational Motion].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Command injection attacks, continuations, and the Lambek calculus

Directory of Open Access Journals (Sweden)

Hayo Thielecke

2016-06-01

Full Text Available This paper shows connections between command injection attacks, continuations, and the Lambek calculus: certain command injections, such as the tautology attack on SQL, are shown to be a form of control effect that can be typed using the Lambek calculus, generalizing the double-negation typing of continuations. Lambek's syntactic calculus is a logic with two implicational connectives taking their arguments from the left and right, respectively. These connectives describe how strings interact with their left and right contexts when building up syntactic structures. The calculus is a form of propositional logic without structural rules, and so a forerunner of substructural logics like Linear Logic and Separation Logic.

Thunks and the λ-calculus

DEFF Research Database (Denmark)

Hatcliff, John; Danvy, Olivier

1997-01-01

Thirty-five years ago, thunks were used to simulate call-by-name under call-by-value in Algol 60. Twenty years ago, Plotkin presented continuation-based simulations of call-by-name under call-by-value and vice versa in the λ-calculus. We connect all three of these classical simulations by factori......Thirty-five years ago, thunks were used to simulate call-by-name under call-by-value in Algol 60. Twenty years ago, Plotkin presented continuation-based simulations of call-by-name under call-by-value and vice versa in the λ-calculus. We connect all three of these classical simulations...

Secure Data Flow in a Calculus for Context Awareness

DEFF Research Database (Denmark)

Bucur, Doina; Nielsen, Mogens

2008-01-01

We present a Mobile-Ambients-based process calculus to describe context-aware computing in an infrastructure-based Ubiquitous Computing setting. In our calculus, computing agents can provide and discover contextual information and are owners of security policies. Simple access control to contextual...

AP calculus AB & BC crash course

CERN Document Server

Rosebush, J

2012-01-01

AP Calculus AB & BC Crash Course - Gets You a Higher Advanced Placement Score in Less Time Crash Course is perfect for the time-crunched student, the last-minute studier, or anyone who wants a refresher on the subject. AP Calculus AB & BC Crash Course gives you: Targeted, Focused Review - Study Only What You Need to Know Crash Course is based on an in-depth analysis of the AP Calculus AB & BC course description outline and actual AP test questions. It covers only the information tested on the exams, so you can make the most of your valuable study time. Written by experienced math teachers, our

Enabling students to learn: Design, implementation and assessment of a supplemental study strategies course for an introductory undergraduate biology course

Science.gov (United States)

Sriram, Jayanthi Sanjeevi

Attrition in the STEM disciplines is a national problem and one of the important reasons for this is student experiences in introductory courses. A myriad of factors influence students' experiences in those courses; inadequate student preparation is one of the most cited reasons. Incoming freshmen often lack the learning strategies required to meaningfully learn and succeed in college courses. Unfortunately, the instructors have limited time and/or have little experience in teaching learning strategies. In this paper, the design, implementation, and evaluation of a Supplemental Course (SC) model that emphasizes learning strategies is presented. SC was offered concurrently with the introductory biology courses for four consecutive semesters (fall 2011 to spring 2013); for 10 weeks in fall 2012 and 7 weeks in the other semesters at Miami University. 10 weeks SC began earlier in the semester than the shorter SC. This study evaluated the effects of the SC on students' (1) performance in the introductory biology course, (2) perceived changes in self-regulation and social support, and (3) experiences in the introductory biology course before, during, and after participation in the SC. A mixed methods approach was used to address these goals. A pre-post survey was administered to obtain students' use of self-regulation strategies and social-support data. Quantitative methods were utilized to analyze content exam grades and changes in self-regulation strategies and social-support. To explore the experiences of the students, semi-structured interviews were conducted, followed by analysis using grounded theory. The findings reveal that participants of the longer duration SC (with an earlier start date) significantly improved in content exam performance, perceived use of self-regulation strategies, and social support compared to the non-participants. Participants of the shorter duration SC (with a later start date) did not significantly improve in content exam performance

Peer Instruction in introductory physics: A method to bring about positive changes in students’ attitudes and beliefs

Directory of Open Access Journals (Sweden)

Ping Zhang

2017-01-01

Full Text Available This paper analyzes pre-post matched gains in the epistemological views of science students taking the introductory physics course at Beijing Normal University (BNU in China. In this study we examined the attitudes and beliefs of science majors (n=441 in four classes, one taught using traditional (lecture teaching methods, and the other three taught with Peer Instruction (PI. In two of the PI classes, student peer groups were constantly changing throughout the semester, while in the other PI class student groups remained fixed for the duration of the semester. The results of the pre- and post-test using the Colorado Learning Attitudes about Science Survey showed that students in traditional lecture settings became significantly more novicelike in their beliefs about physics and learning physics over the course of a semester, a result consistent with what was reported in the literature. However, all three of the classes taught using the PI method improved student attitudes and beliefs about physics and learning physics. In the PI class with fixed peer groups, students exhibited a greater positive shift in attitudes and beliefs than in the other PI class with changing peer groups. The study also looked at gender differences in student learning attitudes. Gender results revealed that female science majors in the PI classes achieved a greater positive shift in attitudes and beliefs after instruction than did male students.

Tuplix calculus

NARCIS (Netherlands)

Bergstra, J.A.; Ponse, A.; van der Zwaag, M.B.

2008-01-01

We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive

Three-plus-one formulation of Regge calculus

International Nuclear Information System (INIS)

Piran, T.; Williams, R.M.

1986-01-01

Following the work of Lund and Regge for homogeneous spaces, we construct the action for Regge calculus in its three-plus-one form for general space-times. This is achieved in two ways: a first-order formalism and a second-order formalism. We describe the Regge-calculus analogue of solving the initial-value equations using conformal transformations. The second-order formalism is used to study the time development of two simple model universes

Calculus with applications

CERN Document Server

Lax, Peter D

2014-01-01

This new edition of Lax, Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of  functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduc...

Discrete fractional calculus

CERN Document Server

Goodrich, Christopher

2015-01-01

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...

Unisex Math: Narrowing the Gender Gap.

Science.gov (United States)

Tapia, Martha; Marsh, George E., II

This study examined gender differences in attitudes toward mathematics of undergraduate students. The Attitudes Toward Mathematics Instrument (ATMI) was administered to students enrolled in introductory mathematics classes (Pre-Calculus, Calculus, and Business Calculus) at two Southeast universities, one a large state university and the other one…

Characteristics of subgingival calculus detection by multiphoton fluorescence microscopy

Science.gov (United States)

Tung, Oi-Hong; Lee, Shyh-Yuan; Lai, Yu-Lin; Chen, How-Foo

2011-06-01

Subgingival calculus has been recognized as a major cause of periodontitis, which is one of the main chronic infectious diseases of oral cavities and a principal cause of tooth loss in humans. Bacteria deposited in subgingival calculus or plaque cause gingival inflammation, function deterioration, and then periodontitis. However, subgingival calculus within the periodontal pocket is a complicated and potentially delicate structure to be detected with current dental armamentaria, namely dental x-rays and dental probes. Consequently, complete removal of subgingival calculus remains a challenge to periodontal therapies. In this study, the detection of subgingival calculus employing a multiphoton autofluorescence imaging method was characterized in comparison with a one-photon confocal fluorescence imaging technique. Feasibility of such a system was studied based on fluorescence response of gingiva, healthy teeth, and calculus with and without gingiva covered. The multiphoton fluorescence technology perceived the tissue-covered subgingival calculus that cannot be observed by the one-photon confocal fluorescence method.

Teaching assistants’ performance at identifying common introductory student difficulties in mechanics revealed by the Force Concept Inventory

Directory of Open Access Journals (Sweden)

Alexandru Maries

2016-05-01

Full Text Available The Force Concept Inventory (FCI has been widely used to assess student understanding of introductory mechanics concepts by a variety of educators and physics education researchers. One reason for this extensive use is that many of the items on the FCI have strong distractor choices which correspond to students’ alternate conceptions in mechanics. Instruction is unlikely to be effective if instructors do not know the common alternate conceptions of introductory physics students and explicitly take into account students’ initial knowledge states in their instructional design. Here, we discuss research involving the FCI to evaluate one aspect of the pedagogical content knowledge of teaching assistants (TAs: knowledge of introductory student alternate conceptions in mechanics as revealed by the FCI. For each item on the FCI, the TAs were asked to identify the most common incorrect answer choice of introductory physics students. This exercise was followed by a class discussion with the TAs related to this task, including the importance of knowing student difficulties in teaching and learning. Then, we used FCI pretest and post-test data from a large population (∼900 of introductory physics students to assess the extent to which TAs were able to identify alternate conceptions of introductory students related to force and motion. In addition, we carried out think-aloud interviews with graduate students who had more than two semesters of teaching experience in recitations to examine how they reason about the task. We find that while the TAs, on average, performed better than random guessing at identifying introductory students’ difficulties with FCI content, they did not identify many common difficulties that introductory physics students have after traditional instruction. We discuss specific alternate conceptions, the extent to which TAs are able to identify them, and results from the think-aloud interviews that provided valuable information

Using News Media Databases (LexisNexis) To Identify Relevant Topics For Introductory Earth Science Classes

Science.gov (United States)

Cervato, C.; Jach, J. Y.; Ridky, R.

2003-12-01

Introductory Earth science courses are undergoing pedagogical changes in universities across the country and are focusing more than ever on the non-science majors. Increasing enrollment of non-science majors in these introductory Earth science courses demands a new look at what is being taught and how the content can be objectively chosen. Assessing the content and effectiveness of these courses requires a quantitative investigation of introductory Earth science topics and their relevance to current issues and concerns. Relevance of Earth science topics can be linked to improved students' attitude toward science and a deeper understanding of concepts. We have used the Internet based national news search-engine LexisNexis Academic Universe (http://www.lexisnexis.org/) to select the occurrence of Earth science terms over the last 12 months, five and ten years both regionally and nationally. This database of term occurrences is being used to examine how Earth sciences have evolved in the news through the last 10 years and is also compared with textbook contents and course syllabi from randomly selected introductory earth science courses across the nation. These data constitute the quantitative foundation for this study and are being used to evaluate the relevance of introductory earth science course content. The relevance of introductory course content and current real-world issues to student attitudes is a crucial factor when considering changes in course curricula and pedagogy. We have examined students' conception of the nature of science and attitudes towards science and learning science using a Likert-scale assessment instrument in the fall 2002 Geology 100 classes at Iowa State University. A pre-test and post-test were administered to see if the students' attitudes changed during the semester using as reference a control group comprised of geoscience undergraduate and graduate students, and faculty. The results of the attitude survey have been analyzed in terms

LETTERS AND COMMENTS: Energy in one-dimensional linear waves in a string

Science.gov (United States)

Burko, Lior M.

2010-09-01

We consider the energy density and energy transfer in small amplitude, one-dimensional waves on a string and find that the common expressions used in textbooks for the introductory physics with calculus course give wrong results for some cases, including standing waves. We discuss the origin of the problem, and how it can be corrected in a way appropriate for the introductory calculus-based physics course.

The ZX-calculus is complete for stabilizer quantum mechanics

International Nuclear Information System (INIS)

Backens, Miriam

2014-01-01

The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer QM, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations. (paper)

Exploring the experiences of female students in introductory project-based engineering courses at two- and four-year institutions

Science.gov (United States)

Swan, Amy K.

2011-12-01

This qualitative study explored the experiential and contextual factors that shaped female students' pathways into introductory project-based engineering classes at two community colleges and one four-year institution, as well as female students' experiences within and outside of these classes. The study was framed by Social Cognitive Career Theory (SCCT) (Lent, Brown & Hackett, 1996) and Bronfenbrenner's (1979) ecological systems theory. Findings were based on analyses of data gathered through multiple methods: observations; individual interviews with female students; focus group interviews with project teams; and document collection. The findings of this study revealed that while positive experiences with math or science were a likely pre-cursor to engineering interest, experiential learning appeared to be a more powerful force in fostering students' engineering interest. Specifically, participants developed an interest in engineering through academic, professional, and extracurricular engineering- and design-related activities that familiarized them with the tasks and skills involved in engineering work and helped them develop a sense of selfefficacy with regard to this work. Interest and self-efficacy, in turn, played a role in students' postsecondary educational decision-making processes, as did contextual factors including families and finances. This study's findings also showed that participants' project teams were a critically important microsystem within participants' ecological environments. Within this sometimes "chilly" microsystem, female students negotiated intrateam processes, which were in some cases affected by gender norms. Intrateam processes that influenced female students' project-based learning experiences included: interpersonal dynamics; leadership; and division of labor. This study also identified several ways in which the lived experiences of participants at the community colleges were different from, or similar to, those of participants

Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus

Science.gov (United States)

Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.

2015-05-01

We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.

The dagger lambda calculus

Directory of Open Access Journals (Sweden)

Philip Atzemoglou

2014-12-01

Full Text Available We present a novel lambda calculus that casts the categorical approach to the study of quantum protocols into the rich and well established tradition of type theory. Our construction extends the linear typed lambda calculus with a linear negation of "trivialised" De Morgan duality. Reduction is realised through explicit substitution, based on a symmetric notion of binding of global scope, with rules acting on the entire typing judgement instead of on a specific subterm. Proofs of subject reduction, confluence, strong normalisation and consistency are provided, and the language is shown to be an internal language for dagger compact categories.

Superconformal tensor calculus in five dimensions

International Nuclear Information System (INIS)

Fujita, Tomoyuki; Ohashi, Keisuke

2001-01-01

We present a full superconformal tensor calculus in five spacetime dimensions in which the Weyl multiplet has 32 Bose plus 32 Fermi degrees of freedom. It is derived using dimensional reduction from the 6D superconformal tensor calculus. We present two types of 32+32 Weyl multiplets, a vector multiplet, linear multiplet, hypermultiplet and nonlinear multiplet. Their superconformal transformation laws and the embedding and invariant action formulas are given. (author)

A semester-long project-oriented biochemistry laboratory based on Helicobacter pylori urease.

Science.gov (United States)

Farnham, Kate R; Dube, Danielle H

2015-01-01

Here we present the development of a 13 week project-oriented biochemistry laboratory designed to introduce students to foundational biochemical techniques and then enable students to perform original research projects once they have mastered these techniques. In particular, we describe a semester-long laboratory that focuses on a biomedically relevant enzyme--Helicobacter pylori (Hp) urease--the activity of which is absolutely required for the gastric pathogen Hp to colonize the human stomach. Over the course of the semester, students undertake a biochemical purification of Hp urease, assess the success of their purification, and investigate the activity of their purified enzyme. In the final weeks of the semester, students design and implement their own experiments to study Hp urease. This laboratory provides students with an understanding of the importance of biochemistry in human health while empowering them to engage in an active area of research. © 2015 The International Union of Biochemistry and Molecular Biology.

Engaging Students in a Large-Enrollment Physics Class Using an Academically Focused Social Media Platform

Science.gov (United States)

Gavrin, Andy; Lindell, Rebecca

2017-03-01

There are many reasons for an instructor to consider using social media, particularly in a large introductory course. Improved communications can lessen the sense of isolation some students feel in large classes, and students may be more likely to respond to faculty announce-ments in a form that is familiar and comfortable. Furthermore, many students currently establish social media sites for their classes, without the knowledge or participation of their instructors. Such "shadow" sites can be useful, but they can also become distributors of misinformation, or venues for inappropriate or disruptive discussions. CourseNetworking (CN) is a social media platform designed for the academic environment. It combines many features common among learning management systems (LMS's) with an interface that looks and feels more like Facebook than a typical academic system. We have recently begun using CN as a means to engage students in an introductory calculus-based mechanics class, with enrollments of 150-200 students per semester. This article presents basic features of CN, and details our initial experiences and observations.

Calculus of one variable

CERN Document Server

Grossman, Stanley I

1986-01-01

Calculus of One Variable, Second Edition presents the essential topics in the study of the techniques and theorems of calculus.The book provides a comprehensive introduction to calculus. It contains examples, exercises, the history and development of calculus, and various applications. Some of the topics discussed in the text include the concept of limits, one-variable theory, the derivatives of all six trigonometric functions, exponential and logarithmic functions, and infinite series.This textbook is intended for use by college students.

Time scales: from Nabla calculus to Delta calculus and vice versa via duality

OpenAIRE

Caputo, M. Cristina

2009-01-01

In this note we show how one can obtain results from the nabla calculus from results on the delta calculus and vice versa via a duality argument. We provide applications of the main results to the calculus of variations on time scales.

The calculus lifesaver all the tools you need to excel at calculus

CERN Document Server

Banner, Adrian

2009-01-01

For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it. All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of

Factors associated with the success of first-time African American freshmen taking introductory science lecture courses at a private HBCU

Science.gov (United States)

Smith, Kendra Leigh

This study had four purposes: (1) to investigate the relationship between performance in introductory biology or introductory chemistry lecture courses and their accompanying laboratory courses, (2) to investigate the relationship between performance in introductory biology or introductory chemistry lecture courses and a student's gender, (3) to investigate the relationship between performance in introductory biology or introductory chemistry lecture courses and a student's major, and (4) to investigate the relationship between performance in introductory biology or introductory chemistry lecture courses and a student's ACT scores. The sample consisted of 195 first--time freshmen who enrolled in and completed an introductory biology or an introductory chemistry lecture and laboratory courses during the fall semesters of 2007-2012. Of the 195 students, 61 were enrolled in introductory chemistry and 134 were enrolled in introductory biology courses. Logistic regression, via the Statistical Package for the Social Sciences (SPSS), was utilized to analyze several variables as they related to success in the lecture courses. Data were extracted from the university's student information system (BANNER), and analyses were conducted on biology and chemistry separately. The dependent variable for this study was a dichotomous variable for success and nonsuccess in introductory biology or introductory chemistry lecture course. The independent variables analyzed were student's gender, major, final grade in an accompanying biology or chemistry laboratory course, and ACT test scores (composite, mathematics, and science). Results indicate that concurrent enrollment in a biology laboratory course increased the likelihood of success by 15.64 times in the lecture course. Gender was found to not be a significant predictor of success for either introductory biology or introductory chemistry lecture courses. STEM majors were 9.6 times more likely to be successful than non-STEM majors in

Study Modules for Calculus-Based General Physics. [Includes Modules 11-14: Collisions; Equilibrium of Rigid Bodies; Rotational Dynamics; and Fluid Mechanics].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Study Modules for Calculus-Based General Physics. [Includes Modules 27-30: Direct-Current Circuits; Magnetic Forces; Ampere's Law; and Faraday's Law].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules indlude study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Comparing Student Success and Understanding in Introductory Statistics under Consensus and Simulation-Based Curricula

Science.gov (United States)

Hldreth, Laura A.; Robison-Cox, Jim; Schmidt, Jade

2018-01-01

This study examines the transferability of results from previous studies of simulation-based curriculum in introductory statistics using data from 3,500 students enrolled in an introductory statistics course at Montana State University from fall 2013 through spring 2016. During this time, four different curricula, a traditional curriculum and…

On the refinement calculus

CERN Document Server

Vickers, Trevor

1992-01-01

On the Refinement Calculus gives one view of the development of the refinement calculus and its attempt to bring together - among other things - Z specifications and Dijkstra's programming language. It is an excellent source of reference material for all those seeking the background and mathematical underpinnings of the refinement calculus.

Weeded Out? Gendered Responses to Failing Calculus.

Science.gov (United States)

Sanabria, Tanya; Penner, Andrew

2017-06-01

Although women graduate from college at higher rates than men, they remain underrepresented in science, technology, engineering, and mathematics (STEM) fields. This study examines whether women react to failing a STEM weed-out course by switching to a non-STEM major and graduating with a bachelor's degree in a non-STEM field. While competitive courses designed to weed out potential STEM majors are often invoked in discussions around why students exit the STEM pipeline, relatively little is known about how women and men react to failing these courses. We use detailed individual-level data from the National Educational Longitudinal Study (NELS) Postsecondary Transcript Study (PETS): 1988-2000 to show that women who failed an introductory calculus course are substantially less likely to earn a bachelor's degree in STEM. In doing so, we provide evidence that weed-out course failure might help us to better understand why women are less likely to earn degrees.

Evaluating Two Models of Collaborative Tests in an Online Introductory Statistics Course

Science.gov (United States)

Björnsdóttir, Auðbjörg; Garfield, Joan; Everson, Michelle

2015-01-01

This study explored the use of two different types of collaborative tests in an online introductory statistics course. A study was designed and carried out to investigate three research questions: (1) What is the difference in students' learning between using consensus and non-consensus collaborative tests in the online environment?, (2) What is…

Teaching Green and Sustainable Chemistry: A Revised One-Semester Course Based on Inspirations and Challenges

Science.gov (United States)

Marteel-Parrish, Anne E.

2014-01-01

An elective course, "Toward the Greening of Our Minds": Green and Sustainable Chemistry, has been offered at Washington College since 2005. This new course without laboratory is designed for chemistry and biology majors and minors who have previously taken two semesters of general chemistry and organic chemistry. Due to the popularity of…

Applying π-Calculus to Practice

DEFF Research Database (Denmark)

Abendroth, Jorg

2003-01-01

The π-Calculus has been developed to reason about behavioural equivalence. Different notations of equivalence are defined in terms of process interactions, as well as the context of processes. There are various extensions of the π-Calculus, such as the SPI calculus, which has primitives...... modles are instantiated correctly. In this paper we will utilize the to π-Calculus reason about access control policies and mechanism. An equivalence of different policy implementations, as well as access control mechanism will be shown. Finally some experiences regarding the use of π-Calculus...

Energy in one-dimensional linear waves in a string

International Nuclear Information System (INIS)

Burko, Lior M

2010-01-01

We consider the energy density and energy transfer in small amplitude, one-dimensional waves on a string and find that the common expressions used in textbooks for the introductory physics with calculus course give wrong results for some cases, including standing waves. We discuss the origin of the problem, and how it can be corrected in a way appropriate for the introductory calculus-based physics course. (letters and comments)

Introductory speeches

International Nuclear Information System (INIS)

2001-01-01

This CD is multimedia presentation of programme safety upgrading of Bohunice V1 NPP. This chapter consist of introductory commentary and 4 introductory speeches (video records): (1) Introductory speech of Vincent Pillar, Board chairman and director general of Slovak electric, Plc. (SE); (2) Introductory speech of Stefan Schmidt, director of SE - Bohunice Nuclear power plants; (3) Introductory speech of Jan Korec, Board chairman and director general of VUJE Trnava, Inc. - Engineering, Design and Research Organisation, Trnava; Introductory speech of Dietrich Kuschel, Senior vice-president of FRAMATOME ANP Project and Engineering

A generalized nonlocal vector calculus

Science.gov (United States)

Alali, Bacim; Liu, Kuo; Gunzburger, Max

2015-10-01

A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.

White noise calculus and Fock space

CERN Document Server

Obata, Nobuaki

1994-01-01

White Noise Calculus is a distribution theory on Gaussian space, proposed by T. Hida in 1975. This approach enables us to use pointwise defined creation and annihilation operators as well as the well-established theory of nuclear space.This self-contained monograph presents, for the first time, a systematic introduction to operator theory on fock space by means of white noise calculus. The goal is a comprehensive account of general expansion theory of Fock space operators and its applications. In particular,first order differential operators, Laplacians, rotation group, Fourier transform and their interrelations are discussed in detail w.r.t. harmonic analysis on Gaussian space. The mathematical formalism used here is based on distribution theory and functional analysis , prior knowledge of white noise calculus is not required.

Multivariable calculus with applications

CERN Document Server

Lax, Peter D

2017-01-01

This text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathemat...

Calculus of variations

CERN Document Server

Elsgolc, L E; Stark, M

1961-01-01

Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency

Use of a supplementary internet based education program improves sleep literacy in college psychology students.

Science.gov (United States)

Quan, Stuart F; Anderson, Janis L; Hodge, Gordon K

2013-02-01

Knowledge regarding the importance of sleep in health and performance and good sleep hygiene practices is low, especially among adolescents and young adults. It is important to improve sleep literacy. Introductory psychology is one of the most highly enrolled courses at colleges and universities. This study tested the impact of an Internet-based learning module on improving sleep literacy in this venue. An Internet-based supplementary learning module containing sleep physiology and hygiene information was developed using content from the Harvard Medical School sleep educational website http://www.understandingsleep.org. Access to the module was provided as an extra credit activity for 2 of 4 sections (Supplemental Sleep, SS, N = 889) of an introductory college psychology course during their standard instruction on sleep and dreaming. The remaining 2 sections (Standard Instruction, SI, N = 878) only were encouraged to visit the website without further direction. Level of knowledge was assessed before and after availability to the module/website and at the end of the semester. Students were asked to complete a survey at the end of the semester inquiring whether they made any changes in their sleep behaviors. Two hundred fifty students participated in the extra credit activity and had data available at all testing points. Students in the SS Group had a significant improvement in sleep knowledge test scores after interacting with the website in comparison to the SI group (19.41 ± 3.15 vs. 17.94 ± 3.08, p students enrolled in an introductory college psychology course.

The European Project Semester at ISEP: The Challenge of Educating Global Engineers

Science.gov (United States)

Malheiro, Benedita; Silva, Manuel; Ribeiro, Maria Cristina; Guedes, Pedro; Ferreira, Paulo

2015-01-01

Current engineering education challenges require approaches that promote scientific, technical, design and complementary skills while fostering autonomy, innovation and responsibility. The European Project Semester (EPS) at Instituto Superior de Engenharia do Porto (ISEP) (EPS@ISEP) is a one semester project-based learning programme (30 European…

Assessment of student knowledge of the weak and strong nuclear forces

Science.gov (United States)

Shakya, Pramila

The purpose of this study was to determine if the use of active-learning activities to teach weak force and strong force to students enrolled in various courses at The University of Southern Mississippi, Hattiesburg campus and Gulf Park campus at different class times would increase their knowledge. There were eighty-six students that took part in this study. The study was conducted in the lab classes of an introductory astronomy survey course (AST 111), an introductory algebra-based physics course (PHY 112), and an introductory calculus-based physics course (PHY 202) during fall semester, 2014. Each class was randomly assigned as active-learning or direct instruction. A pretest followed by lecture was administered to all groups. The active-learning group performed four activities whereas the direct group watched a video irrelevant to the lesson. At the end of the lesson, the same post-test was given to all groups. Various statistical methods were used to analyze the differences in mean pretest and posttest scores. Overall, results show that the mean posttest scores were higher than the mean pretest scores. Findings support the use of active-learning activities work to the small number of students or the equal number of students in a group. The mean posttest scores of the direct instruction classes were higher than those of the active-learning groups.

Study Modules for Calculus-Based General Physics. [Includes Modules 31-34: Inductance; Wave Properties of Light; Interference; and Introduction to Quantum Physics].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is Part of a series of 41 Calculus Based Physics (CBP) modules totaling about 1,000 Pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized courses in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Evidence for calcifying nanoparticles in gingival crevicular fluid and dental calculus in periodontitis.

Science.gov (United States)

Zhang, Song-Mei; Tian, Fei; Jiang, Xin-Quan; Li, Jing; Xu, Chun; Guo, Xiao-Kui; Zhang, Fu-Qiang

2009-09-01

Calcifying nanoparticles (CNPs), also known as nanobacteria, can produce carbonate apatite on their cell walls and initiate pathologic calcification. The objective of this study was to determine whether CNPs are present in the gingival crevicular fluid (GCF) from subjects with periodontal disease and whether they can induce the pathologic calcification of primary cultured human gingival epithelial cells. GCF and dental calculus samples were collected from 10 subjects with gingivitis and 10 subjects with chronic periodontitis. CNPs in GCF and calculus filtrates were detected with nanocapture enzyme-linked immunosorbent assay kits. The CNPs in cultures of dental calculus filtrates were also identified using immunofluorescence staining, transmission electron microscopy (TEM), and chemical analysis. Pathologic changes in the CNP-treated gingival epithelial cells were observed with TEM, alizarin red staining, and disk-scanning confocal microscopy. CNPs were found in GCF samples from two subjects with chronic periodontitis. Based on chemical analysis, the surface-associated material from CNPs isolated and cultured from calculus has a composition similar to dental calculus. The pathologic calcification of CNP-treated gingival epithelial cells was also observed. Self-replicating calcifying nanoparticles can be cultured and identified from dental calculus. This raises the issue of whether CNPs contribute to the pathogenesis of periodontitis.

Group Theory with Applications in Chemical Physics

Science.gov (United States)

Jacobs, Patrick

2005-10-01

Group Theory is an indispensable mathematical tool in many branches of chemistry and physics. This book provides a self-contained and rigorous account on the fundamentals and applications of the subject to chemical physics, assuming no prior knowledge of group theory. The first half of the book focuses on elementary topics, such as molecular and crystal symmetry, whilst the latter half is more advanced in nature. Discussions on more complex material such as space groups, projective representations, magnetic crystals and spinor bases, often omitted from introductory texts, are expertly dealt with. With the inclusion of numerous exercises and worked examples, this book will appeal to advanced undergraduates and beginning graduate students studying physical sciences and is an ideal text for use on a two-semester course. An introductory and advanced text that comprehensively covers fundamentals and applications of group theory in detail Suitable for a two-semester course with numerous worked examples and problems Includes several topics often omitted from introductory texts, such as rotation group, space groups and spinor bases

Polynomial Calculus: Rethinking the Role of Calculus in High Schools

Science.gov (United States)

Grant, Melva R.; Crombie, William; Enderson, Mary; Cobb, Nell

2016-01-01

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…

Calculus for dummies

CERN Document Server

Ryan, Mark

2014-01-01

Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable-even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the ""how"" and ""why"" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll s

Removal of artificial dental calculus by use of conventional and diamond ultrasound tips.

Directory of Open Access Journals (Sweden)

Roberto Carlos Mourão Pinho

2017-04-01

Full Text Available Introduction: Periodontal disease is considered a public health problem and may lead to serious complications as the general health of patient. The main therapeutic procedure is scaling and root planing, which can be performed by a variety of techniques and instruments Objective:The aim of the present study was to evaluate the removal of calculus, produced artificially, by using a conventional ultrasonic tip and a diamond – CVD tip. Method: The calculus was produced with artificial sawdust and glue-based cyanoacrylate and distributed in twenty areas also standardized on two plates of acrylic resin (chemical activated, holding 10 samples per plate. Standards / samples were divided by lot into two simple groups, being A (treated with conventional tip and B (treated with CVD tip. Results:The treatment in Group A, promoted an average area of 20.48 ± 4.20 mm2 free of artificial calculus which is significantly higher (p <0.05 than the area removed in Group B (15.37 ± 5.29 mm2. Conclusion:The results showed that the conventional tip presented higher results than CVD tip for efficacy in the removal of calculus.

Engineering-Based Problem Solving Strategies in AP Calculus: An Investigation into High School Student Performance on Related Rate Free-Response Problems

Science.gov (United States)

Thieken, John

2012-01-01

A sample of 127 high school Advanced Placement (AP) Calculus students from two schools was utilized to study the effects of an engineering design-based problem solving strategy on student performance with AP style Related Rate questions and changes in conceptions, beliefs, and influences. The research design followed a treatment-control multiple…

Maxima and Minima Without Calculus.

Science.gov (United States)

Birnbaum, Ian

1982-01-01

Approaches to extrema that do not require calculus are presented to help free maxima/minima problems from the confines of calculus. Many students falsely suppose that these types of problems can only be dealt with through calculus, since few, if any, noncalculus examples are usually presented. (MP)

Adapting research-based curricula at Seattle Pacific University: Results on student learning

Science.gov (United States)

Close, Eleanor; Vokos, Stamatis; Lindberg, John; Seeley, Lane

2004-05-01

Seattle Pacific University is the recent recipient of a NSF CCLI grant to improve student learning in introductory physics and calculus courses. This talk will outline the goals of this collaborative project and present some initial results on student performance. Results from research-based assessments will be presented as well as specific examples of successes and challenges from mechanics and electricity and magnetism.

The quantum probability calculus

International Nuclear Information System (INIS)

Jauch, J.M.

1976-01-01

The Wigner anomaly (1932) for the joint distribution of noncompatible observables is an indication that the classical probability calculus is not applicable for quantum probabilities. It should, therefore, be replaced by another, more general calculus, which is specifically adapted to quantal systems. In this article this calculus is exhibited and its mathematical axioms and the definitions of the basic concepts such as probability field, random variable, and expectation values are given. (B.R.H)

Paragrassmann differential calculus

International Nuclear Information System (INIS)

Filippov, A.T.; Isaev, A.P.; Kurdikov, A.V.

1993-01-01

This paper significantly extends and generalizes the paragrassmann calculus previous paper. Explicit general constructions for paragrassmann calculus with one and many vaiables are discussed. A general construction of many-variable differentiation algebras is given. Some particular examples are related to multi-parametric quantum deformation of the harmonic oscillators

Cognitive Transfer Outcomes for a Simulation-Based Introductory Statistics Curriculum

Science.gov (United States)

Backman, Matthew D.; Delmas, Robert C.; Garfield, Joan

2017-01-01

Cognitive transfer is the ability to apply learned skills and knowledge to new applications and contexts. This investigation evaluates cognitive transfer outcomes for a tertiary-level introductory statistics course using the CATALST curriculum, which exclusively used simulation-based methods to develop foundations of statistical inference. A…

An evaluation of teaching methods in the introductory physics classroom

Science.gov (United States)

Savage, Lauren Michelle Williams

The introductory physics mechanics course at the University of North Carolina at Charlotte has a history of relatively high DFW rates. In 2011, the course was redesigned from the traditional lecture format to the inverted classroom format (flipped). This format inverts the classroom by introducing material in a video assigned as homework while the instructor conducts problem solving activities and guides discussions during the regular meetings. This format focuses on student-centered learning and is more interactive and engaging. To evaluate the effectiveness of the new method, final exam data over the past 10 years was mined and the pass rates examined. A normalization condition was developed to evaluate semesters equally. The two teaching methods were compared using a grade distribution across multiple semesters. Students in the inverted class outperformed those in the traditional class: "A"s increased by 22% and "B"s increased by 38%. The final exam pass rate increased by 12% under the inverted classroom approach. The same analysis was used to compare the written and online final exam formats. Surprisingly, no students scored "A"s on the online final. However, the percent of "B"s increased by 136%. Combining documented best practices from a literature review with personal observations of student performance and attitudes from first hand classroom experience as a teaching assistant in both teaching methods, reasons are given to support the continued use of the inverted classroom approach as well as the online final. Finally, specific recommendations are given to improve the course structure where weaknesses have been identified.

[Fluorescence control of dental calculus removal].

Science.gov (United States)

Bakhmutov, D N; Gonchukov, S A; Lonkina, T V; Sukhinina, A V

2012-01-01

The main condition of periodontitis prevention is the full calculus removal from the teeth surface. This procedure should be fulfilled without harming adjacent unaffected tooth tissues. Nevertheless the problem of sensitive and precise estimating of tooth-calculus interface exists and potential risk of hard tissue damage remains. In the frames of this work it was shown that fluorescence diagnostics during calculus removal can be successfully used for precise detection of tooth-calculus interface. In so doing the simple implementation of this method free from the necessity of spectrometer using can be employed. Such a simple implementation of calculus detection set-up can be aggregated with the devices of calculus removing (as ultrasonic or laser devices).

Study Modules for Calculus-Based General Physics. [Includes Modules 18-20: Sound; Temperature, Heat, and Thermodynamics: First Law; and Kinetic Theory of Gases].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Study Modules for Calculus-Based General Physics. [Includes Modules 15-17: Gravitation; Simple Harmonic Motion; and Traveling Waves; plus a Partial Derivatives Review].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Analysis of student engagement in an online annotation system in the context of a flipped introductory physics class

Directory of Open Access Journals (Sweden)

Kelly Miller

2016-12-01

Full Text Available We discuss student participation in an online social annotation forum over two semesters of a flipped, introductory physics course at Harvard University. We find that students who engage in high-level discussion online, especially by providing answers to their peers’ questions, make more gains in conceptual understanding than students who do not. This is true regardless of students’ physics background. We find that we can steer online interaction towards more productive and engaging discussion by seeding the discussion and managing the size of the sections. Seeded sections produce higher quality annotations and a greater proportion of generative threads than unseeded sections. Larger sections produce longer threads; however, beyond a certain section size, the quality of the discussion decreases.

Reliability of recordings of subgingival calculus detected using an ultrasonic device.

Science.gov (United States)

Corraini, Priscila; López, Rodrigo

2015-04-01

To assess the intra-examiner reliability of recordings of subgingival calculus detected using an ultrasonic device, and to investigate the influence of subject-, tooth- and site-level factors on the reliability of these subgingival calculus recordings. On two occasions, within a 1-week interval, 147 adult periodontitis patients received a full-mouth clinical periodontal examination by a single trained examiner. Duplicate subgingival calculus recordings, in six sites per tooth, were obtained using an ultrasonic device for calculus detection and removal. Agreement was observed in 65 % of the 22,584 duplicate subgingival calculus recordings, ranging 45 % to 83 % according to subject. Using hierarchical modeling, disagreements in the subgingival calculus duplicate recordings were more likely in all other sites than the mid-buccal, and in sites harboring supragingival calculus. Disagreements were less likely in sites with PD ≥  4 mm and with furcation involvement  ≥  degree 2. Bleeding on probing or suppuration did not influence the reliability of subgingival calculus. At the subject-level, disagreements were less likely in patients presenting with the highest and lowest extent categories of the covariate subgingival calculus. The reliability of subgingival calculus recordings using the ultrasound technology is reasonable. The results of the present study suggest that the reliability of subgingival calculus recordings is not influenced by the presence of inflammation. Moreover, subgingival calculus can be more reliably detected using the ultrasound device at sites with higher need for periodontal therapy, i.e., sites presenting with deep pockets and premolars and molars with furcation involvement.

A Logical Process Calculus

Science.gov (United States)

Cleaveland, Rance; Luettgen, Gerald; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

This paper presents the Logical Process Calculus (LPC), a formalism that supports heterogeneous system specifications containing both operational and declarative subspecifications. Syntactically, LPC extends Milner's Calculus of Communicating Systems with operators from the alternation-free linear-time mu-calculus (LT(mu)). Semantically, LPC is equipped with a behavioral preorder that generalizes Hennessy's and DeNicola's must-testing preorder as well as LT(mu's) satisfaction relation, while being compositional for all LPC operators. From a technical point of view, the new calculus is distinguished by the inclusion of: (1) both minimal and maximal fixed-point operators and (2) an unimple-mentability predicate on process terms, which tags inconsistent specifications. The utility of LPC is demonstrated by means of an example highlighting the benefits of heterogeneous system specification.

Scale calculus and the Schroedinger equation

International Nuclear Information System (INIS)

Cresson, Jacky

2003-01-01

This paper is twofold. In a first part, we extend the classical differential calculus to continuous nondifferentiable functions by developing the notion of scale calculus. The scale calculus is based on a new approach of continuous nondifferentiable functions by constructing a one parameter family of differentiable functions f(t,ε) such that f(t,ε)→f(t) when ε goes to zero. This led to several new notions as representations: fractal functions and ε-differentiability. The basic objects of the scale calculus are left and right quantum operators and the scale operator which generalizes the classical derivative. We then discuss some algebraic properties of these operators. We define a natural bialgebra, called quantum bialgebra, associated with them. Finally, we discuss a convenient geometric object associated with our study. In a second part, we define a first quantization procedure of classical mechanics following the scale relativity theory developed by Nottale. We obtain a nonlinear Schroedinger equation via the classical Newton's equation of dynamics using the scale operator. Under special assumptions we recover the classical Schroedinger equation and we discuss the relevance of these assumptions

A Calculus for Context-Awareness

DEFF Research Database (Denmark)

Zimmer, Pascal

2005-01-01

In order to answer the challenge of pervasive computing, we propose a new process calculus, whose aim is to describe dynamic systems composed of agents able to move and react differently depending on their location. This Context-Aware Calculus features a hierarchical structure similar to mobile...... ambients, and a generic multi-agent synchronization mechanism, inspired from the join-calculus. After general ideas and introduction, we review the full calculus' syntax and semantics, as well as some motivating examples, study its expressiveness, and show how the notion of computation itself can be made...

College cafeteria snack food purchases become less healthy with each passing week of the semester.

Science.gov (United States)

Wansink, Brian; Cao, Ying; Saini, Prerna; Shimizu, Mitsuru; Just, David R

2013-07-01

Snacks, stress and parties all contribute to the weight gain – the elusive ‘Freshman 15’ – that some college-goers unfortunately experience. The present study examines how a` la carte snack choice changes on a university campus during each progressing week of the academic calendar. How a` la carte snack choices change on a university campus with each progressing week of the academic calendar was examined. The data were collected from three large cafeterias (or dining halls) on Cornell University’s campus during four semesters (Fall 2006, Spring 2007, Fall 2007 and Spring 2008), for 18 weeks in each semester. After the a` la carte snack items were divided into healthy snacks and unhealthy snacks, the percentage share for each food category was calculated. Within each semester, the unhealthy snack food choices increased consistently by 0?4% per week (b50?00418, P,0?01). Furthermore, a sharp (8 %) increase occurred in the final two weeks of the semester. In contrast, healthy snack food choices decreased by almost 4% (b520?0408, P,0?01) in the final two weeks during the fall semester. These results demonstrate an increased demand for hedonic, or unhealthy, snack foods as the college semester progresses and in particular at the very end of the semester. To counter this tendency towards unhealthy snacking, cafeterias and stores should make extra effort to promote healthy alternatives during the later weeks of the semester.

Developing Web-oriented Homework System to Assess Students’ Introductory Physics Course Performance and Compare to Paper-based Peer Homework

Directory of Open Access Journals (Sweden)

Neset DEMIRCI

2006-07-01

Full Text Available The World Wide Web influences education and our lives in many ways. Nowadays, Web-based homework has been becoming widespread practice in physics courses and some other courses as well. Although are some disputes whether this is an encouraging or risky development for student learning, there is limited research assessing the pedagogical effect of changing the medium from written, hand-graded homework to online oriented, computer-graded homework. In this study, web-oriented homework system is developed to assess students’ introductory physics course performance. Later on, these results are compared with paper-based (peer homework performance for mid enrollment physics courses. One of two identical sections of introductory physics course students received paper-based, hand graded group homework while the other received the individual web-based homework. Then two groups’ on conceptual and problem-solving performance measures are compared. No significant differences were found in students’ Force Concept Inventory (FCI test scores; however, average homework performance scores were significant that could be attributed to the homework method used in favor of paper-based peer homework group.

Inquiry-Based Learning of Transcendental Functions in Calculus

Science.gov (United States)

Ekici, Celil; Gard, Andrew

2017-01-01

In a series of group activities supplemented with independent explorations and assignments, calculus students investigate functions similar to their own derivatives. Graphical, numerical, and algebraic perspectives are suggested, leading students to develop deep intuition into elementary transcendental functions even as they lay the foundation for…

Motivation and Study Habits of College Calculus Students: Does Studying Calculus in High School Make a Difference?

Science.gov (United States)

Gibson, Megan

2013-01-01

Due in part to the growing popularity of the Advanced Placement program, an increasingly large percentage of entering college students are enrolling in calculus courses having already taken calculus in high school. Many students do not score high enough on the AP calculus examination to place out of Calculus I, and many do not take the…

Hands-On Calculus

Science.gov (United States)

Sutherland, Melissa

2006-01-01

In this paper we discuss manipulatives and hands-on investigations for Calculus involving volume, arc length, and surface area to motivate and develop formulae which can then be verified using techniques of integration. Pre-service teachers in calculus courses using these activities experience a classroom in which active learning is encouraged and…

Differential calculus and its applications

CERN Document Server

Field, Michael J

2013-01-01

Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.

The malliavin calculus and related topics

CERN Document Server

Nualart, David

1995-01-01

The Malliavin calculus (or stochastic calculus of variations) is an infinite-dimensional differential calculus on the Wiener space Originally, it was developed to prove a probabilistic proof to Hörmander's "sum of squares" theorem, but more recently it has found application in a variety of stochastic differential equation problems This monograph presents the main features of the Malliavin calculus and discusses in detail its connection with the anticipating stochastic calculus The author begins by developing analysis on the Wiener space, and then uses this to analyze the regularity of probability laws and to prove Hörmander's theorem Subsequent chapters apply the Malliavin calculus to anticipating stochastic differential equations and to studying the Markov property of solutions to stochastic differential equations with boundary conditions

The Vectorial $\\lambda$-Calculus

OpenAIRE

Arrighi, Pablo; Díaz-Caro, Alejandro; Valiron, Benoît

2013-01-01

We describe a type system for the linear-algebraic $\\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\\lambda$-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed $\\lambda$-calculus is strongly normalising and fea...

Regge calculus from discontinuous metrics

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2003-01-01

Regge calculus is considered as a particular case of the more general system where the linklengths of any two neighbouring 4-tetrahedra do not necessarily coincide on their common face. This system is treated as that one described by metric discontinuous on the faces. In the superspace of all discontinuous metrics the Regge calculus metrics form some hypersurface defined by continuity conditions. Quantum theory of the discontinuous metric system is assumed to be fixed somehow in the form of quantum measure on (the space of functionals on) the superspace. The problem of reducing this measure to the Regge hypersurface is addressed. The quantum Regge calculus measure is defined from a discontinuous metric measure by inserting the δ-function-like phase factor. The requirement that continuity conditions be imposed in a 'face-independent' way fixes this factor uniquely. The term 'face-independent' means that this factor depends only on the (hyper)plane spanned by the face, not on it's form and size. This requirement seems to be natural from the viewpoint of existence of the well-defined continuum limit maximally free of lattice artefacts

Teaching the Calculus

Science.gov (United States)

Sauerheber, Richard D.

2012-01-01

Methods of teaching the Calculus are presented in honour of Sir Isaac Newton, by discussing an extension of his original proofs and discoveries. The methods, requested by Newton to be used that reflect the historical sequence of the discovered Fundamental Theorems, allow first-time students to grasp quickly the basics of the Calculus from its…

Probabilistic Analysis of the Quality Calculus

DEFF Research Database (Denmark)

Nielson, Hanne Riis; Nielson, Flemming

2013-01-01

We consider a fragment of the Quality Calculus, previously introduced for defensive programming of software components such that it becomes natural to plan for default behaviour in case the ideal behaviour fails due to unreliable communication. This paper develops a probabilistically based trust...... analysis supporting the Quality Calculus. It uses information about the probabilities that expected input will be absent in order to determine the trustworthiness of the data used for controlling the distributed system; the main challenge is to take accord of the stochastic dependency between some...

Reggeon calculus as a low-order perturbation theory for the Pomeron

International Nuclear Information System (INIS)

DeTar, C.

1975-01-01

We review the foundations of the Gribov Reggeon calculus with an emphasis on the relationship between the energy-plane and J-plane descriptions of the diagrams of the calculus. The question of the ''large-rapidity-gap cutoff'' for the Pomeron and the problem of signature are treated in more detail than in the traditional approach to the calculus. Except for some slight differences, the main results agree with Gribov's original formulation. We advocate the use of the Reggeon calculus as a refinement on the contemporary ''two-component'' model for the Pomeron and collect some formulas useful for phenomenological applications

Dental Calculus Arrest of Dental Caries.

Science.gov (United States)

Keyes, Paul H; Rams, Thomas E

An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. These observations further document the potential protective effects of dental calculus mineralization against dental caries.

Dental Calculus Arrest of Dental Caries

Science.gov (United States)

Keyes, Paul H.; Rams, Thomas E.

2016-01-01

Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human teeth for the presence and location of dental caries, dental calculus, and dental plaque biofilms. Materials and methods A total of 1,200 teeth were preserved in 10% buffered formal saline, and viewed while moist by a single experienced examiner using a research stereomicroscope at 15-25× magnification. Representative teeth were sectioned and photographed, and their dental plaque biofilms subjected to gram-stain examination with light microscopy at 100× magnification. Results Dental calculus was observed on 1,140 (95%) of the extracted human teeth, and no dental carious lesions were found underlying dental calculus-covered surfaces on 1,139 of these teeth. However, dental calculus arrest of dental caries was found on one (0.54%) of 187 evaluated teeth that presented with unrestored proximal enamel caries. On the distal surface of a maxillary premolar tooth, dental calculus mineralization filled the outer surface cavitation of an incipient dental caries lesion. The dental calculus-covered carious lesion extended only slightly into enamel, and exhibited a brown pigmentation characteristic of inactive or arrested dental caries. In contrast, the tooth's mesial surface, without a superficial layer of dental calculus, had a large carious lesion going through enamel and deep into dentin. Conclusions These observations further document the potential protective effects of dental calculus mineralization against dental caries. PMID:27446993

Students’ understanding and application of the area under the curve concept in physics problems

Directory of Open Access Journals (Sweden)

Dong-Hai Nguyen

2011-06-01

Full Text Available This study investigates how students understand and apply the area under the curve concept and the integral-area relation in solving introductory physics problems. We interviewed 20 students in the first semester and 15 students from the same cohort in the second semester of a calculus-based physics course sequence on several problems involving the area under the curve concept. We found that only a few students could recognize that the concept of area under the curve was applicable in physics problems. Even when students could invoke the area under the curve concept, they did not necessarily understand the relationship between the process of accumulation and the area under a curve, so they failed to apply it to novel situations. We also found that when presented with several graphs, students had difficulty in selecting the graph such that the area under the graph corresponded to a given integral, although all of them could state that “the integral equaled the area under the curve.” The findings in this study are consistent with those in previous mathematics education research and research in physics education on students’ use of the area under the curve.

Pre-calculus workbook for dummies

CERN Document Server

Kuang, Yang

2011-01-01

Get the confidence and math skills you need to get started with calculus Are you preparing for calculus? This hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in the course. You'll get hundreds of valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. Pre-Calculus Workbook For Dummies is the perfect tool for anyone who wa

Stochastic calculus in physics

International Nuclear Information System (INIS)

Fox, R.F.

1987-01-01

The relationship of Ito-Stratonovich stochastic calculus to studies of weakly colored noise is explained. A functional calculus approach is used to obtain an effective Fokker-Planck equation for the weakly colored noise regime. In a smooth limit, this representation produces the Stratonovich version of the Ito-Stratonovich calculus for white noise. It also provides an approach to steady state behavior for strongly colored noise. Numerical simulation algorithms are explored, and a novel suggestion is made for efficient and accurate simulation of white noise equations

Covariant differential calculus on quantum spheres of odd dimension

International Nuclear Information System (INIS)

Welk, M.

1998-01-01

Covariant differential calculus on the quantum spheres S q 2N-1 is studied. Two classification results for covariant first order differential calculi are proved. As an important step towards a description of the noncommutative geometry of the quantum spheres, a framework of covariant differential calculus is established, including first and higher order calculi and a symmetry concept. (author)

Stochastic Pi-calculus Revisited

DEFF Research Database (Denmark)

Cardelli, Luca; Mardare, Radu Iulian

2013-01-01

We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...

Modeling an Outbreak of Anthrax

Science.gov (United States)

Sturdivant, Rod; Watts, Krista

2010-01-01

This article presents material that has been used as a classroom activity in a calculus-based probability and statistics course. The application was used in the first few lessons of this course. Students had three previous semesters of math, including calculus (single and multivariable), differential equations, and a course in mathematical…

Semester-Long Inquiry-Based Molecular Biology Laboratory: Transcriptional Regulation in Yeast

Science.gov (United States)

Oelkers, Peter M.

2017-01-01

A single semester molecular biology laboratory has been developed in which students design and execute a project examining transcriptional regulation in "Saccharomyces cerevisiae." Three weeks of planning are allocated to developing a hypothesis through literature searches and use of bioinformatics. Common experimental plans address a…

Metric regularity and subdifferential calculus

International Nuclear Information System (INIS)

Ioffe, A D

2000-01-01

The theory of metric regularity is an extension of two classical results: the Lyusternik tangent space theorem and the Graves surjection theorem. Developments in non-smooth analysis in the 1980s and 1990s paved the way for a number of far-reaching extensions of these results. It was also well understood that the phenomena behind the results are of metric origin, not connected with any linear structure. At the same time it became clear that some basic hypotheses of the subdifferential calculus are closely connected with the metric regularity of certain set-valued maps. The survey is devoted to the metric theory of metric regularity and its connection with subdifferential calculus in Banach spaces

A numerical study of the Regge calculus and smooth lattice methods on a Kasner cosmology

International Nuclear Information System (INIS)

Brewin, Leo

2015-01-01

Two lattice based methods for numerical relativity, the Regge calculus and the smooth lattice relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge calculus is of the order of 110 times slower than the smooth lattice method. (paper)

The stochastic quality calculus

DEFF Research Database (Denmark)

Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis

2014-01-01

We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated...... with the outputs and at the same time the inputs impose constraints on the waiting times. Consequently, the expected inputs may not be available when needed and therefore the calculus allows to express the absence of data.The communication delays are expressed by general distributions and the resulting semantics...

Advanced calculus

CERN Document Server

Nickerson, HK; Steenrod, NE

2011-01-01

""This book is a radical departure from all previous concepts of advanced calculus,"" declared the Bulletin of the American Mathematics Society, ""and the nature of this departure merits serious study of the book by everyone interested in undergraduate education in mathematics."" Classroom-tested in a Princeton University honors course, it offers students a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors introduce a single basic derivative in an invariant form. All other derivatives - gradient, divergent, curl,

Golden quantum oscillator and Binet–Fibonacci calculus

International Nuclear Information System (INIS)

Pashaev, Oktay K; Nalci, Sengul

2012-01-01

The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = φ and Q = −1/φ, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n → ∞ it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)

Golden quantum oscillator and Binet-Fibonacci calculus

Energy Technology Data Exchange (ETDEWEB)

Pashaev, Oktay K; Nalci, Sengul, E-mail: oktaypashaev@iyte.edu.tr [Department of Mathematics, Izmir Institute of Technology, Urla-Izmir 35430 (Turkey)

2012-01-13

The Binet formula for Fibonacci numbers is treated as a q-number and a q-operator with Golden ratio bases q = {phi} and Q = -1/{phi}, and the corresponding Fibonacci or Golden calculus is developed. A quantum harmonic oscillator for this Golden calculus is derived so that its spectrum is given only by Fibonacci numbers. The ratio of successive energy levels is found to be the Golden sequence, and for asymptotic states in the limit n {yields} {infinity} it appears as the Golden ratio. We call this oscillator the Golden oscillator. Using double Golden bosons, the Golden angular momentum and its representation in terms of Fibonacci numbers and the Golden ratio are derived. Relations of Fibonacci calculus with a q-deformed fermion oscillator and entangled N-qubit states are indicated. (paper)

Use of a Supplementary Internet Based Education Program Improves Sleep Literacy in College Psychology Students

Science.gov (United States)

Quan, Stuart F.; Anderson, Janis L.; Hodge, Gordon K.

2013-01-01

Introduction: Knowledge regarding the importance of sleep in health and performance and good sleep hygiene practices is low, especially among adolescents and young adults. It is important to improve sleep literacy. Introductory psychology is one of the most highly enrolled courses at colleges and universities. This study tested the impact of an Internet-based learning module on improving sleep literacy in this venue. Methods: An Internet-based supplementary learning module containing sleep physiology and hygiene information was developed using content from the Harvard Medical School sleep educational website http://www.understandingsleep.org. Access to the module was provided as an extra credit activity for 2 of 4 sections (Supplemental Sleep, SS, N = 889) of an introductory college psychology course during their standard instruction on sleep and dreaming. The remaining 2 sections (Standard Instruction, SI, N = 878) only were encouraged to visit the website without further direction. Level of knowledge was assessed before and after availability to the module/website and at the end of the semester. Students were asked to complete a survey at the end of the semester inquiring whether they made any changes in their sleep behaviors. Results: Two hundred fifty students participated in the extra credit activity and had data available at all testing points. Students in the SS Group had a significant improvement in sleep knowledge test scores after interacting with the website in comparison to the SI group (19.41 ± 3.15 vs. 17.94 ± 3.08, p sleep habits after participation in the extra credit sleep activity (p sleep learning module has the potential to enhance sleep literacy and change behavior among students enrolled in an introductory college psychology course. Citation: Quan SF; Anderson JL; Hodge GK. Use of a supplementary internet based education program improves sleep literacy in college psychology students. J Clin Sleep Med 2013;9(2):155-160. PMID:23372469

Noncommutative operational calculus

Directory of Open Access Journals (Sweden)

Henry E. Heatherly

1999-12-01

Full Text Available Oliver Heaviside's operational calculus was placed on a rigorous mathematical basis by Jan Mikusinski, who constructed an algebraic setting for the operational methods. In this paper, we generalize Mikusi'{n}ski's methods to solve linear ordinary differential equations in which the unknown is a matrix- or linear operator-valued function. Because these functions can be zero-divisors and do not necessarily commute, Mikusi'{n}ski's one-dimensional calculus cannot be used. The noncommuative operational calculus developed here,however, is used to solve a wide class of such equations. In addition, we provide new proofs of existence and uniqueness theorems for certain matrix- and operator valued Volterra integral and integro-differential equations. Several examples are given which demonstrate these new methods.

Duality and calculus of convex objects (theory and applications)

International Nuclear Information System (INIS)

Brinkhuis, Ya; Tikhomirov, V M

2007-01-01

A new approach to convex calculus is presented, which allows one to treat from a single point of view duality and calculus for various convex objects. This approach is based on the possibility of associating with each convex object (a convex set or a convex function) a certain convex cone without loss of information about the object. From the duality theorem for cones duality theorems for other convex objects are deduced as consequences. The theme 'Duality formulae and the calculus of convex objects' is exhausted (from a certain precisely formulated point of view). Bibliography: 5 titles.

Provability Calculus of Constructions

DEFF Research Database (Denmark)

Nyblad, Kasten

This thesis presents a type system, Provability Calculus of Constructions (PCoC) that can be used for the formalization of logic. In a theorem prover based on the system, the user can extend the prover with new inference rules in a logically consistent manner. This is done by representing PCo...

Newton Binomial Formulas in Schubert Calculus

OpenAIRE

Cordovez, Jorge; Gatto, Letterio; Santiago, Taise

2008-01-01

We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.

Fractional and multivariable calculus model building and optimization problems

CERN Document Server

Mathai, A M

2017-01-01

This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations. The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of multivariable ...

Disappearing renal calculus.

Science.gov (United States)

Cui, Helen; Thomas, Johanna; Kumar, Sunil

2013-04-10

We present a case of a renal calculus treated solely with antibiotics which has not been previously reported in the literature. A man with a 17 mm lower pole renal calculus and concurrent Escherichia coli urine infection was being worked up to undergo percutaneous nephrolithotomy. However, after a course of preoperative antibiotics the stone was no longer seen on retrograde pyelography or CT imaging.

Essential calculus with applications

CERN Document Server

Silverman, Richard A

1989-01-01

Rigorous but accessible text introduces undergraduate-level students to necessary background math, then clear coverage of differential calculus, differentiation as a tool, integral calculus, integration as a tool, and functions of several variables. Numerous problems and a supplementary section of ""Hints and Answers."" 1977 edition.

Pre-Calculus For Dummies

CERN Document Server

Kuang, Yang

2012-01-01

The fun and easy way to learn pre-calculus Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an un-intimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. With this guide's help you'll quickly and painlessly get a handle on all of the concepts - not just the number crunching - and understand how to perform all pre-calc tasks, from graphing to tackling proofs. You'll also get a new appreciation for

On Flipping the Classroom in Large First Year Calculus Courses

Science.gov (United States)

Jungic, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy

2015-01-01

Over the course of two years, 2012-2014, we have implemented a "flipping" the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of…

Retention of Statistical Concepts in a Preliminary Randomization-Based Introductory Statistics Curriculum

Science.gov (United States)

Tintle, Nathan; Topliff, Kylie; VanderStoep, Jill; Holmes, Vicki-Lynn; Swanson, Todd

2012-01-01

Previous research suggests that a randomization-based introductory statistics course may improve student learning compared to the consensus curriculum. However, it is unclear whether these gains are retained by students post-course. We compared the conceptual understanding of a cohort of students who took a randomization-based curriculum (n = 76)…

Fractional calculus phenomenology in two-dimensional plasma models

Science.gov (United States)

Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

2006-10-01

Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

Leveraging Prior Calculus Study with Embedded Review

Science.gov (United States)

Nikolov, Margaret C.; Withers, Wm. Douglas

2016-01-01

We propose a new course structure to address the needs of college students with previous calculus study but no course validations as an alternative to repeating the first year of calculus. Students are introduced directly to topics from Calculus III unpreceded by a formal review of topics from Calculus I or II, but with additional syllabus time…

Study Modules for Calculus-Based General Physics. [Includes Modules 35-37: Reflection and Refraction; Electric Fields and Potentials from Continuous Charge Distributions; and Maxwell's Predictions].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

Rethinking the Privacy Calculus: On the Role of Dispositional Factors and Affect

OpenAIRE

Kehr, Flavius; Wentzel, Daniel; Mayer, Peter

2013-01-01

Existing research on information privacy has mostly relied on the privacy calculus model which views privacy-related decision making as a rational process where individuals weigh the anticipated risks of disclosing personal data against the potential benefits. However, scholars have recently challenged two basic propositions of the privacy calculus model. First, some authors have distinguished between general and situational factors in the context of privacy calculus and have argued that ...

Projects for calculus the language of change

CERN Document Server

Stroyan, Keith D

1999-01-01

Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology.Subjects including:* Medicine* Engineering* Economics* Ecology* Physics* Biology

Generalized Gaussian Error Calculus

CERN Document Server

Grabe, Michael

2010-01-01

For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large. The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions. The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence inter...

Calculus: A Computer Oriented Presentation, Part 1 [and] Part 2.

Science.gov (United States)

Stenberg, Warren; Walker, Robert J.

Parts one and two of a one-year computer-oriented calculus course (without analytic geometry) are presented. The ideas of calculus are introduced and motivated through computer (i.e., algorithmic) concepts. An introduction to computing via algorithms and a simple flow chart language allows the book to be self-contained, except that material on…

Unification and matching in Church's Original Lambda Calculus

OpenAIRE

Hustadt, U.

1992-01-01

In current implementations of higher-order logics higher-orderunification is used to lift the resolution principle from the first-order case to the higher-order case. Higher-order matching is the core of implementations of higher-order rewriting systems and some systems for program transformation. In this paper I argue that Church's original lambda calculus, called non-forgetful lambda calculus, is an appropriate basis for higher-order matching. I provide two correct and complete algorithms f...

Modular invariance and covariant loop calculus

International Nuclear Information System (INIS)

Petersen, J.L.; Roland, K.O.; Sidenius, J.R.

1988-01-01

The covariant loop calculus provides an efficient technique for computing explicit expressions for the density on moduli space corresponding to arbitrary (bosonic string) loop diagrams. Since modular invariance is not manifest, however, we carry out a detailed comparison with known explicit two- and three-loop results derived using analytic geometry (one loop is known to be okay). We establish identity to 'high' order in some moduli and exactly in others. Agreement is found as a result of various nontrivial cancellations, in part related to number theory. We feel our results provide very strong support for the correctness of the covariant loop calculus approach. (orig.)

Dynamical Regge calculus as lattice gravity

International Nuclear Information System (INIS)

Hagura, Hiroyuki

2001-01-01

We propose a hybrid approach to lattice quantum gravity by combining simultaneously the dynamical triangulation with the Regge calculus, called the dynamical Regge calculus (DRC). In this approach lattice diffeomorphism is realized as an exact symmetry by some hybrid (k, l) moves on the simplicial lattice. Numerical study of 3D pure gravity shows that an entropy of the DRC is not exponetially bounded if we adopt the uniform measure Π i dl i . On the other hand, using the scale-invariant measure Π i dl i /l i , we can calculate observables and observe a large hysteresis between two phases that indicates the first-order nature of the phase transition

Laparoscopic Cholecystectomy in Chronic Calculus Cholecystitis

Directory of Open Access Journals (Sweden)

Prakash Sapkota

2013-12-01

Full Text Available Introduction: Laparoscopic cholecystectomy has clearly become the choice over open cholecystectomy in the treatment of hepatobiliary disease since its introduction by Mouret in 1987. This study evaluates a series of patients with chronic calculus cholecystitis who were treated with laparoscopic and open cholecystectomy and assesses the outcomes of both techniques. Objective: To evaluate the efficacy of laparoscopic vs open cholecystectomy in chronic calculus cholecystitis and establish the out-comes of this treatment modality at Lumbini Medical College and Teaching Hospital. Methods: This was a retrospective analysis over a one-year period (January 1, 2012 to December 31, 2012, per-formed by single surgeon at Lumbini Medical College and Teaching Hospital located midwest of Nepal. 166 patients underwent surgical treatment for chronic calculus cholecystitis. Patients included were only chronic calculus cholecystitis proven histopathologocally and the rest were excluded. Data was collected which included patients demographics, medical history, presentation, complications, conversion rates from laparoscopic. cholecystectomy to open cholecystectomy, operative and postoperative time. Results: Patients treated with laparoscopic cholecystectomy for chronic calculus cholecystitis had shorter operating times and length of stay compared to patients treated with open cholecystectomy for chronic calculus cholecystitis. Conversion rates were 3.54% in chronic calculus cholecystitis during the study period. Complications were also lower in patients who underwent laparoscopic cholecystectomy versus open cholecystectomy for cholelithiasis. Conclusions: Laparoscopic cholecystectomy appears to be a reliable, safe, and cost-effective treatment modality for chronic calculus cholecystitis.

[Single and combining effects of Calculus Bovis and zolpidem on inhibitive neurotransmitter of rat striatum corpora].

Science.gov (United States)

Liu, Ping; He, Xinrong; Guo, Mei

2010-04-01

To investigate the correlation effects between single or combined administration of Calculus Bovis or zolpidem and changes of inhibitive neurotransmitter in rat striatum corpora. Sampling from rat striatum corpora was carried out through microdialysis. The content of two inhibitive neurotransmitters in rat corpus striatum- glycine (Gly) and gama aminobutyric acid (GABA), was determined by HPLC, which involved pre-column derivation with orthophthaladehyde, reversed-phase gradient elution and fluorescence detection. GABA content of rat striatum corpora in Calculus Bovis group was significantly increased compared with saline group (P Calculus Boris plus zolpidem group were increased largely compared with saline group as well (P Calculus Bovis group was higher than combination group (P Calculus Bovis or zolpidem group was markedly increased compared with saline group or combination group (P Calculus Bovis group, zolpidem group and combination group. The magnitude of increase was lower in combination group than in Calculus Bovis group and Zolpidem group, suggesting that Calculus Bovis promoted encephalon inhibition is more powerful than zolpidem. The increase in two inhibitive neurotransmitters did not show reinforcing effect in combination group, suggesting that Calculus Bovis and zolpidem may compete the same receptors. Therefore, combination of Calculus Bovis containing drugs and zolpidem has no clinical significance. Calculus Bovis shouldn't as an aperture-opening drugs be used for resuscitation therapy.

A κ-symmetry calculus for superparticles

International Nuclear Information System (INIS)

Gauntlett, J.P.

1991-01-01

We develop a κ-symmetry calculus for the d=2 and d=3, N=2 massive superparticles, which enables us to construct higher order κ-invariant actions. The method relies on a reformulation of these models as supersymmetric sigma models that are invariant under local worldline superconformal transformations. We show that the κ-symmetry is embedded in the superconformal symmetry so that a calculus for the κ-symmetry is equivalent to a tensor calculus for the latter. We develop such a calculus without the introduction of a wordline supergravity multiplet. (orig.)

TASK BASED APPROACH IN WRITING ARTICLE (A Field Study: The Seventh Semester Students of PBI 2008 D of STKIP Ponorogo in Academic Year 2011/2012

Directory of Open Access Journals (Sweden)

Tintin Susilowati

2012-06-01

Full Text Available Abstrak: Menulis adalah salah satu skill dari keterampilan bahasa yang masih menjadi masalah serius  bagi mahasiswa secara umum bahkan bagi mahasiswa semester tujuh jurusan pendidikan bahasa Inggris. Berdasarkan data ditemukan bahwa banyak mahasiswa semester tujuh memiliki keterbatasan pengetahuan tentang struktur paragrap terkait dengan esensi dan proposi dalam penulisan pendahuluan, tubuh dari paragrap untuk mengembangkan ide, serta kesimpulan bahkan mereka juga masih mengalami kesulitan dalam menulis sebuah paragrap. Paragrap seharusnya telah dikuasai oleh mahasiswa semester atas. Sebagai mahasiswa semester tujuh, mereka seharusnya telah mampu untuk menghasilkan tulisan jurnalistik seperti artikel. Penulisan artikel artikel, diterapkan dalam pembelajaran di kelas  menulis. Dalam materi menulis, diuraikan melalui serangkaian kegiatan dari langkah awal sampai produk akhir secara sisematis menggunakan “Task-Based Approach”. Implementasi dari pembelajaran ini menggunakan pendekatan kualitatif. Data diambil dari hasil tulisan mahasiswa dan di analisa menggunakan skala rubrik. Dengan Task-Based Approach, mahasiswa diarahkan untuk mampu menulis artikel. Pembelajaran dilakukan berbasis tugas dengan fokus yang berbeda untuk tiap pertemuan namun tujuan akhirnya mahasiswa mampu menulis artikel secara utuh setelah melakukan  tugas-tugas yang diberikan.

Bacterial Viability within Dental Calculus: An Untrodden, Inquisitive Clinico-Patho- Microbiological Research.

Science.gov (United States)

Gupta, Swati; Jain, P K; Kumra, Madhumani; Rehani, Shweta; Mathias, Yulia; Gupta, Ramakant; Mehendiratta, Monica; Chander, Anil

2016-07-01

Chronic inflammatory periodontal diseases i.e. gingivitis and periodontitis are one of the most common afflictions faced by human beings. Dental plaque, which is a pool of pathogenic microorganisms, remains to be current mainstay in etiopathogenesis. Dental calculus, which is a mineralized product of this plaque remains ignored and is considered merely as an ash heap of minor significance. However, the intriguing array in disease etiopathogenesis bulldozed researchers to suspect the role of calculus in disease chrysalis but still the viability of bacteria inside calculus and thus its pathogenicity remains an intricacy; the answer to which lies in the Pandora's Box. The present study was undertaken to investigate the viability of bacteria within dental calculus along with their identification. Also, to classify dental calculus on the basis of mineralization and to observe the variation of viable microflora found in dental calculus with the extent of mineralization and disease severity. A total of 60 samples were obtained, by harvesting two samples of supragingival calculus from each patient having chronic inflammatory periodontal disease. These samples were divided into two groups (Group A and Group B). Samples of Group A were kept non-irradiated and samples of Group B were exposed to UV radiation. The samples were categorized into less, moderately and highly mineralized according to the force required for crushing them. All the crushed calculus samples were then divided into three parts. These were used for dark-field microscopy, gram staining and bacterial cultures. Bacterial identification of the cultures obtained was also carried out by performing various biochemical assays. The present study revealed the presence of motile spirochaetes within the samples under dark-field microscope. Gram staining revealed presence of numerous gram positive cocci and gram negative bacilli. Bacterial cultures showed growth of variety of aerobic and capnophilic microorganisms. The

An AP Calculus Classroom Amusement Park

Science.gov (United States)

Ferguson, Sarah

2016-01-01

Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.…

Motivating Calculus-Based Kinematics Instruction with Super Mario Bros

Science.gov (United States)

Nordine, Jeffrey C.

2011-09-01

High-quality physics instruction is contextualized, motivates students to learn, and represents the discipline as a way of investigating the world rather than as a collection of facts and equations. Inquiry-oriented pedagogy, such as problem-based instruction, holds great promise for both teaching physics content and representing the process of doing real science.2 A challenge for physics teachers is to find instructional contexts that are meaningful, accessible, and motivating for students. Today's students are spending a growing fraction of their lives interacting with virtual environments, and these environments—physically realistic or not—can provide valuable contexts for physics explorations3-5 and lead to thoughtful discussions about decisions that programmers make when designing virtual environments. In this article, I describe a problem-based approach to calculus-based kinematics instruction that contextualizes students' learning within the Super Mario Bros. video game—a game that is more than 20 years old, but still remarkably popular with today's high school and college students.

Learning, Retention, and Forgetting of Newton's Third Law throughout University Physics

Science.gov (United States)

Sayre, Eleanor C.; Franklin, Scott V.; Dymek, Stephanie; Clark, Jessica; Sun, Yifei

2012-01-01

We present data from a between-student study on student response to questions on Newton's third law given in two introductory calculus-based physics classes (Mechanics and Electromagnetism) at a large northeastern university. Construction of a response curve reveals subtle dynamics in student learning not capturable by pretesting and post-testing.…

On flipping the classroom in large first year calculus courses

Science.gov (United States)

Jungić, Veselin; Kaur, Harpreet; Mulholland, Jamie; Xin, Cindy

2015-05-01

Over the course of two years, 2012--2014, we have implemented a 'flipping' the classroom approach in three of our large enrolment first year calculus courses: differential and integral calculus for scientists and engineers. In this article we describe the details of our particular approach and share with the reader some experiences of both instructors and students.

Advanced calculus

CERN Document Server

Friedman, Avner

2007-01-01

This rigorous two-part treatment advances from functions of one variable to those of several variables. Intended for students who have already completed a one-year course in elementary calculus, it defers the introduction of functions of several variables for as long as possible, and adds clarity and simplicity by avoiding a mixture of heuristic and rigorous arguments.The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable functions, integration, and sequences and series of functions. The second part examines functions of several

The untyped stack calculus and Bohm's theorem

Directory of Open Access Journals (Sweden)

Alberto Carraro

2013-03-01

Full Text Available The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We present a simple extension of stack calculus which is for the stack calculus what Saurin's Lambda-mu is for lambda-mu.

Discounted Duration Calculus

DEFF Research Database (Denmark)

Ody, Heinrich; Fränzle, Martin; Hansen, Michael Reichhardt

2016-01-01

To formally reason about the temporal quality of systems discounting was introduced to CTL and LTL. However, these logic are discrete and they cannot express duration properties. In this work we introduce discounting for a variant of Duration Calculus. We prove decidability of model checking...... for a useful fragment of discounted Duration Calculus formulas on timed automata under mild assumptions. Further, we provide an extensive example to show the usefulness of the fragment....

Extended finite operator calculus as an example of algebraization of analysis

OpenAIRE

Kwasniewski, A. K.; Borak, E.

2004-01-01

A wardian calculus of sequences started almost seventy years ago constitutes the general scheme for extensions of the classical umbral operator calculus considered by many afterwards . At the same time this calculus is an example of the algebraization of the analysis here restricted to the algebra of formal series. This is a review article based on the recent first author contributions. As the survey article it is supplemented by the short indicatory glossaries of notation and terms used by p...

Development and Assessment of a Preliminary Randomization-Based Introductory Statistics Curriculum

Science.gov (United States)

Tintle, Nathan; VanderStoep, Jill; Holmes, Vicki-Lynn; Quisenberry, Brooke; Swanson, Todd

2011-01-01

The algebra-based introductory statistics course is the most popular undergraduate course in statistics. While there is a general consensus for the content of the curriculum, the recent Guidelines for Assessment and Instruction in Statistics Education (GAISE) have challenged the pedagogy of this course. Additionally, some arguments have been made…

The perturbative Regge-calculus regime of loop quantum gravity

International Nuclear Information System (INIS)

Bianchi, Eugenio; Modesto, Leonardo

2008-01-01

The relation between loop quantum gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In this paper we study a semiclassical regime of loop quantum gravity and show that it admits an effective description in terms of perturbative area-Regge-calculus. The regime of interest is identified by a class of states given by superpositions of four-valent spin networks, peaked on large spins. As a probe of the dynamics in this regime, we compute explicitly two- and three-area correlation functions at the vertex amplitude level. We find that they match with the ones computed perturbatively in area-Regge-calculus with a single 4-simplex, once a specific perturbative action and measure have been chosen in the Regge-calculus path integral. Correlations of other geometric operators and the existence of this regime for other models for the dynamics are briefly discussed

Algorithms, The λ Calculus and Programming

Indian Academy of Sciences (India)

IAS Admin

developed a model to understand ... Hence the ¸ calculus also served as an alternate model ...... Practical programming using usual languages based on .... and return values as. 'answers'. This style of programming that emerges is therefore.

How a gender gap in belonging contributes to the gender gap in physics participation

Science.gov (United States)

Stout, Jane G.; Ito, Tiffany A.; Finkelstein, Noah D.; Pollock, Steven J.

2013-01-01

A great deal of research indicates that feeling a secure sense of belonging in academic settings is critical to students' achievement. In the current work, we present data collected over multiple semesters of a calculus-based introductory physics class indicating that women feel a lower sense of belonging than men in physics. This finding is important because our data also indicate that having a strong sense of belonging in physics positively predicts the degree to which all students see the value of physics in their daily life (an outcome that predicts motivation and persistence in achievement settings) as well as performance on exams in the course. We identify one potential antecedent of women's relatively lower sense of belonging in physics, namely, negative cultural stereotypes about women's inferior ability in physics compared to men. We then discuss pedagogical strategies that might be employed to enhance women's sense of belonging in physics.

Introduction to the operational calculus

CERN Document Server

Berg, Lothar

2013-01-01

Introduction to the Operational Calculus is a translation of ""Einfuhrung in die Operatorenrechnung, Second Edition."" This book deals with Heaviside's interpretation, on the Laplace integral, and on Jan Mikusinki's fundamental work ""Operational Calculus."" Throughout the book, basic algebraic concepts appear as aids to understanding some relevant points of the subject. An important field for research in analysis is asymptotic properties. This text also discusses examples to show the potentialities in applying operational calculus that run beyond ordinary differential equations with constant

Synthesizing controllers from duration calculus

DEFF Research Database (Denmark)

Fränzle, Martin

1996-01-01

Duration Calculus is a logic for reasoning about requirements for real-time systems at a high level of abstraction from operational detail, which qualifies it as an interesting starting point for embedded controller design. Such a design activity is generally thought to aim at a control device...... the physical behaviours of which satisfy the requirements formula, i.e. the refinement relation between requirements and implementations is taken to be trajectory inclusion. Due to the abstractness of the vocabulary of Duration Calculus, trajectory inclusion between control requirements and controller designs...... for embedded controller design and exploit this fact for developing an automatic procedure for controller synthesis from specifications formalized in Duration Calculus. As far as we know, this is the first positive result concerning feasibility of automatic synthesis from dense-time Duration Calculus....

Testicular calculus: A rare case.

Science.gov (United States)

Sen, Volkan; Bozkurt, Ozan; Demır, Omer; Tuna, Burcin; Yorukoglu, Kutsal; Esen, Adil

2015-01-01

Testicular calculus is an extremely rare case with unknown etiology and pathogenesis. To our knowledge, here we report the third case of testicular calculus. A 31-year-old man was admitted to our clinic with painful solid mass in left testis. After diagnostic work-up for a possible testicular tumour, he underwent inguinal orchiectomy and histopathologic examination showed a testicular calculus. Case hypothesis: Solid testicular lesions in young adults generally correspond to testicular cancer. Differential diagnosis should be done carefully. Future implications: In young adults with painful and solid testicular mass with hyperechogenic appearance on scrotal ultrasonography, testicular calculus must be kept in mind in differential diagnosis. Further reports on this topic may let us do more clear recommendations about the etiology and treatment of this rare disease.

Study Modules for Calculus-Based General Physics. [Includes Modules 21-23: Second Law and Entropy; Coulomb's Law and the Electric Field; and Flux and Gauss' Law].

Science.gov (United States)

Fuller, Robert G., Ed.; And Others

This is part of a series of 42 Calculus Based Physics (CBP) modules totaling about 1,000 pages. The modules include study guides, practice tests, and mastery tests for a full-year individualized course in calculus-based physics based on the Personalized System of Instruction (PSI). The units are not intended to be used without outside materials;…

The stack calculus

Directory of Open Access Journals (Sweden)

Alberto Carraro

2013-03-01

Full Text Available We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without any restriction. Its type system enforces strong normalization of expressions and it is a sound and complete system for full implicational Classical Logic. We give a very simple denotational semantics which allows easy calculations of the interpretation of expressions.

Site specific mineral composition and microstructure of human supra-gingival dental calculus.

Science.gov (United States)

Hayashizaki, Junko; Ban, Seiji; Nakagaki, Haruo; Okumura, Akihiko; Yoshii, Saori; Robinson, Colin

2008-02-01

Dental calculus has been implicated in the aetiology of several periodontal conditions. Its prevention and removal are therefore desirable clinical goals. While it is known that calculus is very variable in chemical composition, crystallinity and crystallite size little is known about site specific variability within a dentition and between individuals. With this in mind, a study was undertaken to investigate the comparative site specific nature and composition of human dental supra-gingival dental calculus obtained from 66 male patients visiting for their dental check-up using fluorescent X-ray spectroscopy, X-ray diffractometry and Fourier transform infrared spectroscopy. The supra-gingival dental calculus formed on the lingual surfaces of lower anterior teeth and the buccal surfaces of upper molar teeth were classified into four types based on calcium phosphate phases present. There was significant difference in composition of the crystal phase types between lower and upper teeth (pdental calculus on anterior or molar teeth of all samples. The degree of crystallinity of dental calculus formed on the upper molar teeth was higher than that formed on the lower anterior teeth (pdental calculus formed on the lower anterior teeth were higher than on upper molar teeth (pdental supra-gingival dental calculus is related to its location in the mouth.

Quantum calculus new concepts, impulsive IVPs and BVPs, inequalities

CERN Document Server

Ahmad, Bashir; Tariboon, Jessada

2016-01-01

The main objective of this book is to extend the scope of the q-calculus based on the definition of q-derivative [Jackson (1910)] to make it applicable to dense domains. As a matter of fact, Jackson's definition of q-derivative fails to work for impulse points while this situation does not arise for impulsive equations on q-time scales as the domains consist of isolated points covering the case of consecutive points. In precise terms, we study quantum calculus on finite intervals.In the first part, we discuss the concepts of qk-derivative and qk-integral, and establish their basic properties. As applications, we study initial and boundary value problems of impulsive qk-difference equations and inclusions equipped with different kinds of boundary conditions. We also transform some classical integral inequalities and develop some new integral inequalities for convex functions in the context of qk-calculus. In the second part, we develop fractional quantum calculus in relation to a new qk-shifting operator and e...

Lacroix and the calculus

CERN Document Server

Domingues, João Caramalho

2008-01-01

Silvestre François Lacroix (Paris, 1765 - ibid., 1843) was a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral (1797-1800; 2nd ed. 1810-1819) – an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through much of the 19th century, in spite of Cauchy's reform of the subject in the 1820's. Lacroix and the Calculus is the first major study of Lacroix’s large Traité. It uses the unique and massive bibliography given by Lacroix to explore late 18th-century calculus, and the way it is reflected in Lacroix’s account. Several particular aspects are addressed in detail, including: the foundations of differential calculus, analytic and differential geometry, conceptions of the integral, and types of solutions of differential equations (singular/complete/general integrals, geometrical interpretations, and generality of arbitrary functions). Lacroix’s large Traité... was a...

A General Schema for Constructing One-Point Bases in the Lambda Calculus

DEFF Research Database (Denmark)

Goldberg, Mayer

2001-01-01

In this paper, we present a schema for constructing one-point bases for recursively enumerable sets of lambda terms. The novelty of the approach is that we make no assumptions about the terms for which the one-point basis is constructed: They need not be combinators and they may contain constants...... and free variables. The significance of the construction is twofold: In the context of the lambda calculus, it characterises one-point bases as ways of ``packaging'' sets of terms into a single term; And in the context of realistic programming languages, it implies that we can define a single procedure...

Raw beef bones as chewing items to reduce dental calculus in Beagle dogs.

Science.gov (United States)

Marx, F R; Machado, G S; Pezzali, J G; Marcolla, C S; Kessler, A M; Ahlstrøm, Ø; Trevizan, L

2016-01-01

Evaluate the effect of raw bovine cortical bone (CB) (medullary bone cross-sectioned) and marrow or epiphyseal 'spongy' bone (SB) as chew items to reduce dental calculus in adult dogs. Eight 3-year-old Beagle dogs were observed in two study periods. In the first study, the dogs each received a piece of bovine femur CB (122 ± 17 g) daily and in the second study, a piece of bovine femur SB (235 ± 27 g). The first study lasted 12 days and the second 20 days. Dental calculus was evaluated using image integration software. At the start of the studies, dental calculus covered 42.0% and 38.6% of the dental arcade areas, respectively. In study one, the chewing reduced the established dental calculus area to 27.1% (35.5% reduction) after 3 days and after 12 days the dental calculus covering was reduced to 12.3% (70.6% reduction). In study two, the dental calculus covered 16.8% (56.5% reduction) after 3 days, 7.1% (81.6% reduction) after 12 days and 4.7% (87.8% reduction) after 20 days. The CB remained largely intact after 24 h, but SB was reduced to smaller pieces and in some cases totally consumed after 24 h. No complications such as tooth fractures, pieces of bone stuck between teeth or intestinal obstructions were observed during the studies. Chewing raw bovine bones was an effective method of removing dental calculus in dogs. The SB bones removed dental calculus more efficiently in the short term. © 2016 Australian Veterinary Association.

Reading the World with Calculus

Science.gov (United States)

Verzosa, Debbie

2015-01-01

It is now increasingly recognized that mathematics is not a neutral value-free subject. Rather, mathematics can challenge students' taken-for-granted realities and promote action. This article describes two issues, namely deforestation and income inequality. These were specifically chosen because they can be related to a range of calculus concepts…

Predicting performance in a first engineering calculus course: implications for interventions

Science.gov (United States)

Hieb, Jeffrey L.; Lyle, Keith B.; Ralston, Patricia A. S.; Chariker, Julia

2015-01-01

At the University of Louisville, a large, urban institution in the south-east United States, undergraduate engineering students take their mathematics courses from the school of engineering. In the fall of their freshman year, engineering students take Engineering Analysis I, a calculus-based engineering analysis course. After the first two weeks of the semester, many students end up leaving Engineering Analysis I and moving to a mathematics intervention course. In an effort to retain more students in Engineering Analysis I, the department collaborated with university academic support services to create a summer intervention programme. Students were targeted for the summer programme based on their score on an algebra readiness exam (ARE). In a previous study, the ARE scores were found to be a significant predictor of retention and performance in Engineering Analysis I. This study continues that work, analysing data from students who entered the engineering school in the fall of 2012. The predictive validity of the ARE was verified, and a hierarchical linear regression model was created using math American College Testing (ACT) scores, ARE scores, summer intervention participation, and several metacognitive and motivational factors as measured by subscales of the Motivated Strategies for Learning Questionnaire. In the regression model, ARE score explained an additional 5.1% of the variation in exam performance in Engineering Analysis I beyond math ACT score. Students took the ARE before and after the summer interventions and scores were significantly higher following the intervention. However, intervention participants nonetheless had lower exam scores in Engineering Analysis I. The following factors related to motivation and learning strategies were found to significantly predict exam scores in Engineering Analysis I: time and study environment management, internal goal orientation, and test anxiety. The adjusted R2 for the full model was 0.42, meaning that the

CLEP calculus

CERN Document Server

Hill, Gregory

2013-01-01

Earn College Credit with REA's Test Prep for CLEP* Calculus Everything you need to pass the exam and get the college credit you deserve.Our test prep for CLEP* Calculus and the free online tools that come with it, will allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your learning style, and your current level of knowledge.Here's how it works:Diagnostic exam at the REA Study Center focuses your studyOur online diagnostic exam pinpoints your strengths and shows you exactly where you need to focus your study. Armed with this information, you

An Introductory Course: The Vector Space Theory of Matter

Science.gov (United States)

Matsen, F. A.

1972-01-01

A course for superior freshmen for both science and liberal arts majors that satisfies the freshman chemistry requirement is discussed. It has been taught for six years and utilizes the new math'' which is based on the elementary concept of a set. A syllabus for the two semesters is included. (DF)

[Does carbonate originate from carbonate-calcium crystal component of the human urinary calculus?].

Science.gov (United States)

Yuzawa, Masayuki; Nakano, Kazuhiko; Kumamaru, Takatoshi; Nukui, Akinori; Ikeda, Hitoshi; Suzuki, Kazumi; Kobayashi, Minoru; Sugaya, Yasuhiro; Morita, Tatsuo

2008-09-01

It gives important information in selecting the appropriate treatment for urolithiasis to confirm the component of urinary calculus. Presently component analysis of the urinary calculus is generally performed by infrared spectroscopy which is employed by companies providing laboratory testing services in Japan. The infrared spectroscopy determines the molecular components from the absorption spectra in consequence of atomic vibrations. It has the drawback that an accurate crystal structure cannot be analyzed compared with the X-ray diffraction method which analyzes the crystal constituent based on the diffraction of X-rays on crystal lattice. The components of the urinary calculus including carbonate are carbonate apatite and calcium carbonate such as calcite. Although the latter is reported to be very rare component in human urinary calculus, the results by infrared spectroscopy often show that calcium carbonate is included in calculus. The infrared spectroscopy can confirm the existence of carbonate but cannot determine whether carbonate is originated from carbonate apatite or calcium carbonate. Thus, it is not clear whether calcium carbonate is included in human urinary calculus component in Japan. In this study, we examined human urinary calculus including carbonate by use of X-ray structural analysis in order to elucidate the origin of carbonate in human urinary calculus. We examined 17 human calculi which were reported to contain calcium carbonate by infrared spectroscopy performed in the clinical laboratory. Fifteen calculi were obtained from urinary tract, and two were from gall bladder. The stones were analyzed by X-ray powder method after crushed finely. The reports from the clinical laboratory showed that all urinary culculi consisted of calcium carbonate and calcium phosphate, while the gallstones consisted of calcium carbonate. But the components of all urinary calculi were revealed to be carbonate apatite by X-ray diffraction. The components of

Null-strut calculus. II. Dynamics

International Nuclear Information System (INIS)

Kheyfets, A.; LaFave, N.J.; Miller, W.A.

1990-01-01

In this paper, we continue from the preceding paper to develop a fully functional Regge calculus geometrodynamic algorithm from the null-strut-calculus construction. The developments discussed include (a) the identification of the Regge calculus analogue of the constraint and evolution equations on the null-strut lattice, (b) a description of the Minkowski solid geometry for the simplicial blocks of the null-strut lattice, (c) a description of the evolution algorithm for the geometrodynamic scheme and an analysis of its consistency, and (d) a presentation of the dynamical degrees of freedom for a simplicial hypersurface and the description of an initial-value prescription. To demonstrate qualitatively this new approach to geometrodynamics, we present the most simple application of null-strut calculus that we know of---the Friedmann cosmology using the three-boundary of a 600-cell simplicial polytope to model the simplicial hypersurface

Introductory statistics for engineering experimentation

CERN Document Server

Nelson, Peter R; Coffin, Marie

2003-01-01

The Accreditation Board for Engineering and Technology (ABET) introduced a criterion starting with their 1992-1993 site visits that "Students must demonstrate a knowledge of the application of statistics to engineering problems." Since most engineering curricula are filled with requirements in their own discipline, they generally do not have time for a traditional two semesters of probability and statistics. Attempts to condense that material into a single semester often results in so much time being spent on probability that the statistics useful for designing and analyzing engineering/scientific experiments is never covered. In developing a one-semester course whose purpose was to introduce engineering/scientific students to the most useful statistical methods, this book was created to satisfy those needs. - Provides the statistical design and analysis of engineering experiments & problems - Presents a student-friendly approach through providing statistical models for advanced learning techniques - Cove...

The calculus primer

CERN Document Server

Schaaf, William L

2011-01-01

Comprehensive but concise, this introduction to differential and integral calculus covers all the topics usually included in a first course. The straightforward development places less emphasis on mathematical rigor, and the informal manner of presentation sets students at ease. Many carefully worked-out examples illuminate the text, in addition to numerous diagrams, problems, and answers.Bearing the needs of beginners constantly in mind, the treatment covers all the basic concepts of calculus: functions, derivatives, differentiation of algebraic and transcendental functions, partial different

Computing for calculus

CERN Document Server

Christensen, Mark J

1981-01-01

Computing for Calculus focuses on BASIC as the computer language used for solving calculus problems.This book discusses the input statement for numeric variables, advanced intrinsic functions, numerical estimation of limits, and linear approximations and tangents. The elementary estimation of areas, numerical and string arrays, line drawing algorithms, and bisection and secant method are also elaborated. This text likewise covers the implicit functions and differentiation, upper and lower rectangular estimates, Simpson's rule and parabolic approximation, and interpolating polynomials. Other to

Giant calculus: review and report of a case.

Science.gov (United States)

Woodmansey, Karl; Severine, Anthony; Lembariti, Bakari S

2013-01-01

Dental calculus is a common oral finding. The term giant calculus is used to describe unusually large deposits of dental calculus. Several extreme cases have been reported in the dental literature. The specific etiology of these cases remains uncertain. This paper reviews previously reported cases, and presents another extreme example of giant calculus.

Hands-on-Entropy, Energy Balance with Biological Relevance

Science.gov (United States)

Reeves, Mark

2015-03-01

Entropy changes underlie the physics that dominates biological interactions. Indeed, introductory biology courses often begin with an exploration of the qualities of water that are important to living systems. However, one idea that is not explicitly addressed in most introductory physics or biology textbooks is important contribution of the entropy in driving fundamental biological processes towards equilibrium. From diffusion to cell-membrane formation, to electrostatic binding in protein folding, to the functioning of nerve cells, entropic effects often act to counterbalance deterministic forces such as electrostatic attraction and in so doing, allow for effective molecular signaling. A small group of biology, biophysics and computer science faculty have worked together for the past five years to develop curricular modules (based on SCALEUP pedagogy). This has enabled students to create models of stochastic and deterministic processes. Our students are first-year engineering and science students in the calculus-based physics course and they are not expected to know biology beyond the high-school level. In our class, they learn to reduce complex biological processes and structures in order model them mathematically to account for both deterministic and probabilistic processes. The students test these models in simulations and in laboratory experiments that are biologically relevant such as diffusion, ionic transport, and ligand-receptor binding. Moreover, the students confront random forces and traditional forces in problems, simulations, and in laboratory exploration throughout the year-long course as they move from traditional kinematics through thermodynamics to electrostatic interactions. This talk will present a number of these exercises, with particular focus on the hands-on experiments done by the students, and will give examples of the tangible material that our students work with throughout the two-semester sequence of their course on introductory

Solitary main pancreatic ductal calculus of possible biliary origin causing acute pancreatitis.

Science.gov (United States)

Chaparala, Ramakrishna Prasad Chowdary; Patel, Rafiuddin; Guthrie, James Ahsley; Davies, Mervyn Huw; Guillou, Pierre J; Menon, Krishna V

2005-09-10

Pancreatic ductal calculi are most often associated with chronic pancreatitis. Radiological features of chronic pancreatitis are readily evident in the presence of these calculi. However, acute pancreatitis due to a solitary main pancreatic ductal calculus of biliary origin is rare. A 59-year-old man presented with a first episode of acute pancreatitis. Contrast enhanced computerized tomography (CT) scan and endoscopic retrograde cholangiopancreatography (ERCP) revealed a calculus in the main pancreatic duct in the head of the pancreas causing acute pancreatitis. There were no features suggestive of chronic pancreatitis on CT scanning. The episode acute pancreatitis was managed conservatively. ERCP extraction of the calculus failed as the stone was impacted in the main pancreatic duct resulting in severe acute pancreatitis. Once this resolved, a transduodenal exploration and extraction of the pancreatic ductal calculus was performed successfully. Crystallographic analysis revealed the composition of the calculus was different to that seen in chronic pancreatitis, but more in keeping with a calculus of biliary origin. This could be explained by migration of the biliary calculus via the common channel into the main pancreatic duct. Following the operation the patient made an uneventful recovery and was well at two-year follow up. Acute pancreatitis due to a solitary main pancreatic ductal calculus of biliary origin is rare. Failing endoscopic extraction, transduodenal exploration and extraction is a safe option after resolution of acute pancreatitis.

Calculus with vectors

CERN Document Server

Treiman, Jay S

2014-01-01

Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM. fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. All three-dimensional graphs have rotatable versions included as extra source materials and may be freely downloaded and manipulated with Maple Player; a free Maple Player App is available for the iPad on iTunes. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits, and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additio...

Interpreting Assessments of Student Learning in the Introductory Physics Classroom and Laboratory

Science.gov (United States)

Dowd, Jason Edward

Assessment is the primary means of feedback between students and instructors. However, to effectively use assessment, the ability to interpret collected information is essential. We present insights into three unique, important avenues of assessment in the physics classroom and laboratory. First, we examine students' performance on conceptual surveys. The goal of this research project is to better utilize the information collected by instructors when they administer the Force Concept Inventory (FCI) to students as a pre-test and post-test of their conceptual understanding of Newtonian mechanics. We find that ambiguities in the use of the normalized gain, g, may influence comparisons among individual classes. Therefore, we propose using stratagrams, graphical summaries of the fraction of students who exhibit "Newtonian thinking," as a clearer, more informative method of both assessing a single class and comparing performance among classes. Next, we examine students' expressions of confusion when they initially encounter new material. The goal of this research project is to better understand what such confusion actually conveys to instructors about students' performance and engagement. We investigate the relationship between students' self-assessment of their confusion over material and their performance, confidence in reasoning, pre-course self-efficacy and several other measurable characteristics of engagement. We find that students' expressions of confusion are negatively related to initial performance, confidence and self-efficacy, but positively related to final performance when all factors are considered together. Finally, we examine students' exhibition of scientific reasoning abilities in the instructional laboratory. The goal of this research project is to explore two inquiry-based curricula, each of which proposes a different degree of scaffolding. Students engage in sequences of these laboratory activities during one semester of an introductory physics

Particular case of operator calculus for generalized functions with supports in cone

Directory of Open Access Journals (Sweden)

A. V. Solomko

2009-06-01

Full Text Available In this work the construction of functional calculus for strongly continuous semigroups of operators in Schwartz distribution algebra on some cone is generalized. The partial case of vector valued calculus on the base of modification operator Fourier transformation is researched.

Sleep and Final Exam Performance in Introductory Physics

Science.gov (United States)

Coletta, Vincent; Wikholm, Colin; Pascoe, Daniel

2018-03-01

Most physics instructors believe that adequate sleep is important in order for students to perform well on problem solving, and many instructors advise students to get plenty of sleep the night before an exam. After years of giving such advice to students at Loyola Marymount University (LMU), one of us decided to find out how many hours students actually do sleep the night before an exam, and how that would relate to their performance. The effect of inadequate sleep on exam performance was explored in a second-semester introductory physics course. At the end of the final exam, students reported the number of hours they slept the night before. Sleep deprivation corresponded to lower final exam scores. The main purpose of this study is to provide evidence that instructors can provide to their students to convince them that their time is better spent sleeping rather than studying all night before an exam.

Stochastic Model Checking of the Stochastic Quality Calculus

DEFF Research Database (Denmark)

Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin

2015-01-01

The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for input....... This gives rise to Generalised Semi-Markov Decision Processes for which few analytical techniques are available. We restrict delays on output actions to be exponentially distributed while still admitting real-time constraints on the quality binders. This facilitates developing analytical techniques based...

A Semester-Long Project-Oriented Biochemistry Laboratory Based on "Helicobacter pylori" Urease

Science.gov (United States)

Farnham, Kate R.; Dube, Danielle H.

2015-01-01

Here we present the development of a 13 week project-oriented biochemistry laboratory designed to introduce students to foundational biochemical techniques and then enable students to perform original research projects once they have mastered these techniques. In particular, we describe a semester-long laboratory that focuses on a biomedically…

On Some Syntactic Properties of the Modalized Heyting Calculus

OpenAIRE

Muravitsky, Alexei

2016-01-01

We show that the modalized Heyting calculus introduced by Leo Esakia admits a normal axiomatization. Then, we prove that the inference rules $\\square\\alpha/\\alpha$ and $\\square\\alpha\\rightarrow\\alpha/\\alpha$ are admissible in this calculus. Finally, we show that this calculus and intuitionistic propositional calculus are assertorically equipollent, which leads to a variant of limited separation property for the modalized Heyting calculus.

Case Study: Students’ Symbolic Manipulation in Calculus Among UTHM Students

Science.gov (United States)

Ali, Maselan; Sufahani, Suliadi; Ahmad, Wan N. A. W.; Ghazali Kamardan, M.; Saifullah Rusiman, Mohd; Che-Him, Norziha

2018-04-01

Words are symbols representing certain aspects of mathematics. The main purpose of this study is to gain insight into students’ symbolic manipulation in calculus among UTHM students. This study make use the various methods in collecting data which are documentation, pilot study, written test and follow up individual interviews. Hence, the results analyzed and interpreted based on action-process-object-schema framework which is based on Piaget’s ideas of reflective abstraction, the concept of relational and instrumental understanding and the zone of proximal development idea. The students’ reply in the interview session is analyzed and then the overall performance is discussed briefly to relate with the students flexibility in symbolic manipulation in linking to the graphical idea, the students interpretation towards different symbolic structure in calculus and the problem that related to overgeneralization in their calculus problems solving.

The calculus a genetic approach

CERN Document Server

Toeplitz, Otto

2007-01-01

When first published posthumously in 1963, this book presented a radically different approach to the teaching of calculus.  In sharp contrast to the methods of his time, Otto Toeplitz did not teach calculus as a static system of techniques and facts to be memorized. Instead, he drew on his knowledge of the history of mathematics and presented calculus as an organic evolution of ideas beginning with the discoveries of Greek scholars, such as Archimedes, Pythagoras, and Euclid, and developing through the centuries in the work of Kepler, Galileo, Fermat, Newton, and Leibniz. Through this unique a

Pre-calculus workbook for dummies

CERN Document Server

Gilman, Michelle Rose; Neal, Karina

2009-01-01

Get the confidence and the math skills you need to get started with calculus! Are you preparing for calculus? This easy-to-follow, hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in your cour sework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. 100s of Problems! Detailed, fully worked-out solutions to problem

On exterior variational calculus

International Nuclear Information System (INIS)

Aldrovandi, R.; Kraenkel, R.A.

1987-01-01

Exterior variational calculus is introduced through examples in field theory. It provides a very simple technique to decide on the existence of Lagrangians for given equations of motions and, in the case, to find them. Only local aspects are discussed but the analogy to exterior calculus on finite dimensional manifolds is complete, strongly suggesting its suitability to the study of topological aspects. (Author) [pt

ASSESSING STUDENTS' UNDERSTANDING OF PRE-CALCULUS CONCEPTS

OpenAIRE

Dr. Jyoti Sharma

2017-01-01

Calculus is one of the most momentous achievements of the human intellect (Boyer, 1949). It has given a new direction to the work of mathematicians and scientists. Calculus has exponentially expanded the scope and use of mathematics in other fields. Learning calculus is important to pursue career in applied mathematics.

Stochastic calculus an introduction through theory and exercises

CERN Document Server

Baldi, Paolo

2017-01-01

This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions. After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical ...

Generalized calculus with applications to matter and forces

CERN Document Server

Campos, L M B C

2014-01-01

Combining mathematical theory, physical principles, and engineering problems, Generalized Calculus with Applications to Matter and Forces examines generalized functions, including the Heaviside unit jump and the Dirac unit impulse and its derivatives of all orders, in one and several dimensions. The text introduces the two main approaches to generalized functions: (1) as a nonuniform limit of a family of ordinary functions, and (2) as a functional over a set of test functions from which properties are inherited. The second approach is developed more extensively to encompass multidimensional generalized functions whose arguments are ordinary functions of several variables. As part of a series of books for engineers and scientists exploring advanced mathematics, Generalized Calculus with Applications to Matter and Forces presents generalized functions from an applied point of view, tackling problem classes such as: •Gauss and Stokes’ theorems in the differential geometry, tensor calculus, and theory of ...

Dental Calculus Arrest of Dental Caries

OpenAIRE

Keyes, Paul H.; Rams, Thomas E.

2016-01-01

Background An inverse relationship between dental calculus mineralization and dental caries demineralization on teeth has been noted in some studies. Dental calculus may even form superficial layers over existing dental caries and arrest their progression, but this phenomenon has been only rarely documented and infrequently considered in the field of Cariology. To further assess the occurrence of dental calculus arrest of dental caries, this study evaluated a large number of extracted human t...

Graph theory and its applications

CERN Document Server

Gross, Jonathan L

2006-01-01

Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.

Linking First-Year and Senior Engineering Design Teams: Engaging Early Academic Career Students in Engineering Design

Science.gov (United States)

Fox, Garey A.; Weckler, Paul; Thomas, Dan

2015-01-01

In Biosystems Engineering at Oklahoma State University, senior design is a two semester course in which students work on real-world projects provided by clients. First-year (freshmen and trans­fer) students enroll in an introductory engineering course. Historically, these students worked on a team-based analysis project, and the engineering design…

Functional Fractional Calculus

CERN Document Server

Das, Shantanu

2011-01-01

When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with 'ordinary' differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematic

Cadmium Profiles in Dental Calculus: a Cross-Sectional Population-Based Study in Hunan Province of China.

Science.gov (United States)

Zhang, Bo; Tan, Xiaodan; Zhang, Kunlun

2018-01-24

We aimed to investigate whether the cadmium concentrations differ in human dental calculus obtained from the residents with no smoking living in the contaminated area and those with no smoking living in noncontaminated area. In total, there were 260 samples of dental calculus from the adults (n = 50) with no smoking living in contaminated area, the adults (n = 60) with no smoking living in mountainous area, and the adults (n = 150) with no smoking living in low altitude area in Hunan province of China. All samples were analyzed by inductively coupled plasma mass spectrometry (ICP-MS) for cadmium levels. The cadmium levels in dental calculus were significantly higher in the adults with no smoking living in contaminated area than those living in mountainous area and in low altitude area (p dental calculus were also higher in the adults with no smoking living in low altitude area than those living in mountainous region (p dental calculus may be a useful noninvasive method for analysis of environmental exposure to cadmium in the human oral cavity. The low altitude region may have an area contaminated with cadmium in Hunan province of China.

Online Calculus: The Course and Survey Results.

Science.gov (United States)

Allen, G. Donald

2001-01-01

Describes the development and implementation of a Web-based calculus course at Texas A & M University. Discusses the course design, layout of content and the contrast with textbook structure, results of course surveys that included student reactions, and how students learn form Web-based materials. (Author/LRW)

The Initial Conditions of Fractional Calculus

International Nuclear Information System (INIS)

Trigeassou, J. C.; Maamri, N.

2011-01-01

During the past fifty years , Fractional Calculus has become an original and renowned mathematical tool for the modelling of diffusion Partial Differential Equations and the design of robust control algorithms. However, in spite of these celebrated results, some theoretical problems have not yet received a satisfying solution. The mastery of initial conditions, either for Fractional Differential Equations (FDEs) or for the Caputo and Riemann-Liouville fractional derivatives, remains an open research domain. The solution of this fundamental problem, also related to the long range memory property, is certainly the necessary prerequisite for a satisfying approach to modelling and control applications. The fractional integrator and its continuously frequency distributed differential model is a valuable tool for the simulation of fractional systems and the solution of initial condition problems. Indeed, the infinite dimensional state vector of fractional integrators allows the direct generalization to fractional calculus of the theoretical results of integer order systems. After a reminder of definitions and properties related to fractional derivatives and systems, this presentation is intended to show, based on the results of two recent publications [1,2], how the fractional integrator provides the solution of the initial condition problem of FDEs and of Caputo and Riemann-Liouville fractional derivatives. Numerical simulation examples illustrate and validate these new theoretical concepts.

A primer on exterior differential calculus

Directory of Open Access Journals (Sweden)

Burton D.A.

2003-01-01

Full Text Available A pedagogical application-oriented introduction to the cal­culus of exterior differential forms on differential manifolds is presented. Stokes' theorem, the Lie derivative, linear con­nections and their curvature, torsion and non-metricity are discussed. Numerous examples using differential calculus are given and some detailed comparisons are made with their tradi­tional vector counterparts. In particular, vector calculus on R3 is cast in terms of exterior calculus and the traditional Stokes' and divergence theorems replaced by the more powerful exterior expression of Stokes' theorem. Examples from classical continuum mechanics and spacetime physics are discussed and worked through using the language of exterior forms. The numerous advantages of this calculus, over more traditional ma­chinery, are stressed throughout the article. .

Model-checking dense-time Duration Calculus

DEFF Research Database (Denmark)

Fränzle, Martin

2004-01-01