Kolman, Bernard
1985-01-01
College Algebra, Second Edition is a comprehensive presentation of the fundamental concepts and techniques of algebra. The book incorporates some improvements from the previous edition to provide a better learning experience. It provides sufficient materials for use in the study of college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, exponential and logarithmic functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter c
Herriott, Scott R.; Dunbar, Steven R.
2009-01-01
The common understanding within the mathematics community is that the role of the college algebra course is to prepare students for calculus. Though exceptions are emerging, the curriculum of most college algebra courses and the content of most textbooks on the market both reflect that assumption. This article calls that assumption into question…
Hegedus, Stephen J.; Dalton, Sara; Tapper, John R.
2015-01-01
We report on two large studies conducted in advanced algebra classrooms in the US, which evaluated the effect of replacing traditional algebra 2 curriculum with an integrated suite of dynamic interactive software, wireless networks and technology-enhanced curriculum on student learning. The first study was a cluster randomized trial and the second…
Hegedus, Stephen J.; Dalton, Sara; Tapper, John R.
2015-01-01
We report on two large studies conducted in advanced algebra classrooms in the US, which evaluated the effect of replacing traditional algebra 2 curriculum with an integrated suite of dynamic interactive software, wireless networks and technology-enhanced curriculum on student learning. The first study was a cluster randomized trial and the second…
Mayes, Robert
2004-01-01
There is a call for change in College Algebra. The traditional focus on skill development is failing, resulting in withdrawal and failure rates that are excessive. In addition, too many students who are successful do not continue on to take a successive mathematics course. The Institute for Mathematics Learning at West Virginia University has been…
What's Wrong with College Algebra?
Gordon, Sheldon P.
2008-01-01
Most college algebra courses are offered in the spirit of preparing the students to move on toward calculus. In reality, only a vanishingly small fraction of the million students a year who take these courses ever get to calculus. This article builds a strong case for the need to change the focus in college algebra to one that better meets the…
Study guide for college algebra
Snow, James W; Shapiro, Arnold
1981-01-01
Study Guide for College Algebra is a supplemental material for the basic text, College Algebra. Its purpose is to make the learning of college algebra and trigonometry easier and enjoyable.The book provides detailed solutions to exercises found in the text. Students are encouraged to use the study guide as a learning tool during the duration of the course, a reviewer prior to an exam, a reference book, and as a quick overview before studying a section of the text. The Study Guide and Solutions Manual consists of four major components: basic concepts that should be learned from each unit, what
Kolman, Bernard; Levitan, Michael L
1985-01-01
Test Bank for College Algebra, Second Edition is a supplementary material for the text, College Algebra, Second Edition. The book is intended for use by mathematics teachers.The book contains standard tests for each chapter in the textbook. Each set of test aims to evaluate the level of understanding the student has achieved during the course. The answers for each chapter test and the final exam are found at the end of the book.Mathematics teachers teaching college algebra will find the book very useful.
Implementing Change in College Algebra
Haver, William E.
2007-01-01
In this paper, departments are urged to consider implementing the type of changes proposed in Beyond Crossroads in College Algebra. The author of this paper is chair of the Curriculum Renewal Across the First Two Years (CRAFTY) Committee of the Mathematical Association of America. The committee has members from two-year colleges, four-year…
Adventures in Flipping College Algebra
Van Sickle, Jenna
2015-01-01
This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…
REA, Editors of
2012-01-01
REA … Real review, Real practice, Real results. An easier path to a college degree - get college credits without the classes. CLEP COLLEGE ALGEBRABased on today's official CLEP exam Are you prepared to excel on the CLEP? * Take the first practice test to discover what you know and what you should know* Set up a flexible study schedule by following our easy timeline* Use REA's advice to ready yourself for proper study and success Study what you need to know to pass the exam * The book's on-target subject review features coverage of all topics on the official CLEP exam, including polyno
Success in Algebra among Community College Students
Reyes, Czarina
2010-01-01
College algebra is a required course for most majors, but is viewed by many as a gatekeeper course for degree completion by students. With almost half a million students taking college algebra each year, faculty are experimenting with new course lengths of time that might result in higher success, completion, and retention rates for college…
Learning and teaching college algebra: challenges and ...
African Journals Online (AJOL)
nokello
Learning and Teaching College Algebra at University level: Challenges and ... students had difficulty in mathematics and gave varied reasons why this was the .... method has been applied in other universities with increased success rate (4).
College Algebra and the Math Laboratory.
Rotman, Jack W.
This study reviews literature related to innovative approaches to the teaching of college algebra, and describes the approach to such a course at Lansing (Michigan) Community College. Recommendations concerning that course are presented, based on the experiences of other schools as described in the literature, and analysis of the Lansing…
Study guide for college algebra and trigonometry
Snow, James W; Shapiro, Arnold
1981-01-01
Study Guide for College Algebra and Trigonometry is a supplement material to the basic text, College Algebra and Trigonometry. It is written to assist the student in learning mathematics effectively.The book provides detailed solutions to exercises found in the text. Students are encouraged to use these solutions to find a way to approach a problem. The Study Guide and Solutions Manual consists of four major components: basic concepts that should be learned from each unit, what was learned upon completion of each unit, solutions to selected problems, and a short chapter quiz, including the ans
College Algebra in Context: A Project Incorporating Social Issues
Michael T. Catalano
2010-01-01
This paper discusses the development of an innovative college algebra text designed for use in a data-driven, activity-oriented college algebra course, incorporating realistic problem situations emphasizing social and economic issues, including hunger and poverty, energy, and the environment. The course incorporates quantitative literacy themes, is informed by existing college algebra texts within the college algebra reform movement, and implements a collaborative pedagogical approach intende...
Should College Algebra be a Prerequisite for Taking Psychology Statistics?
Sibulkin, Amy E.; Butler, J. S.
2008-01-01
In order to consider whether a course in college algebra should be a prerequisite for taking psychology statistics, we recorded students' grades in elementary psychology statistics and in college algebra at a 4-year university. Students who earned credit in algebra prior to enrolling in statistics for the first time had a significantly higher mean…
College students' understanding of parameters in algebra
Postelnicu, Valentina; Postelnicu, Florin
2015-01-01
International audience; A study was conducted with 26 college students with the purpose of gaining insight into students' conceptual understanding of parameters in algebra. Participants contributed to a whole-class discussion, solved problems with parameters, and identified the parameters in each problem. About one third of the students had difficulty identifying parameters. Even when successful at identifying parameters, students had great difficulty solving the problems with parameters. The...
Factors That Shape Curricular Reasoning about College Algebra Reform
Burn, Helen E.
2012-01-01
This multiple case study explores factors that shaped the curricular reasoning of mathematics faculty engaged in college algebra reform in community colleges. Overall, the study found that although proposed reform of college algebra is broad in scope and influenced by the student audience, competing influences emerge that can enable or constrain…
Re"modeling" College Algebra: An Active Learning Approach
Pinzon, D.; Pinzon, K.; Stackpole, M.
2016-01-01
In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15-20 minutes of videos before class. We discuss a…
College Algebra Grades 11, 12, A Tentative Guide.
Ebersole, Benjamin P.; And Others
This teaching guide outlines a college algebra course for use in the secondary school. Units studied are: mathematical induction, functions, groups and fields, linear algebra, and limits. Special emphasis is given to the study of functions and linear algebra. Sequence, textbook references and assignments, and time allotments are suggested. Some…
Promoting Quantitative Literacy in an Online College Algebra Course
Tunstall, Luke; Bossé, Michael J.
2016-01-01
College algebra (a university freshman level algebra course) fulfills the quantitative literacy requirement of many college's general education programs and is a terminal course for most who take it. An online problem-based learning environment provides a unique means of engaging students in quantitative discussions and research. This article…
College Algebra Students' Attitudes toward Mathematics in Their Careers
Champion, Joe; Parker, Frieda; Mendoza-Spencer, Bernadette; Wheeler, Ann
2011-01-01
The purpose of this study was to identify the degree to which college algebra students' value mathematical skills in their prospective careers. A survey was administered to N = 144 students in 6 college algebra classes at a mid-sized doctoral granting university. Students in half the classes completed a data analysis project, and half of the…
Student and Instructor Perceptions of a Flipped College Algebra Classroom
Jaster, Robert W.
2017-01-01
Each year about half a million students fail to make planned academic progress due to college algebra, hence the need for researchers to find ways of improving the quality of instruction in the course. Recent research suggests that flipping college algebra to allow time for active learning in the classroom may improve student performance. Also,…
College Algebra in Context: A Project Incorporating Social Issues
Directory of Open Access Journals (Sweden)
Michael T. Catalano
2010-01-01
Full Text Available This paper discusses the development of an innovative college algebra text designed for use in a data-driven, activity-oriented college algebra course, incorporating realistic problem situations emphasizing social and economic issues, including hunger and poverty, energy, and the environment. The course incorporates quantitative literacy themes, is informed by existing college algebra texts within the college algebra reform movement, and implements a collaborative pedagogical approach intended to provide future K-12 teachers an alternative model for the teaching of mathematics. The paper contains a short history of the project development phase, supported by an NSF grant (DUE #0442979, as well as the perceived role of the project in the college algebra reform and quantitative literacy movements. We make a short case for redefining the content of a college algebra course and acknowledging that for many students, it has become a terminal mathematics course. A description of the contents of the text, its relation to more traditional college algebra content, and four example student activities are included (on the topics of homelessness, the effects of airline deregulation, real estate versus savings as investment instruments, and the 2008 election. A summary of evaluation and assessment data from five years of pilot-testing, done primarily in conjuction with our NSF grant evaluation plan, is provided.
The Application of a Computer Algebra System as a Tool in College Algebra.
Mayes, Robert L.
1995-01-01
Students (n=61) in an experimental course stressing active student involvement and the use of a computer algebra system scored higher than students (n=76) in a traditional college algebra course on final measures of inductive reasoning, visualization, and problem solving while maintaining equivalent manipulation and computation skills. (Author/MLB)
Hegedus, Stephen J.; Tapper, John; Dalton, Sara
2016-01-01
In this study, we examine the relationship between contextual variables related to teachers and student performance in Advanced Algebra classrooms in the USA. The data were gathered from a cluster-randomized study on the effects of SimCalc MathWorlds®, a curricular and technological intervention as a replacement for Algebra 2 curriculum, on…
Hegedus, Stephen J.; Tapper, John; Dalton, Sara
2016-01-01
In this study, we examine the relationship between contextual variables related to teachers and student performance in Advanced Algebra classrooms in the USA. The data were gathered from a cluster-randomized study on the effects of SimCalc MathWorlds®, a curricular and technological intervention as a replacement for Algebra 2 curriculum, on…
Redesigning College Algebra for Student Retention: Results of a Quasi-Experimental Research Study
Thompson, Carla J.; McCann, Patricia
2010-01-01
One prohibitory component to graduation rates in college is the lack of student success in college algebra. The current national passing rate of college students enrolled in college algebra is approximately 40 percent. Lack of success in college algebra creating higher enrollments in remediation courses for students has also been linked to…
Examples in College Algebra Textbooks: Opportunities for Students' Learning
Mesa, Vilma; Suh, Heejoo; Blake, Tyler; Whittemore, Timothy
2012-01-01
We present an analysis of several characteristics of examples in 10 college algebra textbooks used in community colleges or 4-year institutions. We analyzed the examples along four dimensions: cognitive demand, the responses expected, the use of representations, and the strategies available for verifying the correctness of the solutions. We found…
Online Homework Effectiveness for Underprepared and Repeating College Algebra Students
Brewer, David Shane; Becker, Kurt
2010-01-01
This research compared the effectiveness, in terms of mathematical achievement, of online homework to textbook homework over an entire semester for 145 students enrolled in multiple sections of college algebra at a large community college. A quasi-experimental, posttest design was used to analyze the effect on mathematical achievement, as measured…
The Effects of the Content Enhancement Model in College Algebra
VanCleave, Janet Milleret
2010-01-01
The purpose of this study was to investigate The Content Enhancement Model in the field of college algebra in a mid-western community college. The Content Enhancement Model is a teaching technique that teachers use to help students acquire the content information by helping them identify, organize, comprehend, and memorize material. This study…
Walker, Christine
2008-01-01
The purpose of this grounded theory study was to discover the factors that contribute to the success or failure of college algebra for students taking college algebra by distance education Internet, and then generate a theory of success or failure of the group of College Algebra Internet students at one Utah college. Qualitative data were collected and analyzed on students’ perceptions and perspectives of a College Algebra Internet course that they took during the spring or summer 2006 semest...
The Effects of History of Mathematics on Attitudes Toward Mathematics of College Algebra Students
McBride, Cecil; Rollins, James H.
1977-01-01
Two college algebra classes were exposed to items from mathematics history in their classroom instruction, while two other college algebra classes received no such exposure. Results showed a significant positive attitude change of the mathematics history group. (DT)
Flipping College Algebra: Effects on Student Engagement and Achievement
Ichinose, Cherie; Clinkenbeard, Jennifer
2016-01-01
This study compared student engagement and achievement levels between students enrolled in a traditional college algebra lecture course and students enrolled in a "flipped" course. Results showed that students in the flipped class had consistently higher levels of achievement throughout the course than did students in the traditional…
Student Perceptions of the Flipped Classroom in College Algebra
Ogden, Lori
2015-01-01
The flipped classroom approach was implemented across three semesters of a College Algebra course. This paper is part of a larger design and development research study and focuses on student perceptions of the flipped classroom teaching approach. Qualitative methodology was used to describe how students perceived the instruction of their College…
Writing to Promote and Assess Conceptual Understanding in College Algebra
Gay, A. Susan; Peterson, Ingrid
2014-01-01
Concept-focused quiz questions required College Algebra students to write about their understanding. The questions can be viewed in three broad categories: a focus on sense-making, a focus on describing a mathematical object such as a graph or an equation, and a focus on understanding vocabulary. Student responses from 10 classes were analyzed.…
Studying Personal Response Systems in a College Algebra Course
Butler, Melanie; Pyzdrowksi, Laura; Walker, Vennessa; Yoho, Stephanie
2010-01-01
This paper gives results of a study on a Personal Response System (PRS). Three sections of college algebra are compared; one section used PRS and PowerPoint, one used PowerPoint, and one was considered a control. Students were given a pretest and posttest with a retired version of a mathematics ACT test, and all students gained an average of one…
Flipping College Algebra: Effects on Student Engagement and Achievement
Ichinose, Cherie; Clinkenbeard, Jennifer
2016-01-01
This study compared student engagement and achievement levels between students enrolled in a traditional college algebra lecture course and students enrolled in a "flipped" course. Results showed that students in the flipped class had consistently higher levels of achievement throughout the course than did students in the traditional…
A Case Study of Students' Motivation in College Algebra Courses
Nguyen, Giang-Nguyen T.
2015-01-01
This paper examines data from a larger study that focused upon students' experiences and motivations in a college algebra course. The study revealed that students failed this course because of various factors and continued to view this course as a "gatekeeper" class. Through a stepwise multiple regression, the analysis of the ARCS…
Developing Cross-Disciplinary Competencies through College Algebra
Jaafar, Reem; Baishanski, Yelena
2012-01-01
To argue for the importance of an integrative approach to learning in introductory STEM (Science, Technology, Engineering and Mathematics) and other courses, we present a case study of a project incorporating cross-curricular skills in a college algebra course. We analyze student work on the project and responses to surveys, and find the…
Incorporating Study Strategies in Developmental Mathematics/College Algebra
Mireles, Selina Vasquez; Offer, Joey; Ward, Debra P.; Dochen, Carol W.
2011-01-01
The purpose of this paper is to discuss the effectiveness of incorporating study strategies in a developmental mathematics/college algebra program. Both quantitative and qualitative data were collected through a quasiexperimental methodology. Results show that students reported increases on the Learning and Study Strategies Inventory (LASSI)…
Developing Cross-Disciplinary Competencies through College Algebra
Reem Jaafar, PhD; Yelena Baishanski, PhD
2012-01-01
To argue for the importance of an integrative approach to learning in introductory STEM (Science, Technology, Engineering and Mathematics) and other courses, we present a case study of a project incorporating cross-curricular skills in a college algebra course. We analyze student work on the project and responses to surveys, and find the assignment affects positively students’ mastery of specific quantitative skills, perceptions of learning, civic awareness, and sense of relevance of mathemat...
Developing Cross-Disciplinary Competencies through College Algebra
Directory of Open Access Journals (Sweden)
Reem Jaafar, PhD
2012-08-01
Full Text Available To argue for the importance of an integrative approach to learning in introductory STEM (Science, Technology, Engineering and Mathematics and other courses, we present a case study of a project incorporating cross-curricular skills in a college algebra course. We analyze student work on the project and responses to surveys, and find the assignment affects positively students’ mastery of specific quantitative skills, perceptions of learning, civic awareness, and sense of relevance of mathematical study. We use the analysis to suggest guidelines for designing other activities aiming to teach the whole student in introductory courses.
Fuller, Edgar; Deshler, Jessica M.; Kuhn, Betsy; Squire, Douglas
2014-01-01
In 2007 the Department of Mathematics at our institution began developing a placement process designed to identify at-risk students entering mathematics courses at the College Algebra and Calculus levels. Major changes in our placement testing process and the resulting interventions for at-risk students were put in place in Fall of 2008. At the…
Thomas, Ryan Vail
2016-01-01
The goal of this study is to explore and characterize the effects of using a dynamic graphing utility (DGU) on conceptual understanding and attitudes toward mathematics, measured by the responses of college algebra students to an attitude survey and concepts assessment. Two sections of college algebra taught by the primary researcher are included…
A Modeling-Based College Algebra Course and Its Effect on Student Achievement
Ellington, Aimee J.
2005-01-01
In Fall 2004, Virginia Commonwealth University (VCU) piloted a modeling-based approach to college algebra. This paper describes the course and an assessment that was conducted to determine the effect of this approach on student achievement in comparison to a traditional approach to college algebra. The results show that compared with their…
Herron, Sherry; Gandy, Rex; Ye, Ningjun; Syed, Nasser
2012-01-01
A unique aspect of the implementation of a computer algebra system (CAS) at a comprehensive university in the U.S. allowed us to compare the student success and failure rates to the traditional method of teaching college algebra. Due to space limitations, the university offered sections of both CAS and traditional simultaneously and, upon…
Ramos, Mark Louie F.
2008-01-01
The purpose of this study was to construct and evaluate an instrument for determining student preparedness in College Algebra. A 73-item instrument covering prerequisite arithmetic and high school Algebra knowledge for College Algebra was constructed. The instrument was pilot-tested on a freshman population of 595 students. Results of reliability…
Tabak, John
2004-01-01
Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries, and offers biographical data on the key figures. Concise and comprehensive text accompanied by many illustrations presents the ideas and historical development of algebra, showcasing the relevance and evolution of this branch of mathematics.
A Comparison of Web-Based and Paper-and-Pencil Homework on Student Performance in College Algebra
Hauk, Shandy; Powers, Robert A.; Segalla, Angelo
2015-01-01
College algebra fulfills general education requirements at many colleges in the United States. The study reported here investigated differences in mathematics achievement between undergraduates in college algebra classes using one of two homework methods: "WeBWorK," an open-source system for web-based homework, or traditional…
A Comparison of Web-Based and Paper-and-Pencil Homework on Student Performance in College Algebra
Hauk, Shandy; Powers, Robert A.; Segalla, Angelo
2015-01-01
College algebra fulfills general education requirements at many colleges in the United States. The study reported here investigated differences in mathematics achievement between undergraduates in college algebra classes using one of two homework methods: "WeBWorK," an open-source system for web-based homework, or traditional…
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
Through most of Greek history, mathematicians concentrated on geometry, although Euclid considered the theory of numbers. The Greek mathematician Diophantus (3rd century),however, presented problems that had to be solved by what we would today call algebra. His book is thus the first algebra text.
Examining the Relationship between Class Scheduling and Student Achievement in College Algebra
Gallo, Michael A.; Odu, Michael
2009-01-01
This study examines the relationship between scheduling (3-, 2-, and 1-day-per-week classes) and achievement in college algebra. The study is grounded in spacing effect theory, which examines how variations in the frequency and timing of instruction affect student learning, and involves 116 Florida community college students. Regression analyses…
Evaluation of Alternative Delivery Systems on Academic Performance in College Algebra
Wynegar, Robert G.; Fenster, Mark J.
2009-01-01
College Algebra is a required, core course for many science and mathematics majors in community colleges. The course had the lowest passing rate of any class on campus. The administration expressed a clear intent to improve on this high failure rate and provided funds to accomplish this purpose. To increase the pass rate several different…
The Effects of Online Homework on Achievement and Self-Efficacy of College Algebra Students
Brewer, David Shane
2009-01-01
This study compared the effectiveness, in terms of mathematical achievement and mathematics self-efficacy, of online homework to textbook homework over an entire semester for 145 students enrolled in multiple sections of college algebra at a large community college. A quasi-experimental, posttest design was used to analyze the effect on…
Evaluation of Alternative Delivery Systems on Academic Performance in College Algebra
Wynegar, Robert G.; Fenster, Mark J.
2009-01-01
College Algebra is a required, core course for many science and mathematics majors in community colleges. The course had the lowest passing rate of any class on campus. The administration expressed a clear intent to improve on this high failure rate and provided funds to accomplish this purpose. To increase the pass rate several different…
Flanders, Harley
1975-01-01
Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms.Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of a
Teaching Basic Algebra Courses at the College Level
Mallenby, Michel L.; Mallenby, Douglas W.
2004-01-01
Three dysfunctional behaviors of basic algebra students are described: Silence as Camouflage, Wing and a Prayer, and Ignorance is OK. These behavior patterns are explained, and beneficial teaching methods that address the weaknesses are presented.
Teaching Basic Algebra Courses at the College Level
Mallenby, Michel L.; Mallenby, Douglas W.
2004-01-01
Three dysfunctional behaviors of basic algebra students are described: Silence as Camouflage, Wing and a Prayer, and Ignorance is OK. These behavior patterns are explained, and beneficial teaching methods that address the weaknesses are presented.
West, Jerry G.
2013-01-01
Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to…
West, Jerry G.
2013-01-01
Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to…
Sepanski, Mark R
2010-01-01
Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems
Overmyer, Jerry
2015-01-01
This quantitative research compares five sections of College Algebra using flipped classroom methods with six sections using the traditional lecture/homework structure and its effect on student achievement as measured through a common final exam. Common final exam scores were the dependent variables. Instructors of flipped sections who had…
Audio-Tutorial Minicourses for College Algebra and Trigonometry: A Progress Report.
Svoboda, Rudy G.
Preliminary results are reported for courses in college algebra and trigonometry based on the Postlethwait audio-tutorial minicourse system which were developed at Indiana University-Purdue University at Fort Wayne (IPFW). Two IPFW faculty members, two secondary teachers, and two undergraduate mathematics majors formed a minicourse project team…
Blakely, Alan W.
2011-01-01
This article describes the impact of starting with gases in an introductory chemistry course at a community college. Students in the author's class frequently are very weak in algebra skills, and this has a cumulative impact over time that culminates in student struggles when moles and reaction stoichiometry are discussed. The rationale behind…
Studying the Effectiveness of Online Homework for Different Skill Levels in a College Algebra Course
Mathai, Elizabeth; Olsen, Darlene
2013-01-01
A comparison of the performance on the final exam for subpopulations of students in College Algebra was used to assess the effectiveness of online homework. Data was collected for two small groups of students, one with traditional paper homework and the other with online homework. The groups of students were further classified by incoming skill…
The Effect of Access to an Online Tutorial Service on College Algebra Student Outcomes
Kersaint, Gladis; Dogbey, James; Barber, Jeff; Kephart, David
2011-01-01
This study investigated outcomes (achievement, attitude, and retention) of college algebra students who had access to an online tutoring resource using a pre-posttest control group design. Students in the experimental groups were provided access to an online tutoring service unlike the students in the control group. Both groups had access to other…
Taking a College Algebra Course: An Approach that Increased Students' Success Rate
Gonzalez-Muniz, Madeline; Klingler, Lee; Moosai, Susan; Raviv, Daniel
2012-01-01
Florida Atlantic University implemented a number of changes in the College Algebra course in an attempt to improve student success. We summarize these changes, and how they have affected the course. We also discuss possibilities for future improvements. (Contains 3 figures and 1 footnote.)
Overmyer, Jerry
2015-01-01
This quantitative research compares five sections of College Algebra using flipped classroom methods with six sections using the traditional lecture/homework structure and its effect on student achievement as measured through a common final exam. Common final exam scores were the dependent variables. Instructors of flipped sections who had…
An Assessment of Web-Based Homework in the Teaching of College Algebra
Affouf, Mahmoud; Walsh, Thomas P.
2007-01-01
The purpose of this study was to demonstrate the effectiveness of web-based homework (WBH) assignments on the overall comprehension measured by the final examination in a first year college algebra course. This study included 1653 students over a three year period. Results indicate a strong correlation between achievement on the WBH assignments…
Associations of Students' Beliefs with Self-Regulated Problem Solving in College Algebra
Cifarelli, Victor; Goodson-Espy, Tracy; Chae, Jeong-Lim
2010-01-01
This paper reports results from a study of self-regulated problem solving actions of students enrolled in College Algebra (N = 139). The study examined the associations between the expressed mathematical beliefs of students and the students' self-regulated actions in solving mathematics problems. The research questions are: (a) What are some…
Designing Tasks for Math Modeling in College Algebra: A Critical Review
Staats, Susan; Robertson, Douglas
2014-01-01
Over the last decade, the pedagogical approach known as mathematical modeling has received increased interest in college algebra classes in the United States. Math modeling assignments ask students to develop their own problem-solving tools to address non-routine, realistic scenarios. The open-ended quality of modeling activities creates dilemmas…
Implementing a Flipped Instructional Model in College Algebra: Profiles of Student Activity
Lesseig, Kristin; Krouss, Paul
2017-01-01
Flipped instruction is increasing in popularity, however research that moves beyond descriptions of its implementation in mathematics classes is lacking. We sought to better understand how students taking an introductory college algebra course used the resources provided within a flipped instructional model and how students viewed such resources…
Computer-Aided College Algebra: Learning Components that Students Find Beneficial
Aichele, Douglas B.; Francisco, Cynthia; Utley, Juliana; Wescoatt, Benjamin
2011-01-01
A mixed-method study was conducted during the Fall 2008 semester to better understand the experiences of students participating in computer-aided instruction of College Algebra using the software MyMathLab. The learning environment included a computer learning system for the majority of the instruction, a support system via focus groups (weekly…
The Effect of the Math Emporium Instructional Method on Students' Performance in College Algebra
Cousins-Cooper, Kathy; Staley, Katrina N.; Kim, Seongtae; Luke, Nicholas S.
2017-01-01
This study aims to investigate the effectiveness of the Emporium instructional method in a course of college algebra and trigonometry by comparing to the traditional lecture method. The math emporium method is a nontraditional instructional method of learning math that has been implemented at several universities with much success and has been…
Klemke, Roland; Specht, Marcus
2013-01-01
Klemke, R., & Specht, M. (2013, 26-27 September). Technology Enhanced Learning. Presentation at the fourth international conference on eLearning (eLearning 2013), Belgrade, Serbia. http://econference.metropolitan.ac.rs/
Math 3011--College Algebra and Trigonometry. Course Outline.
New York Inst. of Tech., Old Westbury.
This document contains the course syllabus and 12 independent practice modules for a college level mathematics course designed to provide the necessary foundation for success in calculus, develop logical thinking skills, and enhance analytic skills through problem solving. Topics include relations and functions; inequalities; complex numbers;…
Math 3011--College Algebra and Trigonometry. Course Outline.
New York Inst. of Tech., Old Westbury.
This document contains the course syllabus and 12 independent practice modules for a college level mathematics course designed to provide the necessary foundation for success in calculus, develop logical thinking skills, and enhance analytic skills through problem solving. Topics include relations and functions; inequalities; complex numbers;…
Directory of Open Access Journals (Sweden)
Jhemson C. Elis
2013-12-01
Full Text Available The major thrust of this study is to develop a diagnostic test in college algebra to know the level of performance in College Algebra of non – education freshman students of Westmead International School through the use of a diagnostic test. The researcher used the descriptive method of research. The level of performance of freshman non – education students of Westmead International School in Algebraic operation has a mean of 80.66 with the highest score of 88 percent and lowest score of 68, while 22 or 31.43 percent had an average performance ranging from 79 - 84. This indicates that students had average mathematical skills and knowledge acquired from their mathematics foundation during high school. The level of performance of freshman non – education students of Westmead International School in arithmetic operation has 77.78 of the mean score with the highest score of 94 and lowest score of 68, which indicates that the students have difficulties in some areas in arithmetic operations. There was a significant relationship between mathematics foundation and the level of performance of the students. The output made by the researcher was a set of Remedial Activities in College Algebra, which is composed of different topics based on the result of the study and on the suggestions of the college instructors of Westmead International School based on their observation. The topics were operation on integers, operation involving polynomials, and special products. It was recommended that the freshman college students need to take the diagnostic test in College Algebra to determine their level of performance. If they fail in the diagnostic test, they will take Math Plus (Basic Mathematics instead of College Algebra. The students with good performance in the diagnostic test will take College Algebra.
Deshler, Jessica; Fuller, Edgar
2016-01-01
Approximately 30% of students entering West Virginia University (WVU) are not ready for college mathematics. The WVU Department of Mathematics has been tasked with remediating these students and has worked over the last decade to find the most efficient way to teach the Pre-College Algebra Workshop; the prerequisite course students must complete…
Deshler, Jessica; Fuller, Edgar
2016-01-01
Approximately 30% of students entering West Virginia University (WVU) are not ready for college mathematics. The WVU Department of Mathematics has been tasked with remediating these students and has worked over the last decade to find the most efficient way to teach the Pre-College Algebra Workshop; the prerequisite course students must complete…
Emig, Christa
2009-01-01
The study sought to test the hypotheses that effective, guided discussions that facilitate meaningful dialogue about math anxiety would reduce levels of math anxiety in college algebra students, and would enhance course performance and course retention at a large community college in South Texas. The study was quantitative with a qualitative…
Matika, Richard
2012-01-01
Online mathematics courses at Somerset Community College (SCC) have traditionally had a lower retention rate than their in-person counterparts. This study looked at online and in-person students at SCC in the courses "Intermediate Algebra" and "College Algebra." Beginning of semester student demographics were considered to…
Promoting Numeracy in an Online College Algebra Course through Projects and Discussions
Directory of Open Access Journals (Sweden)
Samuel L. Tunstall
2015-07-01
Full Text Available This research stems from efforts to infuse quantitative literacy (QL in an online version of college algebra. College algebra fulfills a QL requirement at many universities, and it is a terminal course for most who take it. In light of the course’s traditional content and teaching methods, students often leave with little gained in QL. An online platform provides a unique means of engaging students in quantitative discussions and research, yet little research exists on online courses in the context of QL. The course studied included weekly news discussions as well as “messy” projects requiring data analysis. Students in online and face-to-face sections of the course took the Quantitative Literacy and Reasoning Assessment ( QLRA; developed by members of the National Numeracy Network during the first and final weeks of the fall 2014 semester. There were significant statistical gains in the online students’ QLRA performance and mathematical affect but none for the face-to-face students. Notwithstanding limitations of the study, the results support the notion that project-based learning in an online environment is a promising strategy for promoting QL in terminal math courses.
Davis, Ann
2009-01-01
This study measured the amounts of different types of metacognitive statements made by students enrolled in Elementary Algebra courses at a community college in California. A total of 17 students were interviewed three times during the course of a semester. All interviews were coded for types of metacognitive statements that fell into one of three…
Hatem, Neil
2010-01-01
This study investigates the relationship between the use of graphing calculators employed as Type II technology and student achievement, as determined by assessing students' problem solving skills associated with the concept of function, at the college algebra and pre-calculus level. In addition, this study explores the integration of graphing…
Hagerty, Gary; Smith, Stanley; Goodwin, Danielle
2010-01-01
In 2001, Black Hills State University (BHSU) redesigned college algebra to use the computer-based mastery learning program, Assessment and Learning in Knowledge Spaces [1], historical development of concepts modules, whole class discussions, cooperative activities, relevant applications problems, and many fewer lectures. This resulted in a 21%…
Hatem, Neil
2010-01-01
This study investigates the relationship between the use of graphing calculators employed as Type II technology and student achievement, as determined by assessing students' problem solving skills associated with the concept of function, at the college algebra and pre-calculus level. In addition, this study explores the integration of graphing…
Lane, Rebekah M.
2011-01-01
This investigation utilized the qualitative case study method. Seventy-one College Algebra students were given a mathematical processing instrument. This testing device measured a student's preference for visual thinking. Two students were purposefully selected using the instrument. The visual mathematical learner (VL) was discussed in this…
Sworder, Steve
2006-01-01
The purpose of this study was to determine the effectiveness of a typical California community college Intermediate Algebra course in preparing students for success in the transfer level mathematics courses for which Intermediate Algebra was the prerequisite. The subsequent mathematics course taken by each of the 986 students who received a grade…
Alster, E H
1997-01-01
The purpose of this study was to assess the effects of extended time on the algebra test performance of community college students with and without learning disabilities. Forty-four students with learning disabilities and 44 students without learning disabilities attending five California community colleges participated in the study. The students each took an algebra test under timed conditions and a comparable test under extended-time conditions. The main results were that the students with learning disabilities scored significantly lower than the students without learning disabilities under timed conditions, the scores of the students with learning disabilities increased significantly with extended time, and the scores of the students with learning disabilities under extended-time conditions did not differ significantly from the timed or extended-time scores of the students without learning disabilities.
Opening a Gateway to College Access: Algebra at the Right Time. Research Brief
Snipes, Jason; Finkelstein, Neal
2015-01-01
Four years of math in high school, with a strong foundation in algebra that builds from middle school, is key to higher education access. Therefore, ensuring that middle and high school students succeed in math--and in algebra in particular--is an important issue for policy and practice. This research brief examines three recent Regional…
Arithmetic: Prerequisite to Algebra?
Rotman, Jack W.
Drawing from research and observations at Lansing Community College (Michigan) (LCC), this paper argues that typical arithmetic courses do little to prepare students to master algebra, and proposes an alternative set of arithmetic skills as actual prerequisites to algebra. The first section offers a description of the algebra sequence at LCC,…
Kitz, W R; Nash, R T
1995-01-01
For many secondary and postsecondary students with dyslexia, passing required algebra courses presents a formidable challenge. Although dyslexic students do have specific and sometimes severe learning deficits that can affect their chances of success in algebra, they can succeed if given appropriate and effective instruction that meets their special and individual needs. This article briefly describes the application of effective instructional practices to the teaching of remedial algebra that have been used with dyslexic students in the University of Wisconsin Oshkosh Project Success program.
Crombie, William
2013-04-01
We take a second look at Saletan's American Journal of Physics article (1973) which describes a method, appropriate to elementary physics courses, for defining the instantaneous velocity of a moving object and for computing derivatives without recourse to limits. The mathematics behind our extended method enters at the level of College Algebra and provides an alternative formulation to the Calculus based on either infinitesimals or limits. This approach holds the promise of providing access to Calculus and those quantitative disciplines that depend upon Calculus to a larger pool of students than is presently engaged in the advanced study of STEM disciplines.
Miller, David; Schraeder, Matthew
2015-01-01
At a research University near the east coast, researchers restructured a College Algebra course by formatting the course into two large lectures a week, an active recitation size laboratory class once a week, and an extra day devoted to active group work called Supplemental Practice (SP). SP was added as an extra day of class where the SP leader…
Jordan, Laurn Reye
2013-01-01
Instructional practices in mathematics courses at two-year colleges include lecture as the predominant instructional form in 78% of two-year colleges, with class sizes averaging about 26 students (AACC, 2005). The National Assessment of Educational Progress (NAEP) indicates that there is a need for change in the practices of mathematics teachers…
Gaps in Developmental Mathematics Course Sequence Impede Success in College Algebra
Gonzales, Hector Espinosa
2012-01-01
Community colleges are undergoing a transformation. Historically, they have been focused on improving access to higher education; now the focus has shifted to student success. This transformation is evident in the concerted effort to improve student graduation rates and decrease the amount of time spent to complete degrees. For community colleges,…
Institute of Scientific and Technical Information of China (English)
周克元; 费绍金
2015-01-01
针对三本院校学生的特点和培养目标，结合教学实践，提出了将数学建模及数学软件融入线性代数，加强线性代数与几何学的联系等教学改革措施，总结并分析了教学改革效果及遇到的问题，并给出相应建议。%Aiming at the characters and trainning goals of the students in the secondary undergraduate college,and combining experience of teaching practice,proposed some linear algebra teaching reformation measures,such as integrating mathematical model and mathematical software into linear algebra teaching.Strengthing the bond between linear algebra and geometry,analyzed problems in the teaching reformation,and gave some recommendations.
Shafarevich, I
1994-01-01
This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.
Left Artinian Algebraic Algebras
Institute of Scientific and Technical Information of China (English)
S. Akbari; M. Arian-Nejad
2001-01-01
Let R be a left artinian central F-algebra, T(R) = J(R) + [R, R],and U(R) the group of units of R. As one of our results, we show that, if R is algebraic and char F = 0, then the number of simple components of -R = R/J(R)is greater than or equal to dimF R/T(R). We show that, when char F = 0 or F is uncountable, R is algebraic over F if and only if [R, R] is algebraic over F. As another approach, we prove that R is algebraic over F if and only if the derived subgroup of U(R) is algebraic over F. Also, we present an elementary proof for a special case of an old question due to Jacobson.
Algebraic partial Boolean algebras
Energy Technology Data Exchange (ETDEWEB)
Smith, Derek [Math Department, Lafayette College, Easton, PA 18042 (United States)
2003-04-04
Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A{sub 5} sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E{sub 8}.
Teachers as designers of technology enhanced learning
Kali, Yael; McKenney, Susan; Sagy, Ornit
2013-01-01
Kali, Y., McKenney, S., & Sagy, O. (2012, 2-6 July). Teachers as designers of technology enhanced learning. Presentation at the Teachers as Designers of Technology Enhanced Learning pre-conference workshop in conjunction with the ISLS annual meeting, Sydney, Australia.
Predicting Grades in Basic Algebra.
Newman, Elise
1994-01-01
Data from (n=470) students at Owens Technical College in Fall 1991 showed that high school GPA was the best predictor of grades in Basic Algebra, followed by high school rank, college GPA, ACT natural sciences, ASSET numerical skills, and ASSET elementary algebra scores. (11 references) (SW)
Readiness and Preparation for Beginning Algebra.
Rotman, Jack W.
Drawing from experience at Lansing Community College (LCC), this paper discusses how to best prepare students for success in a beginning algebra course. First, an overview is presented of LCC's developmental math sequence, which includes Basic Arithmetic (MTH 008), Pre-Algebra (MTH 009), Beginning Algebra (MTH 012), and Intermediate Algebra (MTH…
Norén, Patrik
2013-01-01
Algebraic statistics brings together ideas from algebraic geometry, commutative algebra, and combinatorics to address problems in statistics and its applications. Computer algebra provides powerful tools for the study of algorithms and software. However, these tools are rarely prepared to address statistical challenges and therefore new algebraic results need often be developed. This way of interplay between algebra and statistics fertilizes both disciplines. Algebraic statistics is a relativ...
Teacher Design Knowledge for Technology Enhanced Learning
McKenney-Jensh, Susan E.
2014-01-01
This presentation shares a framework for investigating the knowledge teachers need to be able to design technology-enhanced learning. Specific activities are undertaken to consider elements within the framework
Learning in a technology enhanced world
Specht, Marcus
2010-01-01
Specht, M. (2009). Learning in a technology enhanced world. Invited talk given at the World Conference on E-learning in Corporate, Government, Healthcare & Higher Education. October, 27, 2009, Vancouver, Canada.
Khatri, Daryao
2011-01-01
Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (STEM) discipline. This book fosters mastery of critical math and algebraic concepts and skills essential to all of the STEM disciplines and some of the social sciences.
Khatri, Daryao
2011-01-01
Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (STEM) discipline. This book fosters mastery of critical math and algebraic concepts and skills essential to all of the STEM disciplines and some of the social sciences. This…
Khatri, Daryao
2011-01-01
Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (STEM) discipline. This book fosters mastery of critical math and algebraic concepts and skills essential to all of the STEM disciplines and some of the social sciences. This…
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Beilinson, Alexander
2004-01-01
Chiral algebras form the primary algebraic structure of modern conformal field theory. Each chiral algebra lives on an algebraic curve, and in the special case where this curve is the affine line, chiral algebras invariant under translations are the same as well-known and widely used vertex algebras. The exposition of this book covers the following topics: the "classical" counterpart of the theory, which is an algebraic theory of non-linear differential equations and their symmetries; the local aspects of the theory of chiral algebras, including the study of some basic examples, such as the ch
独立学院线性代数教学的思考%Reflections on "Linear Algebra" Teaching in Independent Colleges
Institute of Scientific and Technical Information of China (English)
潘丽华
2014-01-01
In this paper, through the analysis of the present situa-tion of linear algebra teaching in independent colleges, combining with the teaching practice, this paper proposes the problems in the process of teaching, and puts forward some corresponding suggestions.%本文通过对独立学院线性代数教学现状的分析，结合教学实践，提出了教学过程中应注意的问题，并给出了相应的建议。
Algebra and Algebraic Thinking in School Math: 70th YB
National Council of Teachers of Mathematics, 2008
2008-01-01
Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…
Abstract Algebra to Secondary School Algebra: Building Bridges
Christy, Donna; Sparks, Rebecca
2015-01-01
The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…
Abstract Algebra to Secondary School Algebra: Building Bridges
Christy, Donna; Sparks, Rebecca
2015-01-01
The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…
The Technology Enhanced Conference - A Board Game!
DEFF Research Database (Denmark)
Pedersen, Annette
, and the sharing of knowledge beyond the event days. But how can we help the organizers and participants realize the potential of an interactive conference? Because let's face it: the easier choice is to leave out the technology enhancement and stick with the well-known conference format. We came up with a visual...... been great, and maybe the board game can be used for other areas, where one needs to communicate complicated options for technology enhanced events or teaching and support organizers in making good choices....
Cartooning in Algebra and Calculus
Moseley, L. Jeneva
2014-01-01
This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.
Cartooning in Algebra and Calculus
Moseley, L. Jeneva
2014-01-01
This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.
Teachers as designers of technology enhanced learning
Kali, Yael; McKenney, Susan
2012-01-01
Kali, Y., & McKenney, S. (2012). Teachers as designers of technology enhanced learning. In J. van Aalst, K. Thompson, M. J. Jacobson, & P. Reimann (Eds.), The future of learning: Proceedings of the 10th international conference of the learning sciences (Vol. 2, pp. 582-583). Sydney, NSW, Australia:
Teachers as designers of technology enhanced learning
Kali, Yael; McKenney, Susan; Sagy, Ornit; Voogt, Joke
2015-01-01
Design of (technology-enhanced) learning activities and materials is one fruitful process through which teachers learn and become professionals. To facilitate this process, research is needed to understand how teachers learn through design, how this process may be supported, and how teacher involvem
Teachers as designers of technology enhanced learning
Kali, Yael; McKenney, Susan; Sagy, Ornit; Voogt, Joke
2015-01-01
Design of (technology-enhanced) learning activities and materials is one fruitful process through which teachers learn and become professionals. To facilitate this process, research is needed to understand how teachers learn through design, how this process may be supported, and how teacher involvem
Teacher Learning of Technology Enhanced Formative Assessment
Feldman, Allan; Capobianco, Brenda M.
2008-01-01
This study examined the integration of technology enhanced formative assessment (FA) into teachers' practice. Participants were high school physics teachers interested in improving their use of a classroom response system (CRS) to promote FA. Data were collected using interviews, direct classroom observations, and collaborative discussions. The…
Unifying the Algebra for All Movement
Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.
2015-01-01
There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…
Computer Algebra Systems, Pedagogy, and Epistemology
Bosse, Michael J.; Nandakumar, N. R.
2004-01-01
The advent of powerful Computer Algebra Systems (CAS) continues to dramatically affect curricula, pedagogy, and epistemology in secondary and college algebra classrooms. However, epistemological and pedagogical research regarding the role and effectiveness of CAS in the learning of algebra lags behind. This paper investigates concerns regarding…
Unifying the Algebra for All Movement
Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.
2015-01-01
There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…
Reinhardt, Kevin; Parkins, Sherri
The authors describe their experience over the last 4 years at Seneca College of Applied Arts and Technology, enhancing the vocational opportunities for at risk students through the use of Reading and Writing Technology, primarily, Microsofts word processor, Word and WordQ, a word prediction and text to speech software designed to assist learning…
Pavelle, Richard; And Others
1981-01-01
Describes the nature and use of computer algebra and its applications to various physical sciences. Includes diagrams illustrating, among others, a computer algebra system and flow chart of operation of the Euclidean algorithm. (SK)
Warner, Seth
1990-01-01
Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.
Goodstein, R L
2007-01-01
This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.
2013-01-01
The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology, including persistent homology.
The Technology Enhanced Conference - A Board Game!
DEFF Research Database (Denmark)
Pedersen, Annette
ITMEDIA at the University of Copenhagen have been working with taking the academic conference online for years. Streaming events, using backchannel chat systems and Twitter, producing introductory pre-event videos, setting up audio debates with keynotes to enrich and prolong the conference...... been great, and maybe the board game can be used for other areas, where one needs to communicate complicated options for technology enhanced events or teaching and support organizers in making good choices....
Lloris Ruiz, Antonio; Parrilla Roure, Luis; García Ríos, Antonio
2014-01-01
This book presents a complete and accurate study of algebraic circuits, digital circuits whose performance can be associated with any algebraic structure. The authors distinguish between basic algebraic circuits, such as Linear Feedback Shift Registers (LFSRs) and cellular automata, and algebraic circuits, such as finite fields or Galois fields. The book includes a comprehensive review of representation systems, of arithmetic circuits implementing basic and more complex operations, and of the residue number systems (RNS). It presents a study of basic algebraic circuits such as LFSRs and cellular automata as well as a study of circuits related to Galois fields, including two real cryptographic applications of Galois fields.
Teaching Reform of Elementary Algebra in Normal Colleges and Universities%高师"初等代数研究"课程教学改革探索
Institute of Scientific and Technical Information of China (English)
张彦春
2015-01-01
初等代数研究课程是高师院校数学与应用数学专业开设的专业必修课. 为了实现"上通数学,下达课堂"的目的,对课程目标、内容、教学模式以及考核评价进行了一系列的改革并取得初步成效. 在学生的小组合作、研究性学习的评价以及学生解题能力的培养上还需进一步研究.%Elementary algebra is a required course for Mathematics and Applied Mathematics in normal colleges and universities. In order to achieve the training objectives,this paper has carried out a series of reforms on the course objectives,teaching content,and teaching modes,and it has achieved initial success in teaching elementary algebra. It has also found that students' group cooperation,evaluation of research study and students' problem-solving ability needs to be further studied.
高师院校近世代数课程教学策略%The Teaching Strategy on Modern Algebra Course in Normal Colleges
Institute of Scientific and Technical Information of China (English)
程晓亮
2015-01-01
结合高师院校的培养目标，阐述近世代数课程教学中，以历史主线贯穿教学始终，知识结构图贯穿教学过程始终，知识点教学贯穿与中学数学知识的联系，课堂教学渗透学科交叉与应用等教学策略。%In this paper,we discuss the teaching strategy on modern algebra courseby according to the training goal of normal colleges,including history through out the teaching,structure map of knowledge through out teaching process,key knowledge through out teaching process by contacting mathematical knowledge in the middle school,infiltration of interdisciplinary and application.
应用型本科院校中线性代数教学的探讨%Explore Applied Undergraduate Colleges Linear Algebra Teaching
Institute of Scientific and Technical Information of China (English)
杨伟
2015-01-01
Based on the characteristic of application-oriented college and university, the current situation of education of Liner Algebra and the practical teaching experience, this paper discusses how to further improve the teaching quality in tea-ching process, and shares the teaching experience and result.%文章针对当前应用型本科院校的特点和线性代数教学的现状,根据实际教学经验,阐述在实际教学过程中如何进一步提高教学质量,探讨线性代数课堂教学的一些心得和体会.
Issa, A Nourou
2010-01-01
Non-Hom-associative algebras and Hom-Akivis algebras are introduced. The commutator-Hom-associator algebra of a non-Hom-associative algebra is a Hom-Akivis algebra. It is shown that non-Hom-associative algebras can be obtained from nonassociative algebras by twisting along algebra automorphisms while Hom-Akivis algebras can be obtained from Akivis algebras by twisting along algebra endomorphisms.
Energy Technology Data Exchange (ETDEWEB)
Odesskii, A V [L.D. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow (Russian Federation)
2002-12-31
This survey is devoted to associative Z{sub {>=}}{sub 0}-graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt condition (PBW-algebras). Examples are considered of such algebras, depending on two continuous parameters (namely, on an elliptic curve and a point on it), that are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras are described, together with their relations to integrable systems, deformation quantization, moduli spaces, and other directions of modern investigations.
Algebraic Statistics for Network Models
2014-02-19
AFRL-OSR-VA-TR-2014-0070 (DARPA) Algebraic Statistics for Network Models SONJA PETROVIC PENNSYLVANIA STATE UNIVERSITY 02/19/2014 Final Report...DARPA GRAPHS Phase I Algebraic Statistics for Network Models FA9550-12-1-0392 Sonja Petrović petrovic@psu.edu1 Department of Statistics Pennsylvania...Department of Statistics, Heinz College , Machine Learning Department, Cylab Carnegie Mellon University 1. Abstract This project focused on the family of
Linear Algebra and Smarandache Linear Algebra
Vasantha, Kandasamy
2003-01-01
The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and ve...
Linear Algebra and Smarandache Linear Algebra
Vasantha, Kandasamy
2003-01-01
The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and ve...
Cavanagh, Sean
2009-01-01
As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…
Cavanagh, Sean
2009-01-01
As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…
Technology enhanced peer learning and peer assessment
DEFF Research Database (Denmark)
Henriksen, Christian Bugge; Bregnhøj, Henrik; Rosthøj, Susanne
2016-01-01
This paper explores the application of learning designs featuring formalised and structured technology enhanced peer learning. These include student produced learning elements, peer review discussions and peer assessment in the BSc/MSc level summer course Restoration of European Ecosystems...... and Freshwaters (REEF), the Master thesis preparation seminars for the Master of Public Health (MPH) and the MOOC course Global Environmental Management (GEM). The application of student produced learning elements and peer review discussions is investigated by analyzing quotes from course evaluations...... and performing focus group interviews. The application of peer assessment is investigated by analyzing the agreement of peer assessment between students assessing the same assignment. Our analyses confirm previous research on the value of peer learning and peer assessment and we argue that there could also...
Technology enhanced peer learning and peer assessment
Directory of Open Access Journals (Sweden)
Christian Bugge Henriksen
2016-11-01
Full Text Available This paper explores the application of learning designs featuring formalised and structured technology enhanced peer learning. These include student produced learning elements, peer review discussions and peer assessment in the BSc/MSc level summer course Restoration of European Ecosystems and Freshwaters (REEF, the Master thesis preparation seminars for the Master of Public Health (MPH and the MOOC course Global Environmental Management (GEM. The application of student produced learning elements and peer review discussions is investigated by analyzing quotes from course evaluations and performing focus group interviews. The application of peer assessment is investigated by analyzing the agreement of peer assessment between students assessing the same assignment. Our analyses confirm previous research on the value of peer learning and peer assessment and we argue that there could also be a huge benefit from developing learning design patterns that facilitate informal peer learning and reinforce knowledge sharing practices.
Algebra-Geometry of Piecewise Algebraic Varieties
Institute of Scientific and Technical Information of China (English)
Chun Gang ZHU; Ren Hong WANG
2012-01-01
Algebraic variety is the most important subject in classical algebraic geometry.As the zero set of multivariate splines,the piecewise algebraic variety is a kind generalization of the classical algebraic variety.This paper studies the correspondence between spline ideals and piecewise algebraic varieties based on the knowledge of algebraic geometry and multivariate splines.
普通高校中“线性代数”教学方法研究%Research on the Teaching Methods of Linear Algebra in Common Colleges
Institute of Scientific and Technical Information of China (English)
周伟平
2014-01-01
Through the teaching practice of linear algebra for many years, according to the characteristics of the course and students' actual situation, it studied some problems in the teach-ing of linear algebra,and some methods of improving the teaching quality were given. By the properties of linear algebra and college students how to learn autonomously, etc., it carried out some sug-gestions to improve the quality of linear algebra teaching, and those were good for students to study linear algebra.%本文根据多年的线性代数的教学实践，针对课程特点和学生的实际情况，研究了在线性代数教学中存在的一些问题，提出改进教学质量的方法。根据线性代数课程的主要性质和大学生如何自主学习等方面，提出提高线性代数教学质量的几点建议，易于学生更好地学习线性代数，以获得良好的教学效果。
Nyman, Melvin A.; Lapp, Douglas A.; St. John, Dennis; Berry, John S.
2010-01-01
This paper discusses student difficulties in grasping concepts from Linear Algebra--in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student…
独立学院线性代数教学改革的实践与思考%On the Reform of Linear Algebra Teaching for Independent Colleges
Institute of Scientific and Technical Information of China (English)
王志华
2012-01-01
从大纲修订、教材建设、教学方法、师资素质四个方面，阐述独立学院为应对培养应用型人才的任务与要求，应如何践行线性代数教学改革．%Linear algebra is an important foundation course for institutions and colleges. In this paper, it is elaborated from the four aspects, including syllabus amendment, reconstruction of teaching material, exploration of teaching methods, and quality of teachers, to explain how to carry out the reform of linear algebra through teaching practice in independent colleges for practical tertiary education.
Chisolm, Eric
2012-01-01
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines a product that's strongly motivated by geometry and can be taken between any two objects. For example, the product of two vectors taken in a certain way represents their common plane. This system was invented by William Clifford and is more commonly known as Clifford algebra. It's actually older than the vector algebra that we use today (due to Gibbs) and includes it as a subset. Over the years, various parts of Clifford algebra have been reinvented independently by many people who found they needed it, often not realizing that all those parts belonged in one system. This suggests that Clifford had the right idea, and that geometric algebra, not the reduced version we use today, deserves to be the standard "vector algebra." My goal in these notes is to describe geometric al...
Garrett, Paul B
2007-01-01
Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal
Fontana, Marco; Olberding, Bruce; Swanson, Irena
2011-01-01
Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigrou
Computational intelligence for technology enhanced learning
Energy Technology Data Exchange (ETDEWEB)
Xhafa, Fatos [Polytechnic Univ. of Catalonia, Barcelona (Spain). Dept. of Languages and Informatics Systems; Caballe, Santi; Daradoumis, Thanasis [Open Univ. of Catalonia, Barcelona (Spain). Dept. of Computer Sciences Multimedia and Telecommunications; Abraham, Ajith [Machine Intelligence Research Labs (MIR Labs), Auburn, WA (United States). Scientific Network for Innovation and Research Excellence; Juan Perez, Angel Alejandro (eds.) [Open Univ. of Catalonia, Barcelona (Spain). Dept. of Information Sciences
2010-07-01
E-Learning has become one of the most wide spread ways of distance teaching and learning. Technologies such as Web, Grid, and Mobile and Wireless networks are pushing teaching and learning communities to find new and intelligent ways of using these technologies to enhance teaching and learning activities. Indeed, these new technologies can play an important role in increasing the support to teachers and learners, to shorten the time to learning and teaching; yet, it is necessary to use intelligent techniques to take advantage of these new technologies to achieve the desired support to teachers and learners and enhance learners' performance in distributed learning environments. The chapters of this volume bring advances in using intelligent techniques for technology enhanced learning as well as development of e-Learning applications based on such techniques and supported by technology. Such intelligent techniques include clustering and classification for personalization of learning, intelligent context-aware techniques, adaptive learning, data mining techniques and ontologies in e-Learning systems, among others. Academics, scientists, software developers, teachers and tutors and students interested in e-Learning will find this book useful for their academic, research and practice activity. (orig.)
DEFF Research Database (Denmark)
2007-01-01
The workshop continued a series of Oberwolfach meetings on algebraic groups, started in 1971 by Tonny Springer and Jacques Tits who both attended the present conference. This time, the organizers were Michel Brion, Jens Carsten Jantzen, and Raphaël Rouquier. During the last years, the subject...... of algebraic groups (in a broad sense) has seen important developments in several directions, also related to representation theory and algebraic geometry. The workshop aimed at presenting some of these developments in order to make them accessible to a "general audience" of algebraic group......-theorists, and to stimulate contacts between participants. Each of the first four days was dedicated to one area of research that has recently seen decisive progress: \\begin{itemize} \\item structure and classification of wonderful varieties, \\item finite reductive groups and character sheaves, \\item quantum cohomology...
McKeague, Charles P
1981-01-01
Elementary Algebra 2e, Second Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first tackles the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the substitution method, solving linear systems by graphing, solutions to linear equations in two variables, multiplication property of equality, word problems, addition property of equality, and subtraction, addition, multiplication, and division of real numbers. The manuscript then examines exponents and polynomials, factoring, and rational e
McKeague, Charles P
1986-01-01
Elementary Algebra, Third Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first ponders on the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the elimination method, solving linear systems by graphing, word problems, addition property of equality, solving linear equations, linear inequalities, addition and subtraction of real numbers, and properties of real numbers. The text then takes a look at exponents and polynomials, factoring, and rational expressions. Topics include reducing ra
Ideas in Practice: Graphing Calculators in Beginning Algebra
Martin, Aimee
2008-01-01
This paper reports on a project to improve Beginning Algebra students' understanding of basic algebraic concepts through fully integrated use of the TI-83 graphing calculator. The methodology incorporated an intervention case study including approximately 700 Beginning Algebra students at an open-door community college of 8,500 students in the…
Do we need teachers as designers of technology enhanced learning?
Kirschner, Paul A.
2016-01-01
In this special issue, five teams of researchers discuss different aspects of the teacher as designer of technology enhanced learning situations. This final contribution critically discusses if and how teachers as designers of technology enhanced learning might (not) be feasible or even desirable. T
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.
Institute of Scientific and Technical Information of China (English)
WANG Renhong; ZHU Chungang
2004-01-01
The piecewise algebraic variety is a generalization of the classical algebraic variety. This paper discusses some properties of piecewise algebraic varieties and their coordinate rings based on the knowledge of algebraic geometry.
Data Compression with Linear Algebra
Etler, David
2015-01-01
A presentation on the applications of linear algebra to image compression. Covers entropy, the discrete cosine transform, thresholding, quantization, and examples of images compressed with DCT. Given in Spring 2015 at Ocean County College as part of the honors program.
Marchuk, Nikolay
2011-01-01
Exterior algebras and differential forms are widely used in many fields of modern mathematics and theoretical physics. In this paper we define a notion of $N$-metric exterior algebra, which depends on $N$ matrices of structure constants. The usual exterior algebra (Grassmann algebra) can be considered as 0-metric exterior algebra. Clifford algebra can be considered as 1-metric exterior algebra. $N$-metric exterior algebras for $N\\geq2$ can be considered as generalizations of the Grassmann alg...
Huang, Kai-Yi Clark
2012-01-01
The purpose of this study was to measure the difference in achievement between those students enrolled in a beginning-level, university Algebra course in southeastern Idaho university the spring semester of 2012 who received an Algebra Exponents and Polynomials instructional unit in a traditional face-to-face setting and those students who…
Edwards, Harold M
1995-01-01
In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject
Liesen, Jörg
2015-01-01
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...
Directory of Open Access Journals (Sweden)
G.C. Rao
2012-11-01
Full Text Available A C- algebra is the algebraic form of the 3-valued conditional logic, which was introduced by F. Guzman and C. C. Squier in 1990. In this paper, some equivalent conditions for a C- algebra to become a boolean algebra in terms of congruences are given. It is proved that the set of all central elements B(A is isomorphic to the Boolean algebra of all C-algebras Sa, where a B(A. It is also proved that B(A is isomorphic to the Boolean algebra of all C-algebras Aa, where a B(A.
Stoll, R R
1968-01-01
Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand
Jacobson, Nathan
1979-01-01
Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its
Jacobson, Nathan
2009-01-01
A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as L
Allenby, Reg
1995-01-01
As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics. Dr Allenby has used his experience of teaching linear algebra to write a lively book on the subject that includes historical information about the founders of the subject as well as giving a basic introduction to the mathematics undergraduate. The whole text has been written in a connected way with ideas introduced as they occur naturally. As with the other books in the series, there are many worked examples.Solutions to the exercises are available onlin
Oliver, Bob; Pawałowski, Krzystof
1991-01-01
As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
Indian Academy of Sciences (India)
Tomás L Gómez
2001-02-01
This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector bundles, giving a detailed comparison with the moduli scheme obtained via geometric invariant theory.
Clark, Allan
1984-01-01
This concise, readable, college-level text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems.Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results needed for Galois theory as well as the Sylow theorems, the Jordan-Holder theorem, and a complete treatment of the simplicity of alternating groups. Chapter III (Field Theory)
Goodman-Petrushka, Sharon
This workbook is designed to be used as a review at the end of a college level course in algebra and trigonometry. Four review sheets containing 117 problems provide hints and detailed solutions for each problem. (YP)
The potential use of mobile technology: enhancing accessibility and ...
African Journals Online (AJOL)
The potential use of mobile technology: enhancing accessibility and ... Mobile technology is increasingly being used to support blended learning beyond computer ... limitations of the present study, and suggestions for future research were ...
Technology Enhanced Learning: topics in tel & serious gaming
Van Rosmalen, Peter
2012-01-01
Van Rosmalen, P. (2012, 30 November). Technology Enhanced Learning: topics in tel & serious gaming. Presentation at the course "Hightech Entrepreneurship and new Media (Serious Games)", RWTH Aachen Informatik 5 Information Systems, Aachen, Germany.
Recommender systems for technology enhanced learning research trends and applications
Manouselis, Nikos; Verbert, Katrien
2014-01-01
Presents cutting edge research from leading experts in the growing field of Recommender Systems for Technology Enhanced Learning (RecSys TEL) International contributions are included to demonstrate the merging of various efforts and communities Topics include: Linked Data and the Social Web as Facilitators for TEL Recommender Systems in Research and Practice, Personalised Learning-Plan Recommendations in Game-Based Learning and Recommendations from Heterogeneous Sources in a Technology Enhanced Learning Ecosystem
Central simple Poisson algebras
Institute of Scientific and Technical Information of China (English)
SU Yucai; XU Xiaoping
2004-01-01
Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero.The Lie algebra structures of these Poisson algebras are in general not finitely-graded.
Supporting students' understanding of algebra: Symbolizing in a technology-enhanced classroom
Nickerson, Susan Denise
This dissertation involved an 8-week investigation in a high school classroom to explore how students' prior experiences with dynamic graphs of linear equations supported their efforts to understand systems of linear equations. The researcher and the classroom teacher developed two technology-intensive instructional sequences that were taught by the classroom teacher. The daily collaborative meetings of the researcher and the teacher informed revisions to the instructional sequence. This study used the situated perspective to analyze the collective mathematical development of the class and to compare the ways in which individuals participated in the collective development. According to theorists of the situated perspective, knowing mathematics is considered an aspect of participation in social practices. In order to describe the collective development, the construct of a practice was used to examine the structure, responsibilities, and common activities of the mathematics classroom. I describe four target students' individual growth in terms of a trajectory of participation in the practices of mathematical thinking. Our conjectures about the means of supporting student learning, in the form of curriculum and software, were empirically tested. By providing insight into the process by which a group of students collectively develop understandings of important mathematical ideas, analyses such as this can help teachers and instructional designers anticipate possible ways other groups of students will develop meaning. This work also informs classroom teachers in that situated research such as this embraces the complexity of the classroom. It accounts for what students contribute and what teachers can do to support student learning. This analysis is not prescriptive in the sense of theory informing educational practice. Instead, in this theoretical framework a reflexive relationship exists between theory and practice. Teachers can see how ideas emerged and student conceptions developed within a particular context.
Iachello, F
1995-01-01
1. The Wave Mechanics of Diatomic Molecules. 2. Summary of Elements of Algebraic Theory. 3. Mechanics of Molecules. 4. Three-Body Algebraic Theory. 5. Four-Body Algebraic Theory. 6. Classical Limit and Coordinate Representation. 8. Prologue to the Future. Appendices. Properties of Lie Algebras; Coupling of Algebras; Hamiltonian Parameters
Nonmonotonic logics and algebras
Institute of Scientific and Technical Information of China (English)
CHAKRABORTY Mihir Kr; GHOSH Sujata
2008-01-01
Several nonmonotonie logic systems together with their algebraic semantics are discussed. NM-algebra is defined.An elegant construction of an NM-algebra starting from a Boolean algebra is described which gives rise to a few interesting algebraic issues.
Technology-enhanced suicide prevention interventions: A systematic review.
Kreuze, Elizabeth; Jenkins, Carolyn; Gregoski, Mathew; York, Janet; Mueller, Martina; Lamis, Dorian A; Ruggiero, Kenneth J
2017-07-01
Objective Suicide prevention is a high priority. Scalable and sustainable interventions for suicide prevention are needed to set the stage for population-level impact. This systematic review explores how technology-enhanced interventions target suicide risk and protective factors, using the Centers for Disease Control and Prevention (CDC, 2015) Risk and Protective Factors Ecological Model. Methods Information databases (PsycINFO, PubMed and CINAHL) were systematically searched and records including technology-enhanced interventions for suicide prevention ( n = 3764) were reviewed. Records with varying technologies and diverse methodologies were integrated into the search. Results Review of the records resulted in the inclusion of 16 studies that utilized technology-enhanced interventions to address determinants of suicidal behaviour. This includes the use of standalone or, in most cases, adjunct technology-enhanced interventions for suicide prevention delivered by mobile phone application, text message, telephone, computer, web, CD-ROM and video. Conclusion Intervention effectiveness was variable, but several technology-enhanced interventions have demonstrated effectiveness in reducing suicidal ideation and mental health co-morbidities. Large-scale research and evaluation initiatives are needed to evaluate the costs and long-term population-level impact of these interventions.
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
Solvable quadratic Lie algebras
Institute of Scientific and Technical Information of China (English)
ZHU; Linsheng
2006-01-01
A Lie algebra endowed with a nondegenerate, symmetric, invariant bilinear form is called a quadratic Lie algebra. In this paper, the author investigates the structure of solvable quadratic Lie algebras, in particular, the solvable quadratic Lie algebras whose Cartan subalgebras consist of semi-simple elements, the author presents a procedure to construct a class of quadratic Lie algebras from the point of view of cohomology and shows that all solvable quadratic Lie algebras can be obtained in this way.
DÍaz, R.; Rivas, M.
2010-01-01
In order to study Boolean algebras in the category of vector spaces we introduce a prop whose algebras in set are Boolean algebras. A probabilistic logical interpretation for linear Boolean algebras is provided. An advantage of defining Boolean algebras in the linear category is that we are able to study its symmetric powers. We give explicit formulae for products in symmetric and cyclic Boolean algebras of various dimensions and formulate symmetric forms of the inclusion-exclusion principle.
Bliss, Gilbert Ames
1933-01-01
This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors.... A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on t
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It is a small step toward the Koszul-type algebras. The piecewise-Koszul algebras are,in general, a new class of quadratic algebras but not the classical Koszul ones, simultaneously they agree with both the classical Koszul and higher Koszul algebras in special cases. We give a criteria theorem for a graded algebra A to be piecewise-Koszul in terms of its Yoneda-Ext algebra E(A), and show an A∞-structure on E(A). Relations between Koszul algebras and piecewise-Koszul algebras are discussed. In particular, our results are related to the third question of Green-Marcos.
Methodologies and Intelligent Systems for Technology Enhanced Learning
Gennari, Rosella; Vittorini, Pierpaolo; Prieta, Fernando
2015-01-01
This volume presents recent research on Methodologies and Intelligent Systems for Technology Enhanced Learning. It contains the contributions of MIS4TEL 2015, which took place in Salamanca, Spain,. On June 3rd to 5th 2015. Like the previous edition, this proceedings and the conference is an open forum for discussing intelligent systems for Technology Enhanced Learning and empirical methodologies for their design or evaluation MIS4TEL’15 conference has been organized by University of L’aquila, Free University of Bozen-Bolzano and the University of Salamanca. .
Grätzer, George
1979-01-01
Universal Algebra, heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well-selected additional bibliography of over 1250 papers and books which makes this a fine work for students, instructors, and researchers in the field. "This book will certainly be, in the years to come, the basic reference to the subject." --- The American Mathematical Monthly (First Edition) "In this reviewer's opinion [the author] has more than succeeded in his aim. The problems at the end of each chapter are well-chosen; there are more than 650 of them. The book is especially sui...
Yoneda algebras of almost Koszul algebras
Indian Academy of Sciences (India)
Zheng Lijing
2015-11-01
Let be an algebraically closed field, a finite dimensional connected (, )-Koszul self-injective algebra with , ≥ 2. In this paper, we prove that the Yoneda algebra of is isomorphic to a twisted polynomial algebra $A^!$ [ ; ] in one indeterminate of degree +1 in which $A^!$ is the quadratic dual of , is an automorphism of $A^!$, and = () for each $t \\in A^!$. As a corollary, we recover Theorem 5.3 of [2].
Miyanishi, Masayoshi
2000-01-01
Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. There is a long history of research on projective algebraic surfaces, and there exists a beautiful Enriques-Kodaira classification of such surfaces. The research accumulated by Ramanujan, Abhyankar, Moh, and Nagata and others has established a classification theory of open algebraic surfaces comparable to the Enriques-Kodaira theory. This research provides powerful methods to study the geometry and topology of open algebraic surfaces. The theory of open algebraic surfaces is applicable not only to algebraic geometry, but also to other fields, such as commutative algebra, invariant theory, and singularities. This book contains a comprehensive account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces. Prerequisite to understanding the text is a basic b...
Marchuk, Nikolay
2011-01-01
Exterior algebras and differential forms are widely used in many fields of modern mathematics and theoretical physics. In this paper we define a notion of $N$-metric exterior algebra, which depends on $N$ matrices of structure constants. The usual exterior algebra (Grassmann algebra) can be considered as 0-metric exterior algebra. Clifford algebra can be considered as 1-metric exterior algebra. $N$-metric exterior algebras for $N\\geq2$ can be considered as generalizations of the Grassmann algebra and Clifford algebra. Specialists consider models of gravity that based on a mathematical formalism with two metric tensors. We hope that the considered in this paper 2-metric exterior algebra can be useful for development of this model in gravitation theory. Especially in description of fermions in presence of a gravity field.
Rigidification of algebras over essentially algebraic theories
Rosicky, J
2012-01-01
Badzioch and Bergner proved a rigidification theorem saying that each homotopy simplicial algebra is weakly equivalent to a simplicial algebra. The question is whether this result can be extended from algebraic theories to finite limit theories and from simplicial sets to more general monoidal model categories. We will present some answers to this question.
WEAKLY ALGEBRAIC REFLEXIVITY AND STRONGLY ALGEBRAIC REFLEXIVITY
Institute of Scientific and Technical Information of China (English)
TaoChangli; LuShijie; ChenPeixin
2002-01-01
Algebraic reflexivity introduced by Hadwin is related to linear interpolation. In this paper, the concepts of weakly algebraic reflexivity and strongly algebraic reflexivity which are also related to linear interpolation are introduced. Some properties of them are obtained and some relations between them revealed.
A Framework for Examining the Utility of Technology-Enhanced Items
Russell, Michael
2016-01-01
Interest in and use of technology-enhanced items has increased over the past decade. Given the additional time required to administer many technology-enhanced items and the increased expense required to develop them, it is important for testing programs to consider the utility of technology-enhanced items. The Technology-Enhanced Item Utility…
Sworder, Steven C.
2007-01-01
An experimental two-track intermediate algebra course was offered at Saddleback College, Mission Viejo, CA, between the Fall, 2002 and Fall, 2005 semesters. One track was modeled after the existing traditional California community college intermediate algebra course and the other track was a less rigorous intermediate algebra course in which the…
The Yoneda algebra of a K_2 algebra need not be another K_2 algebra
Cassidy, T.; Phan, Van C.; Shelton, B.
2008-01-01
The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a K2 algebra would be another K2 algebra. We show that this is not necessarily the case by constructing a monomial K2 algebra for which the corresponding Yoneda algebra is not K2.
The Yoneda algebra of a K_2 algebra need not be another K_2 algebra
Cassidy, T; Phan, Van C.; Shelton, B.
2008-01-01
The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a K2 algebra would be another K2 algebra. We show that this is not necessarily the case by constructing a monomial K2 algebra for which the corresponding Yoneda algebra is not K2.
Competence Models in Technology-enhanced Competence-based Learning
Sampson, Demetrios; Fytros, Demetrios
2008-01-01
Please cite as: Sampson, D., & Fytros, D. (2008). Competence Models in Technology-enhanced Competence-based Learning. In H. H. Adelsberger, Kinshuk, J. M. Pawlowski & D. Sampson (Eds.), International Handbook on Information Technologies for Education and Training, 2nd Edition, Springer, June 2008
Competence Models in Technology-enhanced Competence-based Learning
Sampson, Demetrios; Fytros, Demetrios
2008-01-01
Please cite as: Sampson, D., & Fytros, D. (2008). Competence Models in Technology-enhanced Competence-based Learning. In H. H. Adelsberger, Kinshuk, J. M. Pawlowski & D. Sampson (Eds.), International Handbook on Information Technologies for Education and Training, 2nd Edition, Springer, June 2008
Recommender Systems for Technology Enhanced Learning: Research Trends & Applications
Manouselis, Nikos; Verbert, Katrien; Drachsler, Hendrik; Santos, Olga
2014-01-01
As an area, Technology Enhanced Learning (TEL) aims to design, develop and test socio-technical innovations that will support and enhance learning practices of individuals and organizations. Information retrieval is a pivotal activity in TEL and the deployment of recommender systems has attracted in
Modelling Benefits-Oriented Costs for Technology Enhanced Learning
Laurillard, Diana
2007-01-01
The introduction of technology enhanced learning (TEL) methods changes the deployment of the most important resource in the education system: teachers' and learners' time. New technology promises greater personalization and greater productivity, but without careful modeling of the effects on the use of staff time, TEL methods can easily increase…
Organisational Culture and Technology-Enhanced Innovation in Higher Education
Zhu, Chang
2015-01-01
Higher education institutions are evolving and technology often plays a central role in their transformations. Educational changes benefit from a supportive environment. The study examines the relationship between organisational culture and teachers' perceptions of and responses to technology-enhanced innovation among Chinese universities. A…
Critical Approaches to Accessibility for Technology-Enhanced Learning
Lewthwaite, Sarah
2011-01-01
The term "accessibility" is broadly used to describe the degree to which a service or product gives learners the "ability to access" functionality, services or materials. In recent years there has been a push towards accessibility in technology-enhanced learning (TEL) across all levels of education. However, accessibility represents a shifting…
Organisational Culture and Technology-Enhanced Innovation in Higher Education
Zhu, Chang
2015-01-01
Higher education institutions are evolving and technology often plays a central role in their transformations. Educational changes benefit from a supportive environment. The study examines the relationship between organisational culture and teachers' perceptions of and responses to technology-enhanced innovation among Chinese universities. A…
Teacher Learning of Technology-Enhanced Formative Assessment
Beatty, Ian D.; Feldman, Allan; Leonard, William J.; Gerace, William J.; St. Cyr, Karen; Lee, Hyunju; Harris, Robby
2008-01-01
"Technology-Enhanced Formative Assessment" (TEFA) is an innovative pedagogy for teaching secondary school science or mathematics with "classroom response system" technology. "Teacher Learning of TEFA" (TLT) is a five year research project studying teacher change in the context of an intensive, sustained, on-site professional development (PD)…
Algebraic cobordism theory attached to algebraic equivalence
Krishna, Amalendu
2012-01-01
After the algebraic cobordism theory of Levine-Morel, we develop a theory of algebraic cobordism modulo algebraic equivalence. We prove that this theory can reproduce Chow groups modulo algebraic equivalence and the zero-th semi-topological K-groups. We also show that with finite coefficients, this theory agrees with the algebraic cobordism theory. We compute our cobordism theory for some low dimensional or special types of varieties. The results on infinite generation of some Griffiths groups by Clemens and on smash-nilpotence by Voevodsky and Voisin are also lifted and reinterpreted in terms of this cobordism theory.
Workshop on Commutative Algebra
Simis, Aron
1990-01-01
The central theme of this volume is commutative algebra, with emphasis on special graded algebras, which are increasingly of interest in problems of algebraic geometry, combinatorics and computer algebra. Most of the papers have partly survey character, but are research-oriented, aiming at classification and structural results.
Probabilistic Concurrent Kleene Algebra
Directory of Open Access Journals (Sweden)
Annabelle McIver
2013-06-01
Full Text Available We provide an extension of concurrent Kleene algebras to account for probabilistic properties. The algebra yields a unified framework containing nondeterminism, concurrency and probability and is sound with respect to the set of probabilistic automata modulo probabilistic simulation. We use the resulting algebra to generalise the algebraic formulation of a variant of Jones' rely/guarantee calculus.
Introduction to relation algebras relation algebras
Givant, Steven
2017-01-01
The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly ...
Generalized Quantum Current Algebras
Institute of Scientific and Technical Information of China (English)
ZHAO Liu
2001-01-01
Two general families of new quantum-deformed current algebras are proposed and identified both as infinite Hopf family of algebras, a structure which enables one to define "tensor products" of these algebras. The standard quantum affine algebras turn out to be a very special case of the two algebra families, in which case the infinite Hopf family structure degenerates into a standard Hopf algebra. The relationship between the two algebraic families as well as thefr various special examples are discussed, and the free boson representation is also considered.
El-Chaar, Caroline
2012-01-01
In this thesis, four realizations of the Onsager algebra are explored. We begin with its original definition as introduced by Lars Onsager. We then examine how the Onsager algebra can be presented as a Lie algebra with two generators and two relations. The third realization of the Onsager algebra consists of viewing it as an equivariant map algebra which then gives us the tools to classify its closed ideals. Finally, we examine the Onsager algebra as a subalgebra of the tetrahedron algebra. Using this fourth realization, we explicitly describe all its ideals.
Perturbations of planar algebras
Das, Paramita; Gupta, Ved Prakash
2010-01-01
We introduce the concept of {\\em weight} of a planar algebra $P$ and construct a new planar algebra referred as the {\\em perturbation of $P$} by the weight. We establish a one-to-one correspondence between pivotal structures on 2-categories and perturbations of planar algebras by weights. To each bifinite bimodule over $II_1$-factors, we associate a {\\em bimodule planar algebra} bimodule corresponds naturally with sphericality of the bimodule planar algebra. As a consequence of this, we reproduce an extension of Jones' theorem (of associating 'subfactor planar algebras' to extremal subfactors). Conversely, given a bimodule planar algebra, we construct a bifinite bimodule whose associated bimodule planar algebra is the one which we start with using perturbations and Jones-Walker-Shlyakhtenko-Kodiyalam-Sunder method of reconstructing an extremal subfactor from a subfactor planar algebra. We show that the perturbation class of a bimodule planar algebra contains a unique spherical unimodular bimodule planar algeb...
Yangians and transvector algebras
Molev, A. I.
1998-01-01
Olshanski's centralizer construction provides a realization of the Yangian for the Lie algebra gl(n) as a subalgebra in the projective limit of a chain of centralizers in the universal enveloping algebras. We give a modified version of this construction based on a quantum analog of Sylvester's theorem. We then use it to get an algebra homomorphism from the Yangian to the transvector algebra associated with the general linear Lie algebras. The results are applied to identify the elementary rep...
Institute of Scientific and Technical Information of China (English)
赵雪芬
2016-01-01
The problems of the linear algebra in independent college are analyzed. In order to cultivate applied talents, three dimensional teaching mode were explored in independent school by teaching objectives, teaching content, teaching methods, teaching resource and assessment system. Some advice and effective measures of teaching mode are proposed.%文章针对独立学院线性代数教学中出现的问题，根据独立学院培养应用型人才的培养目标，从教学目标、教学内容、教学方法、教学资源及考核方式五个方面对独立学院线性代数课程的立体化教学模式进行探讨，提出了教学模式改革的建议和措施。
Curricular Pathways to Algebra I in Eighth Grade
Griffin, Melinda Rose
2014-01-01
Nationwide, schools are pushing for more students to take Algebra I in eighth grade, prior to formally entering high school. The algebra-for-all movement has been intended to alleviate equity issues which held minority and low-income students back from entering a college-preparatory path in high school. Students with the needed content,…
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
Institute of Scientific and Technical Information of China (English)
Jia-feng; Lü
2007-01-01
[1]Priddy S.Koszul resolutions.Trans Amer Math Soc,152:39-60 (1970)[2]Beilinson A,Ginszburg V,Soergel W.Koszul duality patterns in representation theory.J Amer Math Soc,9:473-525 (1996)[3]Aquino R M,Green E L.On modules with linear presentations over Koszul algebras.Comm Algebra,33:19-36 (2005)[4]Green E L,Martinez-Villa R.Koszul and Yoneda algebras.Representation theory of algebras (Cocoyoc,1994).In:CMS Conference Proceedings,Vol 18.Providence,RI:American Mathematical Society,1996,247-297[5]Berger R.Koszulity for nonquadratic algebras.J Algebra,239:705-734 (2001)[6]Green E L,Marcos E N,Martinez-Villa R,et al.D-Koszul algebras.J Pure Appl Algebra,193:141-162(2004)[7]He J W,Lu D M.Higher Koszul Algebras and A-infinity Algebras.J Algebra,293:335-362 (2005)[8]Green E L,Marcos E N.δ-Koszul algebras.Comm Algebra,33(6):1753-1764 (2005)[9]Keller B.Introduction to A-infinity algebras and modules.Homology Homotopy Appl,3:1-35 (2001)[10]Green E L,Martinez-Villa R,Reiten I,et al.On modules with linear presentations.J Algebra,205(2):578-604 (1998)[11]Keller B.A-infinity algebras in representation theory.Contribution to the Proceedings of ICRA Ⅸ.Beijing:Peking University Press,2000[12]Lu D M,Palmieri J H,Wu Q S,et al.A∞-algebras for ring theorists.Algebra Colloq,11:91-128 (2004)[13]Weibel C A.An Introduction to homological algebra.Cambridge Studies in Avanced Mathematics,Vol 38.Cambridge:Cambridge University Press,1995
A Course in Algebra and Trigonometry with Computer Programming.
Beavers, Mildred; And Others
This textbook was developed by the Colorado Schools Computing Science (CSCS) Curriculum Development Project. It can be used with high school or college students in an integrated presentation of second-year algebra, trigonometry, and beginning computer programing. (MK)
Goldmann, H
1990-01-01
The first part of this monograph is an elementary introduction to the theory of Fréchet algebras. Important examples of Fréchet algebras, which are among those considered, are the algebra of all holomorphic functions on a (hemicompact) reduced complex space, and the algebra of all continuous functions on a suitable topological space.The problem of finding analytic structure in the spectrum of a Fréchet algebra is the subject of the second part of the book. In particular, the author pays attention to function algebraic characterizations of certain Stein algebras (= algebras of holomorphic functions on Stein spaces) within the class of Fréchet algebras.
A Technology Enhanced Learning Model for Quality Education
Sherly, Elizabeth; Uddin, Md. Meraj
Technology Enhanced Learning and Teaching (TELT) Model provides learning through collaborations and interactions with a framework for content development and collaborative knowledge sharing system as a supplementary for learning to improve the quality of education system. TELT deals with a unique pedagogy model for Technology Enhanced Learning System which includes course management system, digital library, multimedia enriched contents and video lectures, open content management system and collaboration and knowledge sharing systems. Open sources like Moodle and Wiki for content development, video on demand solution with a low cost mid range system, an exhaustive digital library are provided in a portal system. The paper depicts a case study of e-learning initiatives with TELT model at IIITM-K and how effectively implemented.
The Impact of New State Accountability Standards on Algebra I Students
Heath, Kyle G.
2013-01-01
The purpose of this quasi-experimental quantitative study was to determine if a new Algebra I curriculum resulted in improved student performance on the state Algebra I exam. The treatment group consisted of 383 9th grade Algebra I students who received the college-ready standards-based (CRSB) curricula. The control group consisted of 338 9th…
What Is the Place of Algebra in the K-12 Mathematics Program?
Fendel, Dan; And Others
1997-01-01
As times change, so has the role of algebra in the educational program. The Interactive Mathematics Program (IMP) offers secondary students an opportunity to learn algebra in a college preparatory sequence that combines basic skills, problem solving, and conceptual understanding while integrating algebra into a problem-based program. Designed for…
The Impact of New State Accountability Standards on Algebra I Students
Heath, Kyle G.
2013-01-01
The purpose of this quasi-experimental quantitative study was to determine if a new Algebra I curriculum resulted in improved student performance on the state Algebra I exam. The treatment group consisted of 383 9th grade Algebra I students who received the college-ready standards-based (CRSB) curricula. The control group consisted of 338 9th…
A Proposed Algebra Assessment for Use in a Problem-Analysis Framework
Walick, Christopher M.; Burns, Matthew K.
2017-01-01
Algebra is critical to high school graduation and college success, but student achievement in algebra frequently falls significantly below expected proficiency levels. While existing research emphasizes the importance of quality algebra instruction, there is little research about how to conduct problem analysis for struggling secondary students.…
Deformed Virasoro Algebras from Elliptic Quantum Algebras
Avan, J.; Frappat, L.; Ragoucy, E.
2017-09-01
We revisit the construction of deformed Virasoro algebras from elliptic quantum algebras of vertex type, generalizing the bilinear trace procedure proposed in the 1990s. It allows us to make contact with the vertex operator techniques that were introduced separately at the same period. As a by-product, the method pinpoints two critical values of the central charge for which the center of the algebra is extended, as well as (in the gl(2) case) a Liouville formula.
Samuel, Pierre
2008-01-01
Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal
Institute of Scientific and Technical Information of China (English)
PENG Jia-yin
2011-01-01
The notions of norm and distance in BCI-algebras are introduced,and some basic properties in normed BCI-algebras are given.It is obtained that the isomorphic(homomorphic)image and inverse image of a normed BCI-algebra are still normed BCI-algebras.The relations of normaled properties between BCI-algebra and Cartesian product of BCIalgebras are investigated.The limit notion of sequence of points in normed BCI-algebras is introduced,and its related properties are investigated.
Clifford Algebra with Mathematica
Aragon-Camarasa, G; Aragon, J L; Rodriguez-Andrade, M A
2008-01-01
The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, a package for Clifford algebra calculations for the computer algebra program Mathematica is introduced through a presentation of the main ideas of Clifford algebras and illustrative examples. This package can be a useful computational tool since allows the manipulation of all these mathematical objects. It also includes the possibility of visualize elements of a Clifford algebra in the 3-dimensional space.
Boicescu, V; Georgescu, G; Rudeanu, S
1991-01-01
The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory.This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as &THgr;-algebras with negation.Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.
Abian, Alexander
1973-01-01
Linear Associative Algebras focuses on finite dimensional linear associative algebras and the Wedderburn structure theorems.The publication first elaborates on semigroups and groups, rings and fields, direct sum and tensor product of rings, and polynomial and matrix rings. The text then ponders on vector spaces, including finite dimensional vector spaces and matrix representation of vectors. The book takes a look at linear associative algebras, as well as the idempotent and nilpotent elements of an algebra, ideals of an algebra, total matrix algebras and the canonical forms of matrices, matrix
Cellularity of diagram algebras as twisted semigroup algebras
Wilcox, Stewart
2010-01-01
The Temperley-Lieb and Brauer algebras and their cyclotomic analogues, as well as the partition algebra, are all examples of twisted semigroup algebras. We prove a general theorem about the cellularity of twisted semigroup algebras of regular semigroups. This theorem, which generalises a recent result of East about semigroup algebras of inverse semigroups, allows us to easily reproduce the cellularity of these algebras.
Hom-alternative algebras and Hom-Jordan algebras
Makhlouf, Abdenacer
2009-01-01
The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a polarization of Hom-associative algebra leads to Hom-Jordan algebra.
Algebra adds value to mathematical biology education
Bland, Susan
2009-01-01
As mathematics continues to become an increasingly important component in undergraduate biology programs, a more comprehensive understanding of the use of algebraic models is needed by the next generation of biologists to facilitate new advances in the life sciences, according to researchers at Sweet Briar College and the Virginia Bioinformatics Institute at Virginia Tech.
Asveld, P.R.J.
1976-01-01
Operaties op formele talen geven aanleiding tot bijbehorende operatoren op families talen. Bepaalde onderwerpen uit de algebra (universele algebra, tralies, partieel geordende monoiden) kunnen behulpzaam zijn in de studie van verzamelingen van dergelijke operatoren.
Lie Algebra of Noncommutative Inhomogeneous Hopf Algebra
Lagraa, M
1997-01-01
We construct the vector space dual to the space of right-invariant differential forms construct from a first order differential calculus on inhomogeneous quantum group. We show that this vector space is equipped with a structure of a Hopf algebra which closes on a noncommutative Lie algebra satisfying a Jacobi identity.
Cylindric-like algebras and algebraic logic
Ferenczi, Miklós; Németi, István
2013-01-01
Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.
Categories and Commutative Algebra
Salmon, P
2011-01-01
L. Badescu: Sur certaines singularites des varietes algebriques.- D.A. Buchsbaum: Homological and commutative algebra.- S. Greco: Anelli Henseliani.- C. Lair: Morphismes et structures algebriques.- B.A. Mitchell: Introduction to category theory and homological algebra.- R. Rivet: Anneaux de series formelles et anneaux henseliens.- P. Salmon: Applicazioni della K-teoria all'algebra commutativa.- M. Tierney: Axiomatic sheaf theory: some constructions and applications.- C.B. Winters: An elementary lecture on algebraic spaces.
Algebraic statistics computational commutative algebra in statistics
Pistone, Giovanni; Wynn, Henry P
2000-01-01
Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model.As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science.
Connecting Arithmetic to Algebra
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
Bergstra, J.A.; Fokkink, W.J.; Middelburg, C.A.
2008-01-01
Timed frames are introduced as objects that can form a basis of a model theory for discrete time process algebra. An algebraic setting for timed frames is proposed and results concerning its connection with discrete time process algebra are given. The presented theory of timed frames captures the ba
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Deficiently Extremal Gorenstein Algebras
Indian Academy of Sciences (India)
Pavinder Singh
2011-08-01
The aim of this article is to study the homological properties of deficiently extremal Gorenstein algebras. We prove that if / is an odd deficiently extremal Gorenstein algebra with pure minimal free resolution, then the codimension of / must be odd. As an application, the structure of pure minimal free resolution of a nearly extremal Gorenstein algebra is obtained.
REAL PIECEWISE ALGEBRAIC VARIETY
Institute of Scientific and Technical Information of China (English)
Ren-hong Wang; Yi-sheng Lai
2003-01-01
We give definitions of real piecewise algebraic variety and its dimension. By using the techniques of real radical ideal, P-radical ideal, affine Hilbert polynomial, Bernstein-net form of polynomials on simplex, and decomposition of semi-algebraic set, etc., we deal with the dimension of the real piecewise algebraic variety and real Nullstellensatz in Cμ spline ring.
Equivariant Algebraic Cobordism
Heller, Jeremiah
2010-01-01
We define equivariant algebraic cobordism for a connected linear algebraic group $G$ over a field of characteristic zero. The construction is based on Totaro's idea of using algebraic approximations for $BG$. We establish the analogous of the properties of an oriented cohomology theory, prove some of the expected properties from an equivariant theory, and make a few computations.
Bases of Schur algebras associated to cellularly stratified diagram algebras
Bowman, C
2011-01-01
We examine homomorphisms between induced modules for a certain class of cellularly stratified diagram algebras, including the BMW algebra, Temperley-Lieb algebra, Brauer algebra, and (quantum) walled Brauer algebra. We define the `permutation' modules for these algebras, these are one-sided ideals which allow us to study the diagrammatic Schur algebras of Hartmann, Henke, Koenig and Paget. We construct bases of these Schur algebras in terms of modified tableaux. On the way we prove that the (quantum) walled Brauer algebra and the Temperley-Lieb algebra are both cellularly stratified and therefore have well-defined Specht filtrations.
International Workshop on Evidence-Based Technology Enhanced Learning
Gennari, Rosella; Marenzi, Ivana; Prieta, Fernando; Rodríguez, Juan
2012-01-01
Research on Technology Enhanced Learning (TEL) investigates how information and communication technologies can be designed in order to support pedagogical activities. The workshop proceedings collects contributions concerning evidence based TEL systems, like their design following EBD principles as well as studies or best practices that educators, education stakeholders or psychologists used to diagnose or improve their students' learning skills, including students with specific difficulties. The international ebTEL’12 workshop wants to be a forum in which TEL researchers and practitioners alike can discuss ideas, projects, and lessons related to ebTEL. The workshop takes place in Salamanca, Spain, on March 28th-30th 2012.
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
Computer algebra and operators
Fateman, Richard; Grossman, Robert
1989-01-01
The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.
Indian Academy of Sciences (India)
Antonio J Calderón Martín; Manuel Forero Piulestán; José M Sánchez Delgado
2012-05-01
We study the structure of split Malcev algebras of arbitrary dimension over an algebraically closed field of characteristic zero. We show that any such algebras is of the form $M=\\mathcal{U}+\\sum_jI_j$ with $\\mathcal{U}$ a subspace of the abelian Malcev subalgebra and any $I_j$ a well described ideal of satisfying $[I_j, I_k]=0$ if ≠ . Under certain conditions, the simplicity of is characterized and it is shown that is the direct sum of a semisimple split Lie algebra and a direct sum of simple non-Lie Malcev algebras.
Lectures on algebraic statistics
Drton, Mathias; Sullivant, Seth
2009-01-01
How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.
The Boolean algebra and central Galois algebras
Directory of Open Access Journals (Sweden)
George Szeto
2001-01-01
Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B∣bx=g(xb for all x∈B} for g∈G, and BJg=Beg for a central idempotent eg. Then a relation is given between the set of elements in the Boolean algebra (Ba,≤ generated by {0,eg∣g∈G} and a set of subgroups of G, and a central Galois algebra Be with a Galois subgroup of G is characterized for an e∈Ba.
On Derivations Of Genetic Algebras
Mukhamedov, Farrukh; Qaralleh, Izzat
2014-11-01
A genetic algebra is a (possibly non-associative) algebra used to model inheritance in genetics. In application of genetics this algebra often has a basis corresponding to genetically different gametes, and the structure constant of the algebra encode the probabilities of producing offspring of various types. In this paper, we find the connection between the genetic algebras and evolution algebras. Moreover, we prove the existence of nontrivial derivations of genetic algebras in dimension two.
Linear algebra meets Lie algebra: the Kostant-Wallach theory
Shomron, Noam; Parlett, Beresford N.
2008-01-01
In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.
Linear algebra meets Lie algebra: the Kostant-Wallach theory
Shomron, Noam; Parlett, Beresford N.
2008-01-01
In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.
The Hall Algebra of Cyclic Serial Algebra
Institute of Scientific and Technical Information of China (English)
郭晋云
1994-01-01
In this paper, orders <1 and <2 on ((Z)+)nm are introduced and also regarded as orders on the isomorphism classes of finite modules of finite .cyclic algebra R with n simple modules and all the indecomposable projective modules have length m through a one-to-one correspondence between ((Z)+)nm and the isomorphism classes of finite R modules. Using this we prove that the Hall algebra of a cyclic serial algebra is identified with its Loewy subalgebra, and its rational extension has a basis of BPW type, and is a (((Z)+)nm, <2) filtered ring with the associated graded ring as an iterated skew polynomial ring. These results are also generalized to the Hall algebra of a tube over a finite field.
Supporting students' knowledge integration with technology-enhanced inquiry curricula
Chiu, Jennifer Lopseen
Dynamic visualizations of scientific phenomena have the potential to transform how students learn and understand science. Dynamic visualizations enable interaction and experimentation with unobservable atomic-level phenomena. A series of studies clarify the conditions under which embedding dynamic visualizations in technology-enhanced inquiry instruction can help students develop robust and durable chemistry knowledge. Using the knowledge integration perspective, I designed Chemical Reactions, a technology-enhanced curriculum unit, with a partnership of teachers, educational researchers, and chemists. This unit guides students in an exploration of how energy and chemical reactions relate to climate change. It uses powerful dynamic visualizations to connect atomic level interactions to the accumulation of greenhouse gases. The series of studies were conducted in typical classrooms in eleven high schools across the country. This dissertation describes four studies that contribute to understanding of how visualizations can be used to transform chemistry learning. The efficacy study investigated the impact of the Chemical Reactions unit compared to traditional instruction using pre-, post- and delayed posttest assessments. The self-monitoring study used self-ratings in combination with embedded assessments to explore how explanation prompts help students learn from dynamic visualizations. The self-regulation study used log files of students' interactions with the learning environment to investigate how external feedback and explanation prompts influence students' exploration of dynamic visualizations. The explanation study compared specific and general explanation prompts to explore the processes by which explanations benefit learning with dynamic visualizations. These studies delineate the conditions under which dynamic visualizations embedded in inquiry instruction can enhance student outcomes. The studies reveal that visualizations can be deceptively clear
Evolution algebras and their applications
Tian, Jianjun Paul
2008-01-01
Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.
Finite-dimensional (*)-serial algebras
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Let A be a finite-dimensional associative algebra with identity over a field k. In this paper we introduce the concept of (*)-serial algebras which is a generalization of serial algebras. We investigate the properties of (*)-serial algebras, and we obtain suficient and necessary conditions for an associative algebra to be (*)-serial.
On the Toroidal Leibniz Algebras
Institute of Scientific and Technical Information of China (English)
Dong LIU; Lei LIN
2008-01-01
Toroidal Leibniz algebras are the universal central extensions of the iterated loop algebras gOC[t±11 ,...,t±v1] in the category of Leibniz algebras. In this paper, some properties and representations of toroidal Leibniz algebras are studied. Some general theories of central extensions of Leibniz algebras are also obtained.
Directory of Open Access Journals (Sweden)
R. A. Borzooei
2006-01-01
Full Text Available We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.
Borzooei, R. A.; Dudek, W. A.; Koohestani, N.
2006-01-01
We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.
Relative Homological Algebra Volume 1
2011-01-01
This is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists. The book is also suitable for an introductory course in commutative and ordinary homological algebra.
Teacher Learning of Technology-Enhanced Formative Assessment
Beatty, Ian D; Leonard, William J; Gerace, William J; Cyr, Karen St; Lee, Hyunju; Harris, Robby
2008-01-01
Technology-Enhanced Formative Assessment (TEFA) is a pedagogy for teaching with classroom response technology. Teacher Learning of TEFA is a five-year research project studying teacher change, in the context of an intensive professional development program designed to help science and mathematics teachers learn TEFA. First, we provide an overview of the project's participating teachers, its intervention (consisting of the technology, the pedagogy, and the professional development program), and its research design. Then, we present narratives describing the unfolding change process experienced by four teachers. Afterward, we present some preliminary findings of the research, describe a "model for the co-evolution of teacher and pedagogy" that we are developing, and identify general implications for professional development.
Knowledge Generation in Technology-Enhanced Health Exhibitions
DEFF Research Database (Denmark)
Magnussen, Rikke; Kharlamov, Nikita; Zachariasssen, Maria
2016-01-01
This paper presents results from eye-tracking studies of audience interaction and knowledge generation in the technology-enhanced health promotion exhibition PULSE at a science centre in Copenhagen, Denmark. The main purpose of the study was to understand what types of knowledge audiences build...... in health promotion exhibitions designed to include direct physical interaction. The current study is part of the larger PULSE project, which aims to develop innovative health promotion activities that include a science museum exhibition as a key setting. The primary target group is families with children...... age 6–12. Health promotion technologies are defined here, as technologies designed specifically for the purpose of health promotion, be they educational or focused on physical activities. The study was conducted in late 2015 and comprised eight families with children in 2nd-6th grade visiting...
Technology-enhanced learning in transnational higher education.
Arunasalam, Nirmala
2016-11-24
Some university schools of nursing in Australia and the UK have developed collaborative links with Malaysia to deliver part-time Transnational Higher Education (TNHE) post-registration top-up nursing degree courses. It enables nurses trained to diploma level to upgrade to a degree qualification. The views of 18 Malaysian nurses who had studied with one Australian and two UK TNHE universities were explored using a hermeneutic phenomenological approach. Participants recruited via convenience and snowball sampling methods were interviewed in English and Bahasa Malaysia (Malaysian language). Thematic analysis were used to analyse data. Findings indicated nurses' frustration with technology-enhanced teaching and learning and a lack of support throughout the programme. Although nurses developed confidence in using computer technology, they remained disappointed with the level of academic support. The data and some useful strategies outlined provide important insights for TNHE providers, the Malaysian Nursing Board and private hospital employers to consider for enhancing nurses learning and experiences.
Iachello, Francesco
2015-01-01
This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...
Developable algebraic surfaces
Institute of Scientific and Technical Information of China (English)
CHEN Dongren; WANG Guojin
2004-01-01
An algebraic surface can be defined by an implicit polynomial equation F(x,y,z)=0. In this paper, general characterizations of developable algebraic surfaces of arbitrary degree are presented. Using the shift operators of the subscripts of Bézier ordinates, the uniform apparent discriminants of developable algebraic surfaces to their Bézier ordinates are given directly. To degree 2 algebraic surfaces, which are widely used in computer aided geometric design and graphics, all possible developable surface types are obtained. For more conveniently applying algebraic surfaces of high degree to computer aided geometric design, the notion of ε-quasi-developable surfaces is introduced, and an example of using a quasi-developable algebraic surface of degree 3 to interpolate three curves of degree 2 is given.
Dougherty, Shaun M.; Goodman, Joshua S.; Hill, Darryl V.; Litke, Erica G.; Page, Lindsay C.
2015-01-01
Taking algebra by eighth grade is considered an important milestone on the pathway to college readiness. We highlight a collaboration to investigate one district's effort to increase middle school algebra course-taking. In 2010, the Wake County Public Schools began assigning middle school students to accelerated math and eighth-grade algebra based…
Dougherty, Shaun M.; Goodman, Joshua S.; Hill, Darryl V.; Litke, Erica G.; Page, Lindsay C.
2015-01-01
Taking algebra by eighth grade is considered an important milestone on the pathway to college readiness. We highlight a collaboration to investigate one district's effort to increase middle school algebra course-taking. In 2010, the Wake County Public Schools began assigning middle school students to accelerated math and eighth-grade algebra based…
Algebra Automorphisms of Quantized Enveloping Algebras Uq(■)
Institute of Scientific and Technical Information of China (English)
查建国
1994-01-01
The algebra automorphisms of the quantized enveloping algebra Uq(g) are discussed, where q is generic. To some extent, all quantum deformations of automorphisms of the simple Lie algebra g have been determined.
Cayley-Dickson and Clifford Algebras as Twisted Group Algebras
Bales, John W
2011-01-01
The effect of some properties of twisted groups on the associated algebras, particularly Cayley-Dickson and Clifford algebras. It is conjectured that the Hilbert space of square-summable sequences is a Cayley-Dickson algebra.
Symmetric Extended Ockham Algebras
Institute of Scientific and Technical Information of China (English)
T.S. Blyth; Jie Fang
2003-01-01
The variety eO of extended Ockham algebras consists of those algealgebra with an additional endomorphism k such that the unary operations f and k commute. Here, we consider the cO-algebras which have a property of symmetry. We show that there are thirty two non-isomorphic subdirectly irreducible symmetric extended MS-algebras and give a complete description of them.2000 Mathematics Subject Classification: 06D15, 06D30
Krichever, Igor M.; Sheinman, Oleg K.
2007-01-01
In this paper we develop a general concept of Lax operators on algebraic curves introduced in [1]. We observe that the space of Lax operators is closed with respect to their usual multiplication as matrix-valued functions. We construct the orthogonal and symplectic analogs of Lax operators, prove that they constitute almost graded Lie algebras and construct local central extensions of those Lie algebras.
Prediction of Algebraic Instabilities
Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael
2016-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.
Albert, A A
1939-01-01
The first three chapters of this work contain an exposition of the Wedderburn structure theorems. Chapter IV contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory. The fifth chapter contains the foundation of the theory of crossed products and of their special case, cyclic algebras. The theory of exponents is derived there as well as the consequent factorization of normal division algebras into direct factors of prime-power degree. Chapter VI con
Kurosh, A G; Stark, M; Ulam, S
1965-01-01
Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the
Directory of Open Access Journals (Sweden)
Frank Roumen
2017-01-01
Full Text Available We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Kunneth and Mayer-Vietoris sequences. The second way involves a chain complex of ordered abelian groups, and gives rise to a cohomological characterization of state extensions on effect algebras. This has applications to no-go theorems in quantum foundations, such as Bell's theorem.
Algebraic extensions of fields
McCarthy, Paul J
1991-01-01
""...clear, unsophisticated and direct..."" - MathThis textbook is intended to prepare graduate students for the further study of fields, especially algebraic number theory and class field theory. It presumes some familiarity with topology and a solid background in abstract algebra. Chapter 1 contains the basic results concerning algebraic extensions. In addition to separable and inseparable extensions and normal extensions, there are sections on finite fields, algebraically closed fields, primitive elements, and norms and traces. Chapter 2 is devoted to Galois theory. Besides the fundamenta
Balan, Adriana
2010-01-01
We extend Barr's well-known characterization of the final coalgebra of a $Set$-endofunctor as the completion of its initial algebra to the Eilenberg-Moore category of algebras for a $Set$-monad $\\mathbf{M}$ for functors arising as liftings. As an application we introduce the notion of commuting pair of endofunctors with respect to the monad $\\mathbf{M}$ and show that under reasonable assumptions, the final coalgebra of one of the endofunctors involved can be obtained as the free algebra generated by the initial algebra of the other endofunctor.
Underwood, Robert G
2015-01-01
This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras, and Hopf algebras. The last chapter (Chapter 4) discusses several applications of Hopf algebras, some of which are further developed in the author’s 2011 publication, An Introduction to Hopf Algebras. The book may be used as the main text or as a supplementary text for a graduate algebra course. Prerequisites for this text include standard material on groups, rings, modules, algebraic extension fields, finite fields, and linearly recursive sequences. The book consists of four chapters. Chapter 1 introduces algebras and coalgebras over a field K; Chapter 2 treats bialgebras; Chapter 3 discusses Hopf algebras and Chapter 4 consists of three applications of Hopf algebras. Each chapter begins with a short overview and ends with a collection of exercises which are designed to review and reinforce the material. Exercises range from straightforw...
Solomon, Alan D
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean
Relations Between BZMVdM-Algebra and Other Algebras
Institute of Scientific and Technical Information of China (English)
高淑萍; 邓方安; 刘三阳
2003-01-01
Some properties of BZMVdM-algebra are proved, and a new operator is introduced. It is shown that the substructure of BZMVdM-algebra can produce a quasi-lattice implication algebra. The relations between BZMVdM-algebra and other algebras are discussed in detail. A pseudo-distance function is defined in linear BZMVdM-algebra, and its properties are derived.
Differential Hopf algebra structures on the universal enveloping algebra ofa Lie algebra
Hijligenberg, N.W. van den; Martini, R.
1995-01-01
We discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of $U(g
Differential Hopf algebra structures on the universal enveloping algebra ofa Lie algebra
N.W. van den Hijligenberg; R. Martini
1995-01-01
textabstractWe discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra
Differential Hopf algebra structures on the universal enveloping algebra of a Lie algebra
van den Hijligenberg, N.W.; van den Hijligenberg, N.W.; Martini, Ruud
1995-01-01
We discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of
Tubular algebras and affine Kac-Moody algebras
Institute of Scientific and Technical Information of China (English)
2007-01-01
The purpose of this paper is to construct quotient algebras L(A)1C/I(A) of complex degenerate composition Lie algebras L(A)1C by some ideals, where L(A)1C is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)1C/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)1C generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)1C generated by simple A-modules.
Tubular algebras and affine Kac-Moody algebras
Institute of Scientific and Technical Information of China (English)
Zheng-xin CHEN; Ya-nan LIN
2007-01-01
The purpose of this paper is to construct quotient algebras L(A)C1/I(A) of complex degenerate composition Lie algebras L(A)C1 by some ideals, where L(A)C1 is defined via Hall algebras of tubular algebras A, and to prove that the quotient algebras L(A)C1/I(A) are isomorphic to the corresponding affine Kac-Moody algebras. Moreover, it is shown that the Lie algebra Lre(A)C1 generated by A-modules with a real root coincides with the degenerate composition Lie algebra L(A)C1 generated by simple A-modules.
The Virasoro vertex algebra and factorization algebras on Riemann surfaces
Williams, Brian
2017-08-01
This paper focuses on the connection of holomorphic two-dimensional factorization algebras and vertex algebras which has been made precise in the forthcoming book of Costello-Gwilliam. We provide a construction of the Virasoro vertex algebra starting from a local Lie algebra on the complex plane. Moreover, we discuss an extension of this factorization algebra to a factorization algebra on the category of Riemann surfaces. The factorization homology of this factorization algebra is computed as the correlation functions. We provide an example of how the Virasoro factorization algebra implements conformal symmetry of the beta-gamma system using the method of effective BV quantization.
Indian Academy of Sciences (India)
Cătălin Ciupală
2005-02-01
In this paper we introduce non-commutative fields and forms on a new kind of non-commutative algebras: -algebras. We also define the Frölicher–Nijenhuis bracket in the non-commutative geometry on -algebras.
Language Approaches to Beginning Algebra.
Rotman, Jack W.
1990-01-01
Ideas which apply language concepts to the study of algebra are presented. Discussed are algebraic notation, vocabulary, vocalization, and written assignments. The careful use of algebraic language in mathematics classes is emphasized. (CW)
Uniform Exponential Growth in Algebras /
Briggs, Christopher Alan
2013-01-01
We consider uniform exponential growth in algebras. We give conditions for the uniform exponential growth of descending-filtered algebras and prove that an N-graded algebra has uniform exponential growth if it has exponential growth. We use this to prove that Golod- Shafarevich algebras and group algebras of Golod- Shafarevich groups have uniform exponential growth. We prove that the twisted Laurent extension of a free commutative polynomial algebra with respect to an endomorphism with some e...
Automorphism groups of some algebras
Institute of Scientific and Technical Information of China (English)
PARK; Hong; Goo; LEE; Jeongsig; CHOI; Seul; Hee; NAM; Ki-Bong
2009-01-01
The automorphism groups of algebras are found in many papers. Using auto-invariance, we find the automorphism groups of the Laurent extension of the polynomial ring and the quantum n-plane (respectively, twisting polynomial ring) in this work. As an application of the results of this work, we can find the automorphism group of a twisting algebra. We define a generalized Weyl algebra and show that the generalized Weyl algebra is simple. We also find the automorphism group of a generalized Weyl algebra. We show that the generalized Weyl algebra Am,m+n is the universal enveloping algebra of the generalized Witt algebra W(m,m + n).
Automorphism groups of some algebras
Institute of Scientific and Technical Information of China (English)
PARK Hong Goo; LEE Jeongsig; CHOI Seul Hee; CHEN XueQing; NAM Ki-Bong
2009-01-01
The automorphism groups of algebras are found in many papers. Using auto-invariance, we find the automorphism groups of the Laurent extension of the polynomial ring and the quantum n-plane (respectively, twisting polynomial ring) in this work. As an application of the results of this work, we can find the automorphism group of a twisting algebra. We define a generalized Weyl algebra and show that the generalized Weyl algebra is simple. We also find the automorphism group of a generalized Weyl algebra. We show that the generalized Weyl algebra Am,m+n is the universal enveloping algebra of the generalized Witt algebra W(m, m+n).
Levy, Alissa Beth
2012-01-01
The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this dissertation,…
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
Derived equivalence of algebras
Institute of Scientific and Technical Information of China (English)
杜先能
1997-01-01
The derived equivalence and stable equivalence of algebras RmA and RmB are studied It is proved, using the tilting complex, that RmA and RmB are derived-equivalent whenever algebras A and B are derived-equivalent
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
Levy, Alissa Beth
2012-01-01
The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this dissertation,…
Levy, Alissa Beth
2012-01-01
The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…
Tolar, Tammy Daun; Lederberg, Amy R.; Fletcher, Jack M.
2009-01-01
The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…
Quesne, C
1997-01-01
Quite recently, a ``coloured'' extension of the Yang-Baxter equation has appeared in the literature and various solutions of it have been proposed. In the present contribution, we introduce a generalization of Hopf algebras, to be referred to as coloured Hopf algebras, wherein the comultiplication, counit, and antipode maps are labelled by some colour parameters. The latter may take values in any finite, countably infinite, or uncountably infinite set. A straightforward extension of the quasitriangularity property involves a coloured universal ${\\cal R}$-matrix, satisfying the coloured Yang-Baxter equation. We show how coloured Hopf algebras can be constructed from standard ones by using an algebra isomorphism group, called colour group. Finally, we present two examples of coloured quantum universal enveloping algebras.
Fundamentals of algebraic topology
Weintraub, Steven H
2014-01-01
This rapid and concise presentation of the essential ideas and results of algebraic topology follows the axiomatic foundations pioneered by Eilenberg and Steenrod. The approach of the book is pragmatic: while most proofs are given, those that are particularly long or technical are omitted, and results are stated in a form that emphasizes practical use over maximal generality. Moreover, to better reveal the logical structure of the subject, the separate roles of algebra and topology are illuminated. Assuming a background in point-set topology, Fundamentals of Algebraic Topology covers the canon of a first-year graduate course in algebraic topology: the fundamental group and covering spaces, homology and cohomology, CW complexes and manifolds, and a short introduction to homotopy theory. Readers wishing to deepen their knowledge of algebraic topology beyond the fundamentals are guided by a short but carefully annotated bibliography.
Elements of mathematics algebra
Bourbaki, Nicolas
2003-01-01
This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's, Algèbre, Chapters 4 to 7 (1981). This completes Algebra, 1 to 3, by establishing the theories of commutative fields and modules over a principal ideal domain. Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. Chapter 5 was entirely rewritten. After the basic theory of extensions (prime fields, algebraic, algebraically closed, radical extension), separable algebraic extensions are investigated, giving way to a section on Galois theory. Galois theory is in turn applied to finite fields and abelian extensions. The chapter then proceeds to the study of general non-algebraic extensions which cannot usually be found in textbooks: p-bases, transcendental extensions, separability criterions, regular extensions. Chapter 6 treats ordered groups and fields and...
Introduction to noncommutative algebra
Brešar, Matej
2014-01-01
Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients. Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.
Global Crop Yields, Climatic Trends and Technology Enhancement
Najafi, E.; Devineni, N.; Khanbilvardi, R.; Kogan, F.
2016-12-01
During the last decades the global agricultural production has soared up and technology enhancement is still making positive contribution to yield growth. However, continuing population, water crisis, deforestation and climate change threaten the global food security. Attempts to predict food availability in the future around the world can be partly understood from the impact of changes to date. A new multilevel model for yield prediction at the country scale using climate covariates and technology trend is presented in this paper. The structural relationships between average yield and climate attributes as well as trends are estimated simultaneously. All countries are modeled in a single multilevel model with partial pooling and/or clustering to automatically group and reduce estimation uncertainties. El Niño Southern Oscillation (ENSO), Palmer Drought Severity Index (PDSI), Geopotential height (GPH), historical CO2 level and time-trend as a relatively reliable approximation of technology measurement are used as predictors to estimate annual agricultural crop yields for each country from 1961 to 2007. Results show that these indicators can explain the variability in historical crop yields for most of the countries and the model performs well under out-of-sample verifications.
Technology-Enhanced Learning in Developing Nations: A review
Directory of Open Access Journals (Sweden)
Shalni Gulati
2008-02-01
Full Text Available Learning ‘using’ technologies has become a global phenomenon. The Internet is often seen as a value-neutral tool that potentially allows individuals to overcome the constraints of traditional elitist spaces and gain unhindered access to learning. It is widely suggested that online technologies can help address issues of educational equity and social exclusion, and open up democratic and accessible educational opportunities. The national governments and non-governmental agencies who fund educational endeavours in developing countries have advocated the use of new technologies to reduce the cost of reaching and educating large numbers of children and adults who are currently missing out on education. This paper presents an overview of the educational developments in open, distance, and technology-facilitated learning that aim to reach the educationally deprived populations of the world. It reveals the challenges encountered by children and adults in developing countries as they attempt to access available educational opportunities. The discussion questions whether, in face of these challenges, developing nations should continue to invest money, time, and effort into e-learning developments. Can technology-enhanced learning help address the poverty, literacy, social, and political problems in developing countries?
The Planar Algebra of a Semisimple and Cosemisimple Hopf Algebra
Indian Academy of Sciences (India)
Vijay Kodiyalam; V S Sunder
2006-11-01
To a semisimple and cosemisimple Hopf algebra over an algebraically closed field, we associate a planar algebra defined by generators and relations and show that it is a connected, irreducible, spherical, non-degenerate planar algebra with non-zero modulus and of depth two. This association is shown to yield a bijection between (the isomorphism classes, on both sides, of) such objects.
Graded Lie Algebra Generating of Parastatistical Algebraic Relations
Institute of Scientific and Technical Information of China (English)
JING Si-Cong; YANG Wei-Min; LI Ping
2001-01-01
A new kind of graded Lie algebra (We call it Z2,2 graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable Bose subspace of the Z2,2 graded Lie algebra and using relevant generalized Jacobi identities, we generate the whole algebraic structure of parastatistics.
Algebraic and analytic Dirac induction for graded affine Hecke algebras
Ciubotaru, D.; Opdam, E.M.; Trapa, P.E.
2014-01-01
We define the algebraic Dirac induction map IndD for graded affine Hecke algebras. The map IndD is a Hecke algebra analog of the explicit realization of the Baum-Connes assembly map in the K-theory of the reduced C∗-algebra of a real reductive group using Dirac operators. The definition of IndD is
An introduction to algebraic geometry and algebraic groups
Geck, Meinolf
2003-01-01
An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles.Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type.The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups
Leibniz algebras associated with representations of filiform Lie algebras
Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.
2015-12-01
In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.
Springer, T A
1998-01-01
"[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text." –Mathematical Reviews (Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of t...
Directory of Open Access Journals (Sweden)
Sinan AYDIN
2009-04-01
Full Text Available Linear algebra is a basic course followed in mathematics, science, and engineering university departments.Generally, this course is taken in either the first or second year but there have been difficulties in teachingand learning. This type of active algebra has resulted in an increase in research by mathematics educationresearchers. But there is insufficient information on this subject in Turkish and therefore it has not beengiven any educational status. This paper aims to give a general overview of this subject in teaching andlearning. These education studies can be considered quadruple: a the history of linear algebra, b formalismobstacles of linear algebra and cognitive flexibility to improve teaching and learning, c the relation betweenlinear algebra and geometry, d using technology in the teaching and learning linear algebra.Mathematicseducation researchers cannot provide an absolute solution to overcome the teaching and learning difficultiesof linear algebra. Epistemological analyses and experimental teaching have shown the learning difficulties.Given these results, further advice and assistance can be offered locally.
On Genetic and Evolution Algebras
Qaralleh, Izzat
2017-03-01
The genetic and evolution algebras generally are non-associative algebra. The concept of evolution and genetic algebras were introduced to answer the question what non-Mendelian genetics offers to mathematics. This paper we review some results of evolution and genetic algebras.
Classification of Noncommutative Domain Algebras
Arias, Alvaro
2012-01-01
Noncommutative domain algebras are noncommutative analogues of the algebras of holomorphic functions on domains of $\\C^n$ defined by holomorphic polynomials, and they generalize the noncommutative Hardy algebras. We present here a complete classification of these algebras based upon techniques inspired by multivariate complex analysis, and more specifically the classification of domains in hermitian spaces up to biholomorphic equivalence.
Network algebra for synchronous dataflow
Bergstra, J.A.; Middelburg, C.A.; Ștefánescu, G.
2013-01-01
We develop an algebraic theory of synchronous dataflow networks. First, a basic algebraic theory of networks, called BNA (Basic Network Algebra), is introduced. This theory captures the basic algebraic properties of networks. For synchronous dataflow networks, it is subsequently extended with
On dibaric and evolution algebras
Ladra, M; Rozikov, U A
2011-01-01
We find conditions on ideals of an algebra under which the algebra is dibaric. Dibaric algebras have not non-zero homomorphisms to the set of the real numbers. We introduce a concept of bq-homomorphism (which is given by two linear maps $f, g$ of the algebra to the set of the real numbers) and show that an algebra is dibaric if and only if it admits a non-zero bq-homomorphism. Using the pair $(f,g)$ we define conservative algebras and establish criteria for a dibaric algebra to be conservative. Moreover, the notions of a Bernstein algebra and an algebra induced by a linear operator are introduced and relations between these algebras are studied. For dibaric algebras we describe a dibaric algebra homomorphism and study their properties by bq-homomorphisms of the dibaric algebras. We apply the results to the (dibaric) evolution algebra of a bisexual population. For this dibaric algebra we describe all possible bq-homomorphisms and find conditions under which the algebra of a bisexual population is induced by a ...
Process algebra for Hybrid systems
Bergstra, J.A.; Middelburg, C.A.
2008-01-01
We propose a process algebra obtained by extending a combination of the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, Chap. 4, 2002] and the process algebra with propositional signals from Baeten and Bergstra [Theoretical Computer
Process algebra for hybrid systems
Bergstra, J.A.; Middelburg, C.A.
2005-01-01
We propose a process algebra obtained by extending a combination of the process algebra with continuous relative timing from Baeten and Middelburg (Process Algebra with Timing, Springer,Berlin, 2002, Chapter 4), and the process algebra with propositional signals from Baeten and Bergstra(Theoret. Com
Cohen, A.M.; Liu, S.
2015-01-01
For each n ≥ 1, we define an algebra having many properties that one might expect to hold for a Brauer algebra of type Bn. It is defined by means of a presentation by generators and relations. We show that this algebra is a subalgebra of the Brauer algebra of type Dn+1 and point out a cellular struc
Schneider, Hans
1989-01-01
Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t
Quantitative Algebraic Reasoning
DEFF Research Database (Denmark)
Mardare, Radu Iulian; Panangaden, Prakash; Plotkin, Gordon
2016-01-01
We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We deﬁne an equality relation indexed by rationals: a =ε b which we think of as saying that “a is approximately equal to b up to an error of ε”. We have 4 interesting examples where we have a quantitative...... equational theory whose free algebras correspond to well known structures. In each case we have ﬁnitary and continuous versions. The four cases are: Hausdorﬀ metrics from quantitive semilattices; pWasserstein metrics (hence also the Kantorovich metric) from barycentric algebras and also from pointed...
Olsson, Martin
2016-01-01
This book is an introduction to the theory of algebraic spaces and stacks intended for graduate students and researchers familiar with algebraic geometry at the level of a first-year graduate course. The first several chapters are devoted to background material including chapters on Grothendieck topologies, descent, and fibered categories. Following this, the theory of algebraic spaces and stacks is developed. The last three chapters discuss more advanced topics including the Keel-Mori theorem on the existence of coarse moduli spaces, gerbes and Brauer groups, and various moduli stacks of curv
Directory of Open Access Journals (Sweden)
J. W. Kitchen
1994-01-01
Full Text Available We study bundles of Banach algebras π:A→X, where each fiber Ax=π−1({x} is a Banach algebra and X is a compact Hausdorff space. In the case where all fibers are commutative, we investigate how the Gelfand representation of the section space algebra Γ(π relates to the Gelfand representation of the fibers. In the general case, we investigate how adjoining an identity to the bundle π:A→X relates to the standard adjunction of identities to the fibers.
Symplectic algebraic dynamics algorithm
Institute of Scientific and Technical Information of China (English)
2007-01-01
Based on the algebraic dynamics solution of ordinary differential equations andintegration of ,the symplectic algebraic dynamics algorithm sn is designed,which preserves the local symplectic geometric structure of a Hamiltonian systemand possesses the same precision of the na ve algebraic dynamics algorithm n.Computer experiments for the 4th order algorithms are made for five test modelsand the numerical results are compared with the conventional symplectic geometric algorithm,indicating that sn has higher precision,the algorithm-inducedphase shift of the conventional symplectic geometric algorithm can be reduced,and the dynamical fidelity can be improved by one order of magnitude.
Tansey, Timothy N.; Schopieray, Scott; Boland, Elizabeth; Lane, Frank; Pruett, Steven R.
2009-01-01
The use of technology-enhanced coursework by rehabilitation counselor educators has increased dramatically over the last decade. In many cases, educators are using new technologies to support traditional modes of teaching and learning. Research conducted in technology-enhanced coursework has primarily focused on the cognitive and psychomotor…
Gordon, Neil
2014-01-01
This publication is part of our five-strand research project "Flexible Pedagogies: preparing for the future". It focuses on a better understanding of technology-enhanced learning (TEL) and: (1) identifies key international drivers in the move towards technology-enhanced learning; (2) highlights some of the challenges and opportunities…
Mooij, Ton
2012-01-01
Mooij, T. (2012, 20 September). Theoretical and practical aspects of self-regulated learning in technology enhanced preschools and primary classrooms. Invited presentation for the symposion Self-regulated learning in technology enhanced learning environments at the ‘European Conference on Educational Research’ (ECER) of the ‘European Educational Research Association’ (EERA), Cádiz, Spain.
Mooij, Ton
2012-01-01
Mooij, T. (2012, 20 September). Theoretical and practical aspects of self-regulated learning in technology enhanced preschools and primary classrooms. Invited presentation for the symposion Self-regulated learning in technology enhanced learning environments at the ‘European Conference on Educationa
Proceedings of the 2nd Workshop on Awareness and Reflection in Technology-Enhanced Learning
Moore, Adam; Pammer, Viktoria; Pannese, Lucia; Prilla, Michael; Rajagopal, Kamakshi; Reinhardt, Wolfgang; Ullman, Thomas; Voigt, Christian
2013-01-01
Moore, A., Pammer, V., Pannese, L., Prilla, M., Rajagopal, K., Reinhardt, W., Ullman, Th. D., & Voigt, Ch. (Eds.) (2012). Proceedings of the 2nd Workshop on Awareness and Reflection in Technology Enhanced Learning. In conjunction with the 7th European Conference on Technology Enhanced Learning: 21st
Social network analysis for technology-enhanced learning: review and future directions
Sie, Rory; Ullmann, Thomas; Rajagopal, Kamakshi; Cela, Karina; Bitter-Rijpkema, Marlies; Sloep, Peter
2013-01-01
Sie, R. L. L., Ullmann, T. D., Rajagopal, K., Cela, K., Bitter-Rijpkema, M., & Sloep, P. B. (2012). Social network analysis for technology-enhanced learning: review and future directions. International Journal of Technology Enhanced Learning, 4(3/4), 172-190.
Introduction to quantum Lie algebras
Delius, G W
1996-01-01
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras \\uqg. The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. In this paper the recent general results about quantum Lie algebras are introduced with the help of the explicit example of (sl_2)_h.
On isomorphisms of integral table algebras
Institute of Scientific and Technical Information of China (English)
FAN; Yun(樊恽); SUN; Daying(孙大英)
2002-01-01
For integral table algebras with integral table basis T, we can consider integral R-algebra RT over a subring R of the ring of the algebraic integers. It is proved that an R-algebra isomorphism between two integral table algebras must be an integral table algebra isomorphism if it is compatible with the so-called normalizings of the integral table algebras.
Differential Hopf algebra structures on the Universal Enveloping Algebra of a Lie Algebra
van den Hijligenberg, N.W.; van den Hijligenberg, N.; Martini, Ruud
1995-01-01
We discuss a method to construct a De Rham complex (differential algebra) of Poincaré–Birkhoff–Witt type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebrastructure of U(g).
Axler, Sheldon
2015-01-01
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the ...
Markarian, Nikita
2017-03-01
We introduce Weyl n-algebras and show how their factorization complex may be used to define invariants of manifolds. In the appendix, we heuristically explain why these invariants must be perturbative Chern-Simons invariants.
Cameron, Peter J
2007-01-01
This Second Edition of a classic algebra text includes updated and comprehensive introductory chapters,. new material on axiom of Choice, p-groups and local rings, discussion of theory and applications, and over 300 exercises. It is an ideal introductory text for all Year 1 and 2 undergraduate students in mathematics. - ;Developed to meet the needs of modern students, this Second Edition of the classic algebra text by Peter Cameron covers all the abstract algebra an undergraduate student is likely to need. Starting with an introductory overview of numbers, sets and functions, matrices, polynomials, and modular arithmetic, the text then introduces the most important algebraic structures: groups, rings and fields, and their properties. This is followed by coverage of vector spaces and modules with. applications to abelian groups and canonical forms before returning to the construction of the number systems, including the existence of transcendental numbers. The final chapters take the reader further into the th...
Parametrizing Algebraic Curves
Lemmermeyer, Franz
2011-01-01
We present the technique of parametrization of plane algebraic curves from a number theorist's point of view and present Kapferer's simple and beautiful (but little known) proof that nonsingular curves of degree > 2 cannot be parametrized by rational functions.
Indian Academy of Sciences (India)
Vijay Kodiyalam; R Srinivasan; V S Sunder
2000-08-01
In this paper, we study a tower $\\{A^G_n(d):n≥ 1\\}$ of finite-dimensional algebras; here, represents an arbitrary finite group, denotes a complex parameter, and the algebra $A^G_n(d)$ has a basis indexed by `-stable equivalence relations' on a set where acts freely and has 2 orbits. We show that the algebra $A^G_n(d)$ is semi-simple for all but a finite set of values of , and determine the representation theory (or, equivalently, the decomposition into simple summands) of this algebra in the `generic case'. Finally we determine the Bratteli diagram of the tower $\\{A^G_n(d): n≥ 1\\}$ (in the generic case).
Andrilli, Stephen
2010-01-01
Elementary Linear Algebra develops and explains in careful detail the computational techniques and fundamental theoretical results central to a first course in linear algebra. This highly acclaimed text focuses on developing the abstract thinking essential for further mathematical study. The authors give early, intensive attention to the skills necessary to make students comfortable with mathematical proofs. The text builds a gradual and smooth transition from computational results to general theory of abstract vector spaces. It also provides flexbile coverage of practical applications, expl
Intermediate algebra & analytic geometry
Gondin, William R
1967-01-01
Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system
Noncommutative algebra and geometry
De Concini, Corrado; Vavilov, Nikolai 0
2005-01-01
Finite Galois Stable Subgroups of Gln. Derived Categories for Nodal Rings and Projective Configurations. Crowns in Profinite Groups and Applications. The Galois Structure of Ambiguous Ideals in Cyclic Extensions of Degree 8. An Introduction to Noncommutative Deformations of Modules. Symmetric Functions, Noncommutative Symmetric Functions and Quasisymmetric Functions II. Quotient Grothendieck Representations. On the Strong Rigidity of Solvable Lie Algebras. The Role of Bergman in Invesigating Identities in Matrix Algebras with Symplectic Involution. The Triangular Structure of Ladder Functors.
Beginning algebra a textworkbook
McKeague, Charles P
1985-01-01
Beginning Algebra: A Text/Workbook, Second Edition focuses on the principles, operations, and approaches involved in algebra. The publication first elaborates on the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on solving linear systems by graphing, elimination method, graphing ordered pairs and straight lines, linear and compound inequalities, addition and subtraction of real numbers, and properties of real numbers. The text then examines exponents and polynomials, factoring, and rational expressions. Topics include multiplication and division
Intermediate algebra a textworkbook
McKeague, Charles P
1985-01-01
Intermediate Algebra: A Text/Workbook, Second Edition focuses on the principles, operations, and approaches involved in intermediate algebra. The publication first takes a look at basic properties and definitions, first-degree equations and inequalities, and exponents and polynomials. Discussions focus on properties of exponents, polynomials, sums, and differences, multiplication of polynomials, inequalities involving absolute value, word problems, first-degree inequalities, real numbers, opposites, reciprocals, and absolute value, and addition and subtraction of real numbers. The text then ex
Generalized braided Hopf algebras
Institute of Scientific and Technical Information of China (English)
LU Zhong-jian; FANG Xiao-li
2009-01-01
The concept of (f, σ)-pair (B, H)is introduced, where B and H are Hopf algebras. A braided tensor category which is a tensor subcategory of the category HM of left H-comodules through an (f, σ)-pair is constructed. In particularly, a Yang-Baxter equation is got. A Hopf algebra is constructed as well in the Yetter-Drinfel'd category HHYD by twisting the multiplication of B.
Institute of Scientific and Technical Information of China (English)
Antonio AIZPURU; Antonio GUTI(E)RREZ-D(A)VILA
2004-01-01
In this paper we will study some families and subalgebras ( ) of ( )(N) that let us characterize the unconditional convergence of series through the weak convergence of subseries ∑i∈A xi, A ∈ ( ).As a consequence, we obtain a new version of the Orlicz-Pettis theorem, for Banach spaces. We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces.
Introduction to abstract algebra
Nicholson, W Keith
2012-01-01
Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."-Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately be
Howard, Keith A.; Scott, Allison; Romero, Martin; Saddler, Derrick
2015-01-01
In this article, the authors use the High School Longitudinal Study 2009 (HSLS:09) national database to analyze the relationships between algebra failure, subsequent performance, motivation, and college readiness. Students who failed eighth-grade Algebra I did not differ significantly in mathematics proficiency from those who passed lower-level…
The Boolean algebra of Galois algebras
Directory of Open Access Journals (Sweden)
Lianyong Xue
2003-02-01
Full Text Available Let B be a Galois algebra with Galois group G, Jg={bÃ¢ÂˆÂˆB|bx=g(xbÃ¢Â€Â‰for allÃ¢Â€Â‰xÃ¢ÂˆÂˆB} for each gÃ¢ÂˆÂˆG, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|gÃ¢ÂˆÂˆG}, e a nonzero element in Ba, and He={gÃ¢ÂˆÂˆG|eeg=e}. Then, a monomial e is characterized, and the Galois extension Be, generated by e with Galois group He, is investigated.
Differential Hopf algebra structures on the universal enveloping algebra of a lie algebra
Hijligenberg, van den, N.W.; Martini, R.
1995-01-01
We discuss a method to construct a De Rham complex (differential algebra) of Poincar'e-Birkhoff-Witt-type on the universal enveloping algebra of a Lie algebra $g$. We determine the cases in which this gives rise to a differential Hopf algebra that naturally extends the Hopf algebra structure of $U(g)$. The construction of such differential structures is interpreted in terms of colour Lie superalgebras.
Topological ∗-algebras with *-enveloping Algebras II
Indian Academy of Sciences (India)
S J Bhatt
2001-02-01
Universal *-algebras *() exist for certain topological ∗-algebras called algebras with a *-enveloping algebra. A Frechet ∗-algebra has a *-enveloping algebra if and only if every operator representation of maps into bounded operators. This is proved by showing that every unbounded operator representation , continuous in the uniform topology, of a topological ∗-algebra , which is an inverse limit of Banach ∗-algebras, is a direct sum of bounded operator representations, thereby factoring through the enveloping pro-* algebra () of . Given a *-dynamical system (, , ), any topological ∗-algebra containing (, ) as a dense ∗-subalgebra and contained in the crossed product *-algebra *(, , ) satisfies ()=*(, , ). If $G = \\mathbb{R}$, if is an -invariant dense Frechet ∗-subalgebra of such that () = , and if the action on is -tempered, smooth and by continuous ∗-automorphisms: then the smooth Schwartz crossed product $S(\\mathbb{R}, B, )$ satisfies $E(S(\\mathbb{R}, B, )) = C^*(\\mathbb{R}, A, )$. When is a Lie group, the ∞-elements ∞(), the analytic elements () as well as the entire analytic elements () carry natural topologies making them algebras with a *-enveloping algebra. Given a non-unital *-algebra , an inductive system of ideals is constructed satisfying $A = C^*-\\mathrm{ind} \\lim I_$; and the locally convex inductive limit $\\mathrm{ind}\\lim I_$ is an -convex algebra with the *-enveloping algebra and containing the Pedersen ideal of . Given generators with weakly Banach admissible relations , we construct universal topological ∗-algebra (, ) and show that it has a *-enveloping algebra if and only if (, ) is *-admissible.
Institute of Scientific and Technical Information of China (English)
An Hui-hui; Wang Zhi-chun
2016-01-01
L-octo-algebra with 8 operations as the Lie algebraic analogue of octo-algebra such that the sum of 8 operations is a Lie algebra is discussed. Any octo-algebra is an L-octo-algebra. The relationships among L-octo-algebras, L-quadri-algebras, L-dendriform algebras, pre-Lie algebras and Lie algebras are given. The close relationships between L-octo-algebras and some interesting structures like Rota-Baxter operators, classical Yang-Baxter equations and some bilinear forms satisfying certain conditions are given also.
Universal Algebra Applied to Hom-Associative Algebras, and More
Hellström, Lars; Makhlouf, Abdenacer; Silvestrov, Sergei D.
2014-01-01
The purpose of this paper is to discuss the universal algebra theory of hom-algebras. This kind of algebra involves a linear map which twists the usual identities. We focus on hom-associative algebras and hom-Lie algebras for which we review the main results. We discuss the envelopment problem, operads, and the Diamond Lemma; the usual tools have to be adapted to this new situation. Moreover we study Hilbert series for the hom-associative operad and free algebra, and describe them up to total...
Axis Problem of Rough 3-Valued Algebras
Institute of Scientific and Technical Information of China (English)
Jianhua Dai; Weidong Chen; Yunhe Pan
2006-01-01
The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras and 3-valued Lukasiewicz algebras. A 3-valued Lukasiewicz algebra is a Stone algebra, a regular double Stone algebra, a semi-simple Nelson algebra, a pre-rough algebra. Thus, we call the algebra constructed by the collection of rough sets of an approximation space a rough 3-valued Lukasiewicz algebra. In this paper,the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras, are studied. Whether the rough 3-valued Lukasiewicz algebra is a axled 3-valued Lukasiewicz algebra is examined.
Hecke algebras with unequal parameters
Lusztig, G
2003-01-01
Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over p-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties. In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives rese...
Sworder, Steven C.
2011-01-01
Background: The Mathematics Department at Saddleback College created a 3-units intermediate algebra course as an alternative to the traditional 5-units intermediate algebra course. Forty percent of the material in the traditional course was composed of review topics from beginning algebra. The 3-units course did not contain that rehash of…
Egodawatte, Gunawardena; Stoilescu, Dorian
2015-01-01
The purpose of this mixed-method study was to investigate grade 11 university/college stream mathematics students' difficulties in applying conceptual knowledge, procedural skills, strategic competence, and algebraic thinking in solving routine (instructional) algebraic problems. A standardized algebra test was administered to thirty randomly…
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Over a field F of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector space A［D]=A［D] from any pair of a commutative associative algebra A with an identity element and the polynomial algebra ［D] of a commutative derivation subalgebra D of A. We prove that A[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only if A is D－simple and A［D] acts faithfully on A. Thus we obtain a lot of simple algebras.
Simple Algebras of Invariant Operators
Institute of Scientific and Technical Information of China (English)
Xiaorong Shen; J.D.H. Smith
2001-01-01
Comtrans algebras were introduced in as algebras with two trilinear operators, a commutator [x, y, z] and a translator , which satisfy certain identities. Previously known simple comtrans algebras arise from rectangular matrices, simple Lie algebras, spaces equipped with a bilinear form having trivial radical, spaces of hermitian operators over a field with a minimum polynomial x2+1. This paper is about generalizing the hermitian case to the so-called invariant case. The main result of this paper shows that the vector space of n-dimensional invariant operators furnishes some comtrans algebra structures, which are simple provided that certain Jordan and Lie algebras are simple.
Algebra II workbook for dummies
Sterling, Mary Jane
2014-01-01
To succeed in Algebra II, start practicing now Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success. Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebr
Davidson, Kenneth R
1996-01-01
The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of K-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty yea
What Are the ACT College Readiness Benchmarks? Information Brief
ACT, Inc., 2013
2013-01-01
The ACT College Readiness Benchmarks are the minimum ACT® college readiness assessment scores required for students to have a high probability of success in credit-bearing college courses--English Composition, social sciences courses, College Algebra, or Biology. This report identifies the College Readiness Benchmarks on the ACT Compass scale…
Interactions Between Representation Ttheory, Algebraic Topology and Commutative Algebra
Pitsch, Wolfgang; Zarzuela, Santiago
2016-01-01
This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest dev...
Quantum cluster algebra structures on quantum nilpotent algebras
Goodearl, K R
2017-01-01
All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts.
Bicycles, Birds, Bats and Balloons: New Applications for Algebra Classes.
Yoshiwara, Bruce; Yoshiwara, Kathy
This collection of activities is intended to enhance the teaching of college algebra through the use of modeling. The problems use real data and involve the representation and interpretation of the data. The concepts addressed include rates of change, linear and quadratic regression, and functions. The collection consists of eight problems, four…
Structure of Solvable Quadratic Lie Algebras
Institute of Scientific and Technical Information of China (English)
ZHU Lin-sheng
2005-01-01
@@ Killing form plays a key role in the theory of semisimple Lie algebras. It is natural to extend the study to Lie algebras with a nondegenerate symmetric invariant bilinear form. Such a Lie algebra is generally called a quadratic Lie algebra which occur naturally in physics[10,12,13]. Besides semisimple Lie algebras, interesting quadratic Lie algebras include the Kac-Moody algebras and the Extended Affine Lie algebras.
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
Wasserman, Nicholas H.
2016-01-01
This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
Algebraic orders on $K_{0}$ and approximately finite operator algebras
Power, S C
1993-01-01
This is a revised and corrected version of a preprint circulated in 1990 in which various non-self-adjoint limit algebras are classified. The principal invariant is the scaled $K_0$ group together with the algebraic order on the scale induced by partial isometries in the algebra.
Approximate Preservers on Banach Algebras and C*-Algebras
Directory of Open Access Journals (Sweden)
M. Burgos
2013-01-01
Full Text Available The aim of the present paper is to give approximate versions of Hua’s theorem and other related results for Banach algebras and C*-algebras. We also study linear maps approximately preserving the conorm between unital C*-algebras.
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
Wasserman, Nicholas H.
2016-01-01
This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
The Planar Algebra Associated to a Kac Algebra
Indian Academy of Sciences (India)
Vijay Kodiyalam; Zeph Landau; V S Sunder
2003-02-01
We obtain (two equivalent) presentations – in terms of generators and relations-of the planar algebra associated with the subfactor corresponding to (an outer action on a factor by) a finite-dimensional Kac algebra. One of the relations shows that the antipode of the Kac algebra agrees with the `rotation on 2-boxes'.
Derived Algebraic Geometry II: Noncommutative Algebra
Lurie, Jacob
2007-01-01
In this paper, we present an infinity-categorical version of the theory of monoidal categories. We show that the infinity category of spectra admits an essentially unique monoidal structure (such that the tensor product preserves colimits in each variable), and thereby recover the classical smash-product operation on spectra. We develop a general theory of algebras in a monoidal infinity category, which we use to (re)prove some basic results in the theory of associative ring spectra. We also develop an infinity-categorical theory of monads, and prove a version of the Barr-Beck theorem.
Nearly projective Boolean algebras
Heindorf, Lutz; Shapiro, Leonid B
1994-01-01
The book is a fairly complete and up-to-date survey of projectivity and its generalizations in the class of Boolean algebras. Although algebra adds its own methods and questions, many of the results presented were first proved by topologists in the more general setting of (not necessarily zero-dimensional) compact spaces. An appendix demonstrates the application of advanced set-theoretic methods to the field. The intended readers are Boolean and universal algebraists. The book will also be useful for general topologists wanting to learn about kappa-metrizable spaces and related classes. The text is practically self-contained but assumes experience with the basic concepts and techniques of Boolean algebras.
Adaptive Algebraic Multigrid Methods
Energy Technology Data Exchange (ETDEWEB)
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
Jarvis, Frazer
2014-01-01
The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the fi...
Durka, R
2016-01-01
We explore the $S$-expansion framework to analyze freedom in closing the multiplication tables for the abelian semigroups. Including possibility of the zero element in the resonant decomposition and relating the Lorentz generator with the semigroup identity element leads to the wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results we find not only all the Maxwell algebras of type $\\mathfrak{B}_m$, $\\mathfrak{C}_m$, and recently introduced $\\mathfrak{D}_m$, but we also produce new examples. We discuss some prospects concerning further enlarging the algebras and provide all necessary constituents for constructing the gravity actions based on the obtained results.
Blyth, T S
2002-01-01
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers:...
Wadsworth, A R
2017-01-01
This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
Durka, R.
2017-04-01
The S-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition, and associating the Lorentz generator with the semigroup identity element, leads to a wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type {{B}m} , {{C}m} , and the recently introduced {{D}m} . The additional new examples complete the resulting generalization of the bosonic enlargements for an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.
Algebraic totality, towards completeness
Tasson, Christine
2009-01-01
Finiteness spaces constitute a categorical model of Linear Logic (LL) whose objects can be seen as linearly topologised spaces, (a class of topological vector spaces introduced by Lefschetz in 1942) and morphisms as continuous linear maps. First, we recall definitions of finiteness spaces and describe their basic properties deduced from the general theory of linearly topologised spaces. Then we give an interpretation of LL based on linear algebra. Second, thanks to separation properties, we can introduce an algebraic notion of totality candidate in the framework of linearly topologised spaces: a totality candidate is a closed affine subspace which does not contain 0. We show that finiteness spaces with totality candidates constitute a model of classical LL. Finally, we give a barycentric simply typed lambda-calculus, with booleans ${\\mathcal{B}}$ and a conditional operator, which can be interpreted in this model. We prove completeness at type ${\\mathcal{B}}^n\\to{\\mathcal{B}}$ for every n by an algebraic metho...
Bloch, Spencer J
2000-01-01
This book is the long-awaited publication of the famous Irvine lectures. Delivered in 1978 at the University of California at Irvine, these lectures turned out to be an entry point to several intimately-connected new branches of arithmetic algebraic geometry, such as regulators and special values of L-functions of algebraic varieties, explicit formulas for them in terms of polylogarithms, the theory of algebraic cycles, and eventually the general theory of mixed motives which unifies and underlies all of the above (and much more). In the 20 years since, the importance of Bloch's lectures has not diminished. A lucky group of people working in the above areas had the good fortune to possess a copy of old typewritten notes of these lectures. Now everyone can have their own copy of this classic work.
Teepe, R.C.; Molenaar, I.; Verhoeven, L.T.W.
2017-01-01
Preschool children's vocabulary mainly develops verbal through interaction. Therefore, the technology-enhanced storytelling (TES) activity Jeffy's Journey is developed to support parent-child interaction and vocabulary in preschool children. TES entails shared verbal storytelling supported by a
Algebra for Gifted Third Graders.
Borenson, Henry
1987-01-01
Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)
Indian Academy of Sciences (India)
Anil K Karn
2003-02-01
Order unit property of a positive element in a *-algebra is defined. It is proved that precisely projections satisfy this order theoretic property. This way, unital hereditary *-subalgebras of a *-algebra are characterized.
Computer Program For Linear Algebra
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
Computer Program For Linear Algebra
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
Linear Mappings of Quaternion Algebra
Kleyn, Aleks
2011-01-01
In the paper I considered linear and antilinear automorphisms of quaternion algebra. I proved the theorem that there is unique expansion of R-linear mapping of quaternion algebra relative to the given set of linear and antilinear automorphisms.
Benefits and Pitfalls of Multimedia and Interactive Features in Technology-Enhanced Storybooks
Takacs, Zsofia K.; Swart, Elise K.; Bus, Adriana G.
2015-01-01
A meta-analysis was conducted on the effects of technology-enhanced stories for young children’s literacy development when compared to listening to stories in more traditional settings like storybook reading. A small but significant additional benefit of technology was found for story comprehension (g+ = 0.17) and expressive vocabulary (g+ = 0.20), based on data from 2,147 children in 43 studies. When investigating the different characteristics of technology-enhanced stories, multimedia featu...
Proceedings of the 2nd Workshop on Awareness and Reflection in Technology-Enhanced Learning
Moore, Adam; Pammer, Viktoria; Pannese, Lucia; Prilla, Michael; Rajagopal, Kamakshi; Reinhardt, Wolfgang; Ullman, Thomas; Voigt, Christian
2013-01-01
Moore, A., Pammer, V., Pannese, L., Prilla, M., Rajagopal, K., Reinhardt, W., Ullman, Th. D., & Voigt, Ch. (Eds.) (2012). Proceedings of the 2nd Workshop on Awareness and Reflection in Technology Enhanced Learning. In conjunction with the 7th European Conference on Technology Enhanced Learning: 21st Century Learning for 21st Century Skills (ARTEL/EC-TEL 2012). September, 18, 2012, Saarbrücken, Germany. Available online at http://ceur-ws.org/Vol-931/.
Automorphism groups of pointed Hopf algebras
Institute of Scientific and Technical Information of China (English)
YANG Shilin
2007-01-01
The group of Hopf algebra automorphisms for a finite-dimensional semisimple cosemisimple Hopf algebra over a field k was considered by Radford and Waterhouse. In this paper, the groups of Hopf algebra automorphisms for two classes of pointed Hopf algebras are determined. Note that the Hopf algebras we consider are not semisimple Hopf algebras.
Kendig, Keith
2015-01-01
Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th
Hohn, Franz E
2012-01-01
This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations - homogeneous or nonhomogeneous - and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology.Other subjects include the complete treatment of the structur
Reed, Nat
2011-01-01
For grades 6-8, our State Standards-based combined resource meets the algebraic concepts addressed by the NCTM standards and encourages the students to review the concepts in unique ways. The task sheets introduce the mathematical concepts to the students around a central problem taken from real-life experiences, while the drill sheets provide warm-up and timed practice questions for the students to strengthen their procedural proficiency skills. Included are opportunities for problem-solving, patterning, algebraic graphing, equations and determining averages. The combined task & drill sheets
Hogben, Leslie
2013-01-01
With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.New to the Second EditionSeparate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of
Algebraic Topology, Rational Homotopy
1988-01-01
This proceedings volume centers on new developments in rational homotopy and on their influence on algebra and algebraic topology. Most of the papers are original research papers dealing with rational homotopy and tame homotopy, cyclic homology, Moore conjectures on the exponents of the homotopy groups of a finite CW-c-complex and homology of loop spaces. Of particular interest for specialists are papers on construction of the minimal model in tame theory and computation of the Lusternik-Schnirelmann category by means articles on Moore conjectures, on tame homotopy and on the properties of Poincaré series of loop spaces.
Division algebras and supersymmetry
Baez, John C
2009-01-01
Supersymmetry is deeply related to division algebras. Nonabelian Yang--Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green--Schwarz superstring. In both cases, supersymmetry relies on the vanishing of a certain trilinear expression involving a spinor field. The reason for this, in turn, is the existence of normed division algebras in dimensions 1, 2, 4 and 8: the real numbers, complex numbers, quaternions and octonions. Here we provide a self-contained account of how this works.
Linear Algebra Thoroughly Explained
Vujičić, Milan
2008-01-01
Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and comprehensive presentation of the basic theory is illustrated throughout with an abundance of worked examples. The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering. It will also be an invaluable addition to research libraries as a comprehensive resource book for the subject.
Reed, Nat
2011-01-01
For grades 3-5, our State Standards-based combined resource meets the algebraic concepts addressed by the NCTM standards and encourages the students to review the concepts in unique ways. The task sheets introduce the mathematical concepts to the students around a central problem taken from real-life experiences, while the drill sheets provide warm-up and timed practice questions for the students to strengthen their procedural proficiency skills. Included are opportunities for problem-solving, patterning, algebraic graphing, equations and determining averages. The combined task & drill sheets
Recollements of extension algebras
Institute of Scientific and Technical Information of China (English)
CHEN; Qinghua(陈清华); LIN; Yanan(林亚南)
2003-01-01
Let A be a finite-dimensional algebra over arbitrary base field k. We prove: if the unbounded derived module category D-(Mod-A) admits symmetric recollement relative to unbounded derived module categories of two finite-dimensional k-algebras B and C:D-(Mod- B) ( ) D-(Mod- A) ( ) D-(Mod- C),then the unbounded derived module category D-(Mod - T(A)) admits symmetric recollement relative to the unbounded derived module categories of T(B) and T(C):D-(Mod - T(B)) ( ) D-(Mod - T(A)) ( ) D-(Mod - T(C)).
Algebraic curves and cryptography
Murty, V Kumar
2010-01-01
It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. Of special interest are the Abelian varieties that are Jacobians of algebraic curves. All of the articles in this volume are centered on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields. The topics covered include Schoof's \\ell-adic point counting algorithm, the p-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on
Energy Technology Data Exchange (ETDEWEB)
Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)
2010-02-26
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
Cooperstein, Bruce
2010-01-01
Vector SpacesFieldsThe Space FnVector Spaces over an Arbitrary Field Subspaces of Vector SpacesSpan and IndependenceBases and Finite Dimensional Vector SpacesBases and Infinite Dimensional Vector SpacesCoordinate VectorsLinear TransformationsIntroduction to Linear TransformationsThe Range and Kernel of a Linear TransformationThe Correspondence and Isomorphism TheoremsMatrix of a Linear TransformationThe Algebra of L(V, W) and Mmn(F)Invertible Transformations and MatricesPolynomialsThe Algebra of PolynomialsRoots of PolynomialsTheory of a Single Linear OperatorInvariant Subspaces of an Operator
Weiss, Edwin
1998-01-01
Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te
Partially ordered algebraic systems
Fuchs, Laszlo
2011-01-01
Originally published in an important series of books on pure and applied mathematics, this monograph by a distinguished mathematician explores a high-level area in algebra. It constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The self-contained treatment features numerous problems, complete proofs, a detailed bibliography, and indexes. It presumes some knowledge of abstract algebra, providing necessary background and references where appropriate. This inexpensive edition of a hard-to-find systematic survey will fill a gap i
Endomorphisms of graph algebras
DEFF Research Database (Denmark)
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D...... that the restriction to the diagonal MASA of an automorphism which globally preserves both D_E and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C...
Algebra & trigonometry super review
2012-01-01
Get all you need to know with Super Reviews! Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Algebra and Trigonometry Super Review includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, equations, linear equations and systems of linear equations, inequalities, relations and functions, quadratic equations, equations of higher order, ratios, proportions, and variations. Take the Super Review quizzes to see how much y
Algebra & trigonometry I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Algebra & Trigonometry I includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, eq
The theory of algebraic numbers
Pollard, Harry
1998-01-01
An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.
Derivations of generalized Weyl algebras
Institute of Scientific and Technical Information of China (English)
SU; Yucai(苏育才)
2003-01-01
A class of the associative and Lie algebras A[D] = A × F[D] of Weyl type are studied, where Ais a commutative associative algebra with an identity element over a field F of characteristic zero, and F[D] isthe polynomial algebra of a finite dimensional commutative subalgebra of locally finite derivations of A suchthat A is D-simple. The derivations of these associative and Lie algebras are precisely determined.
Algebraic Methods to Design Signals
2015-08-27
AFRL-AFOSR-VA-TR-2015-0257 Algebraic Methods to Design Signals Krishnasany Arasu WRIGHT STATE UNIVERSITY Final Report 08/27/2015 DISTRIBUTION A...REPORT TYPE FINAL 3. DATES COVERED (From - To) June 2012 - May 2015 4. TITLE AND SUBTITLE ALGEBRAIC METHODS TO DESIGN SIGNALS 5a. CONTRACT NUMBER...to date on designing signals using algebraic and combinatorial methods. Mathematical tools from algebraic number theory, representation theory and
Algebraic Structure of Dynamical Systems
2017-05-22
Scholar project report; no. 461 (2017) ALGEBRAIC STRUCTURE OF DYNAMICAL SYSTEMS by MIDN 1/C James P. Talisse United States Naval Academy Annapolis, MD...based on the structure of algebraic objects associated with it. In this project we study two algebraic objects, centralizers and topological full groups...group completely defines the system up to time reversal. We apply numerical estimates to draw conclusions about the algebraic properties of this group
Optimal Algorithm for Algebraic Factoring
Institute of Scientific and Technical Information of China (English)
支丽红
1997-01-01
This paper presents on optimized method for factoring multivariate polynomials over algebraic extension fields defined by an irreducible ascending set. The basic idea is to convert multivariate polynomials to univariate polynomials and algebraic extension fields to algebraic number fields by suitable integer substituteions.Then factorize the univariate polynomials over the algebraic number fields.Finally,construct mulativariate factors of the original polynomial by Hensel lemma and TRUEFACTOR test.Some examples with timing are included.
Technology-enhanced focus groups as a component of instrument development.
Strout, Tania D; DiFazio, Rachel L; Vessey, Judith A
2017-06-22
Background Bullying is a critical public health problem and a screening tool for use in healthcare is needed. Focus groups are a common tool for generating qualitative data when developing an instrument and evidence suggests that technology-enhanced focus groups can be effective in simultaneously engaging participants from diverse settings. Aim To examine the use of technology-enhanced focus groups in generating an item pool to develop a youth-bullying screening tool. Discussion The authors explore methodological and ethical issues related to conducting technology-enhanced focus groups, drawing on their experience in developing a youth-bullying measure. They conducted qualitative focus groups with professionals from the front lines of bullying response and intervention. They describe the experience of conducting technology-enhanced focus group sessions, focusing on the methodological and ethical issues that researchers engaging in similar work may encounter. Challenges associated with this methodology include establishing rapport among participants, privacy concerns and limited non-verbal communication. Conclusion The use of technology-enhanced focus groups can be valuable in obtaining rich data from a wide variety of disciplines and contexts. Organising these focus groups was inexpensive and preferred by the study's participants. Implications for practice Researchers should consider using technology-enhanced focus groups to generate data to develop health-related measurement tools.
Assessing Elementary Algebra with STACK
Sangwin, Christopher J.
2007-01-01
This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…
Perturbation semigroup of matrix algebras
Neumann, N.; Suijlekom, W.D. van
2016-01-01
In this article we analyze the structure of the semigroup of inner perturbations in noncommutative geometry. This perturbation semigroup is associated to a unital associative *-algebra and extends the group of unitary elements of this *-algebra. We compute the perturbation semigroup for all matrix algebras.
An algebra of reversible computation
2016-01-01
We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules, basic reversible processes algebra (BRPA), algebra of reversible communicating processes (ARCP), recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.
Process Algebra and Markov Chains
Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
An Algebra of Reversible Computation
Yong WANG
2014-01-01
We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules, basic reversible processes algebra (BRPA), algebra of reversible communicating processes (ARCP), recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.
Denotational semantics for thread algebra
Vu, T.D.
2008-01-01
This paper gives a denotational semantics for thread algebra (TA), an algebraic framework for the description and analysis of recent programming languages such as C# and Java [J.A. Bergstra, C.A. Middelburg, Thread algebra for strategic interleaving, Formal Aspects of Computing, in press.
Thomys, Janus; Zhang, Xiaohong
2013-01-01
We describe weak-BCC-algebras (also called BZ-algebras) in which the condition (x∗y)∗z = (x∗z)∗y is satisfied only in the case when elements x, y belong to the same branch. We also characterize ideals, nilradicals, and nilpotent elements of such algebras. PMID:24311983
An algebra of reversible computation.
Wang, Yong
2016-01-01
We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.
Hochschild homology of structured algebras
DEFF Research Database (Denmark)
Wahl, Nathalie; Westerland, Craig Christopher
2016-01-01
We give a general method for constructing explicit and natural operations on the Hochschild complex of algebras over any prop with A∞-multiplication—we think of such algebras as A∞-algebras “with extra structure”. As applications, we obtain an integral version of the Costello–Kontsevich–Soibelman...
The Maximal Graded Left Quotient Algebra of a Graded Algebra
Institute of Scientific and Technical Information of China (English)
Gonzalo ARANDA PINO; Mercedes SILES MOLINA
2006-01-01
We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms (of left A-modules)from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra,and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra.
Observable Algebra in Field Algebra of G-spin Models
Institute of Scientific and Technical Information of China (English)
蒋立宁
2003-01-01
Field algebra of G-spin models can provide the simplest examples of lattice field theory exhibiting quantum symmetry. Let D(G) be the double algebra of a finite group G and D(H), a sub-algebra of D(G) determined by subgroup H of G. This paper gives concrete generators and the structure of the observable algebra AH, which is a D(H)-invariant sub-algebra in the field algebra of G-spin models F, and shows that AH is a C*-algebra. The correspondence between H and AH is strictly monotonic. Finally, a duality between D(H) and AH is given via an irreducible vacuum C*-representation of F.
On the simplicity of Lie algebras associated to Leavitt algebras
Abrams, Gene
2009-01-01
For any field $K$ and integer $n\\geq 2$ we consider the Leavitt algebra $L = L_K(n)$. $L$ is an associative algebra, but we view $L$ as a Lie algebra using the bracket $[a,b]=ab-ba$ for $a,b \\in L$. We denote this Lie algebra as $L^-$, and consider its Lie subalgebra $[L^-,L^-]$. In our main result, we show that $[L^-,L^-]$ is a simple Lie algebra if and only if char$(K)$ divides $n-1$. For any positive integer $d$ we let $S = M_d(L_K(n))$ be the $d\\times d$ matrix algebra over $L_K(n)$. We give sufficient conditions for the simplicity and non-simplicity of the Lie algebra $[S^-,S^-]$.
Commutative algebra with a view toward algebraic geometry
Eisenbud, David
1995-01-01
Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algeb...
Institute of Scientific and Technical Information of China (English)
SU; Yucai(
2001-01-01
［1］ Kawamoto, N., Generalizations of Witt algebras over a field of characteristic zero, Hiroshima Math. J., 1986, 16: 417.［2］ Osborn, J. M., New simple infinite－dimensional Lie algebras of characteristic 0, J. Alg., 1996, 185: 820.［3］ Dokovic, D. Z., Zhao, K., Derivations, isomorphisms, and second cohomology of generalized Witt algebras, Trans. of Amer. Math. Soc., 1998, 350(2): 643.［4］ Dokovic, D. Z., Zhao, K., Generalized Cartan type W Lie algebras in characteristic zero, J. Alg., 1997, 195: 170.［5］ Osborn, J. M., Zhao, K., Generalized Poisson bracket and Lie algebras of type H in characteristic 0, Math. Z., 1999, 230: 107.［6］ Osborn, J. M., Zhao, K., Generalized Cartan type K Lie algebras in characteristic 0, Comm. Alg., 1997, 25: 3325.［7］ Zhao, K., Isomorphisms between generalized Cartan type W Lie algebras in characteristic zero, Canadian J. Math., 1998, 50: 210.［8］ Passman, D. P., Simple Lie algebras of Witt type, J. Algebra, 1998, 206: 682.［9］ Jordan, D. A., On the simplicity of Lie algebras of derivations of commutative algebras, J. Alg., 2000, 206: 682.［10］ Xu, X., New generalized simple Lie algebras of Cartan type over a field with characteristic 0, J. Alg., 2000, 244: 23.［11］ Su, Y., Xu, X., Zhang, H., Derivation－simple algebras and the structures of Lie algebras of generalized Witt type, J. Alg., 2000, 233: 642.［12］ Dixmer, J., Enveloping Algebras, Amsterdam: North Holland, 1977.
Algebraic Thinking through Origami.
Higginson, William; Colgan, Lynda
2001-01-01
Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)
Thinking Visually about Algebra
Baroudi, Ziad
2015-01-01
Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…
Bergstra, J.A.; Middelburg, C.A.
2015-01-01
We add probabilistic features to basic thread algebra and its extensions with thread-service interaction and strategic interleaving. Here, threads represent the behaviours produced by instruction sequences under execution and services represent the behaviours exhibited by the components of execution
Operation of Algebraic Fractions
Institute of Scientific and Technical Information of China (English)
2008-01-01
<正>The first step in factorizing algebraic expressions is to take out the common factors of all the terms of the expression.For example,2x~2+14x+24=2(x~2+7x+12)=2(x+3)(x+4) The three identities are also useful in factorizing some quadratic expressions:
Pipekaru, T.
1975-01-01
Deze handleiding, geschreven in opdracht van het bestuur van de Afdeling der Algemene Wetenschappen van de T.H. te Delft, is bedoeld als collegedictaat Lineaire Algebra voor het eerste studiejaar van vrijwel alle technische afdelingen. Hopelijk wordt hiermee voorzien in een behoefte die is ontstaan
The Green formula and heredity of algebras
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Green, J. A., Hall algebras, hereditary algebras and quantum groups, Invent. Math. 1995, 120: 361-377.[2]Ringel, C. M., Green's theorem on Hall algebras, in Representations of Algebras and Related Topics, CMS Conference Proceedings 19, Providence, 1996, 185-245.[3]Xiao J., Drinfeld double and Ringel-Green theory of Hall Algebras, J. Algebra, 1997, 190: 100-144.[4]Sevenhant, B., Van den Bergh, M., A relation between a conjecture of Kac and the structure of the Hall algebra,J. Pure Appl. Algebra, 2001, 160: 319-332.[5]Deng B., Xiao, J., On double Ringel-Hall algebras, J. Algebra, 2002, 251: 110-149.
Notes on Piecewise-Koszul Algebras
Institute of Scientific and Technical Information of China (English)
Jia Feng L(U); Xiao Lan YU
2011-01-01
The relationships between piecewise-Koszul algebras and other "Koszul-type" algebras are discussed.. The Yoneda-Ext algebra and the dual algebra of a piecewise-Koszul algebra are studied, and a sufficient condition for the dual algebra A to be piecewise-Koszul is given. Finally, by studying the trivial extension algebras of the path algebras of Dynkin quivers in bipartite orientation, we give explicit constructions for piecewise-Koszul algebras with arbitrary "period" and piecewise-Koszul algebras with arbitrary "jump-degree".
On ultraproducts of operator algebras
Institute of Scientific and Technical Information of China (English)
LI; Weihua
2005-01-01
Some basic questions on ultraproducts of C*-algebras and yon Neumann algebras, including the relation to K-theory of C*-algebras are considered. More specifically,we prove that under certain conditions, the K-groups of ultraproduct of C*-algebras are isomorphic to the ultraproduct of respective K-groups of C*-algebras. We also show that the ultraproducts of factors of type Ⅱ1 are prime, i.e. not isomorphic to any non-trivial tensor product.
Ockham Algebras Arising from Monoids
Institute of Scientific and Technical Information of China (English)
T.S. Blyth; H.J. Silva; J.C. Varlet
2001-01-01
An Ockham algebra (L; f) is of boolean shape if its lattice reduct L is boolean and f is not the complementation. We investigate a natural construction of Ockham algebras of boolean shape from any given monoid. Of particular interest is the question of when such algebras are subdirectly irreducible. In settling this, we obtain what is probably the first example of a subdirectly irreducible Ockham algebra that does not belong to the generalized variety Kω. We also prove that every semigroup can be embedded in the monoid of endomorphisms of an Ockham algebra of boolean shape.
Galois Connections for Flow Algebras
DEFF Research Database (Denmark)
Filipiuk, Piotr; Terepeta, Michal Tomasz; Nielson, Hanne Riis
2011-01-01
We generalise Galois connections from complete lattices to flow algebras. Flow algebras are algebraic structures that are less restrictive than idempotent semirings in that they replace distributivity with monotonicity and dispense with the annihilation property; therefore they are closer...... to the approach taken by Monotone Frameworks and other classical analyses. We present a generic framework for static analysis based on flow algebras and program graphs. Program graphs are often used in Model Checking to model concurrent and distributed systems. The framework allows to induce new flow algebras...
Quantum algebra of $N$ superspace
Hatcher, N; Stephany, J
2006-01-01
We identify the quantum algebra of position and momentum operators for a quantum system in superspace bearing an irreducible representation of the super Poinca\\'e algebra. This algebra is noncommutative for the position operators. We use the properties of superprojectors in D=4 $N$ superspace to construct explicit position and momentum operators satisfying the algebra. They act on wave functions corresponding to different supermultiplets classified by its superspin. We show that the quantum algebra associated to the massive superparticle is a particular case described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently.
Twisted derivations of Hopf algebras
Davydov, Alexei
2012-01-01
In the paper we introduce the notion of twisted derivation of a bialgebra. Twisted derivations appear as infinitesimal symmetries of the category of representations. More precisely they are infinitesimal versions of twisted automorphisms of bialgebras. Twisted derivations naturally form a Lie algebra (the tangent algebra of the group of twisted automorphisms). Moreover this Lie algebra fits into a crossed module (tangent to the crossed module of twisted automorphisms). Here we calculate this crossed module for universal enveloping algebras and for the Sweedler's Hopf algebra.
$A\\mathcal{T}$-Algebras and Extensions of $AT$-Algebras
Indian Academy of Sciences (India)
Hongliang Yao
2010-04-01
Lin and Su classified $A\\mathcal{T}$-algebras of real rank zero. This class includes all $A\\mathbb{T}$-algebras of real rank zero as well as many *-algebras which are not stably finite. An $A\\mathcal{T}$-algebra often becomes an extension of an $A\\mathbb{T}$-algebra by an -algebra. In this paper, we show that there is an essential extension of an $A\\mathbb{T}$-algebra by an -algebra which is not an $A\\mathcal{T}$-algebra. We describe a characterization of an extension of an $A\\mathbb{T}$-algebra by an -algebra if is an $A\\mathcal{T}$-algebra.
Planar Para Algebras, Reflection Positivity
Jaffe, Arthur; Liu, Zhengwei
2017-05-01
We define a planar para algebra, which arises naturally from combining planar algebras with the idea of ZN para symmetry in physics. A subfactor planar para algebra is a Hilbert space representation of planar tangles with parafermionic defects that are invariant under para isotopy. For each ZN, we construct a family of subfactor planar para algebras that play the role of Temperley-Lieb-Jones planar algebras. The first example in this family is the parafermion planar para algebra (PAPPA). Based on this example, we introduce parafermion Pauli matrices, quaternion relations, and braided relations for parafermion algebras, which one can use in the study of quantum information. An important ingredient in planar para algebra theory is the string Fourier transform (SFT), which we use on the matrix algebra generated by the Pauli matrices. Two different reflections play an important role in the theory of planar para algebras. One is the adjoint operator; the other is the modular conjugation in Tomita-Takesaki theory. We use the latter one to define the double algebra and to introduce reflection positivity. We give a new and geometric proof of reflection positivity by relating the two reflections through the string Fourier transform.
Algebraic connectivity and graph robustness.
Energy Technology Data Exchange (ETDEWEB)
Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T. (University of New Mexico)
2009-07-01
Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.
Constructive version of Boolean algebra
Ciraulo, Francesco; Toto, Paola
2012-01-01
The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we first show some properties concerning overlap algebras: we prove that the notion of overlap morphism corresponds classically to that of map preserving arbitrary joins; we provide a description of atomic set-based overlap algebras in the language of formal topology, thus giving a predicative characterization of discrete locales; we show that the power-collection of a set is the free overlap algebra join-generated from the set. Then, we generalize the concept of overlap algebra and overlap morphism in various ways to provide constructive versions of the category of Boolean algebras with maps preserving arbitrary existing joins.
Abstract algebra structure and application
Finston, David R
2014-01-01
This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences. Applications include: Identification numbers and modular arithmetic (linear) error-correcting codes, including cyclic codes ruler and compass constructions cryptography symmetry of patterns in the real plane Abstract Algebra: Structure and Application is suitable as a text for a first course on abstract algebra whose main purpose is to generate interest in the subject, or as a supplementary text for more advanced courses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematics education, computer science, and engineering interested in applications of algebraic concepts.
Hopf algebras in noncommutative geometry
Varilly, J C
2001-01-01
We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of noncommutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups.
Twin TQFTs and Frobenius Algebras
Directory of Open Access Journals (Sweden)
Carmen Caprau
2013-01-01
Full Text Available We introduce the category of singular 2-dimensional cobordisms and show that it admits a completely algebraic description as the free symmetric monoidal category on a twin Frobenius algebra, by providing a description of this category in terms of generators and relations. A twin Frobenius algebra (C,W,z,z∗ consists of a commutative Frobenius algebra C, a symmetric Frobenius algebra W, and an algebra homomorphism z:C→W with dual z∗:W→C, satisfying some extra conditions. We also introduce a generalized 2-dimensional Topological Quantum Field Theory defined on singular 2-dimensional cobordisms and show that it is equivalent to a twin Frobenius algebra in a symmetric monoidal category.
On extensions of Leibniz algebras
Rakhimov, I. S.; Said Husain, Sh. K.; Mohammed, M. A.
2017-09-01
This paper is dedicated to the study extensions of Leibniz algebras using the annihilator approach. The extensions methods have been used earlier to classify certain classes of algebras. In the paper we first review and adjust theoretical background of the method for Leibniz algebras then apply it to classify four-dimensional Leibniz algebras over a field K. We obtain complete classification of four-dimensional nilpotent Leibniz algebras. The main idea of the method is to transfer the “base change” action to an action of automorphism group of the algebras of smaller dimension on cocycles constructed by the annihilator extensions. The method can be used to classify low-dimensional Leibniz algebras over other finite fields as well.
Topological convolution algebras
Alpay, Daniel
2012-01-01
In this paper we introduce a new family of topological convolution algebras of the form $\\bigcup_{p\\in\\mathbb N} L_2(S,\\mu_p)$, where $S$ is a Borel semi-group in a locally compact group $G$, which carries an inequality of the type $\\|f*g\\|_p\\le A_{p,q}\\|f\\|_q\\|g\\|_p$ for $p > q+d$ where $d$ pre-assigned, and $A_{p,q}$ is a constant. We give a sufficient condition on the measures $\\mu_p$ for such an inequality to hold. We study the functional calculus and the spectrum of the elements of these algebras, and present two examples, one in the setting of non commutative stochastic distributions, and the other related to Dirichlet series.
Jaszunska, Joanna
2010-01-01
The structure of the algebra K[M] of the Chinese monoid M over a field K is studied. The minimal prime ideals are described. They are determined by certain homogeneous congruences on M and they are in a one to one correspondence with diagrams of certain special type. There are finitely many such ideals. It is also shown that the prime radical B(K[M]) of K[M] coincides with the Jacobson radical and the monoid M embeds into the algebra K[M]/B(K[M]). A new representation of M as a submonoid of the direct product of finitely many copies of the bicyclic monoid and finitely many copies of the infinite cyclic monoid is derived. Consequently, M satisfies a nontrivial identity.
Practical Algebraic Renormalization
Grassi, P A; Steinhauser, M
1999-01-01
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the Standard Model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustra...
Stable Recursive Subhomogeneous Algebras
Liang, Hutian
2011-01-01
In this paper, we introduce stable recursive subhomogeneous algebras (SRSHAs), which is analogous to recursive subhomogeneous algebras (RSHAs) introduced by N. C. Phillips in the studies of free minimal integer actions on compact metric spaces. The difference between the stable version and the none stable version is that the irreducible representations of SRSHAs are infinite dimensional, but the irreducible representations of the RSHAs are finite dimensional. While RSHAs play an important role in the study of free minimal integer actions on compact metric spaces, SRSHAs play an analogous role in the study of free minimal actions by the group of the real numbers on compact metric spaces. In this paper, we show that simple inductive limits of SRSHAs with no dimension growth in which the connecting maps are injective and non-vanishing have topological stable rank one.
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
Testing algebraic geometric codes
Institute of Scientific and Technical Information of China (English)
CHEN Hao
2009-01-01
Property testing was initially studied from various motivations in 1990's.A code C (∩)GF(r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector's coordinates.The problem of testing codes was firstly studied by Blum,Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs).How to characterize locally testable codes is a complex and challenge problem.The local tests have been studied for Reed-Solomon (RS),Reed-Muller (RM),cyclic,dual of BCH and the trace subcode of algebraicgeometric codes.In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions).We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.
Testing algebraic geometric codes
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Property testing was initially studied from various motivations in 1990’s. A code C GF (r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector’s coordinates. The problem of testing codes was firstly studied by Blum, Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs). How to characterize locally testable codes is a complex and challenge problem. The local tests have been studied for Reed-Solomon (RS), Reed-Muller (RM), cyclic, dual of BCH and the trace subcode of algebraicgeometric codes. In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions). We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.
Operator product expansion algebra
Energy Technology Data Exchange (ETDEWEB)
Holland, Jan [CPHT, Ecole Polytechnique, Paris-Palaiseau (France)
2014-07-01
The Operator Product Expansion (OPE) is a theoretical tool for studying the short distance behaviour of products of local quantum fields. Over the past 40 years, the OPE has not only found widespread computational application in high-energy physics, but, on a more conceptual level, it also encodes fundamental information on algebraic structures underlying quantum field theories. I review new insights into the status and properties of the OPE within Euclidean perturbation theory, addressing in particular the topics of convergence and ''factorisation'' of the expansion. Further, I present a formula for the ''deformation'' of the OPE algebra caused by a quartic interaction. This formula can be used to set up a novel iterative scheme for the perturbative computation of OPE coefficients, based solely on the zeroth order coefficients (and renormalisation conditions) as initial input.
Combinatorics and commutative algebra
Stanley, Richard P
1996-01-01
Some remarkable connections between commutative algebra and combinatorics have been discovered in recent years. This book provides an overview of two of the main topics in this area. The first concerns the solutions of linear equations in nonnegative integers. Applications are given to the enumeration of integer stochastic matrices (or magic squares), the volume of polytopes, combinatorial reciprocity theorems, and related results. The second topic deals with the face ring of a simplicial complex, and includes a proof of the Upper Bound Conjecture for Spheres. An introductory chapter giving background information in algebra, combinatorics and topology broadens access to this material for non-specialists. New to this edition is a chapter surveying more recent work related to face rings, focusing on applications to f-vectors. Included in this chapter is an outline of the proof of McMullen's g-conjecture for simplicial polytopes based on toric varieties, as well as a discussion of the face rings of such special ...
Algebra, Arithmetic, and Geometry
Tschinkel, Yuri
2009-01-01
The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont
Semisimple Metacyclic Group Algebras
Indian Academy of Sciences (India)
Gurmeet K Bakshi; Shalini Gupta; Inder Bir S Passi
2011-11-01
Given a group of order $p_1p_2$, where $p_1,p_2$ are primes, and $\\mathbb{F}_q$, a finite field of order coprime to $p_1p_2$, the object of this paper is to compute a complete set of primitive central idempotents of the semisimple group algebra $\\mathbb{F}_q[G]$. As a consequence, we obtain the structure of $\\mathbb{F}_q[G]$ and its group of automorphisms.
Beigie, Darin
2014-01-01
Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…
Lee, Jaehoon; Wilczek, Frank
2013-11-27
Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.
Lutfiyya, Lutfi A
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Modern Algebra includes set theory, operations, relations, basic properties of the integers, group theory, and ring theory.
Lie algebraic noncommutative gravity
Banerjee, Rabin; Mukherjee, Pradip; Samanta, Saurav
2007-06-01
We exploit the Seiberg-Witten map technique to formulate the theory of gravity defined on a Lie algebraic noncommutative space-time. Detailed expressions of the Seiberg-Witten maps for the gauge parameters, gauge potentials, and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first order correction, exactly as happens for a canonical (i.e. constant) noncommutativity.
Redesigning linear algebra algorithms
Energy Technology Data Exchange (ETDEWEB)
Dongarra, J.J.
1983-01-01
Many of the standard algorithms in linear algebra as implemented in FORTRAN do not achieve maximum performance on today's large-scale vector computers. The author examines the problem and constructs alternative formulations of algorithms that do not lose the clarity of the original algorithm or sacrifice the FORTRAN portable environment, but do gain the performance attainable on these supercomputers. The resulting implementation not only performs well on vector computers but also increases performance on conventional sequential computers. 13 references.
Redesigning linear algebra algorithms
Energy Technology Data Exchange (ETDEWEB)
Dongarra, J.J.
1983-01-01
Many of the standard algorithms in linear algebra as implemented in FORTRAN do not achieve maximum performance on today's large-scale vector computers. In this paper we examine the problem and construct alternative formulations of algorithms that do not lose the clarity of the original algorithm or sacrifice the Fortran portable environment, but do gain the performance attainable on these supercomputers. The resulting implementation not only performs well on vector computers but also increases performance on conventional sequential computers.
Fundamentals of linear algebra
Dash, Rajani Ballav
2008-01-01
FUNDAMENTALS OF LINEAR ALGEBRA is a comprehensive Text Book, which can be used by students and teachers of All Indian Universities. The Text has easy, understandable form and covers all topics of UGC Curriculum. There are lots of worked out examples which helps the students in solving the problems without anybody's help. The Problem sets have been designed keeping in view of the questions asked in different examinations.
Algebra & trigonometry II essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Algebra & Trigonometry II includes logarithms, sequences and series, permutations, combinations and probability, vectors, matrices, determinants and systems of equations, mathematica
Ext algebra of Nichols algebras of type $A_2$
Yu, Xiaolan
2011-01-01
We give the full structure of the Ext algebra of a Nichols algebra of type $A_2$ by using the Hochschild-Serre spectral sequence. As an application, we show that the pointed Hopf algebras $u(\\mathcal{D}, \\lmd, \\mu)$ with Dynkin diagrams of type $A$, $D$, or $E$, except for $A_1$ and $A_1\\times A_1$ with the order $N_{J}>2$ for at least one component $J$, are wild.
LOCAL AUTOMORPHISMS OF SEMISIMPLE ALGEBRAS AND GROUP ALGEBRAS
Institute of Scientific and Technical Information of China (English)
Wang Dengyin; Guan Qi; Zhan9 Dongju
2011-01-01
Let F be a field of characteristic not 2,and let A be a finite-dimensional semisimple F-algebra.All local automorphisms of A are characterized when all the degrees of A are larger than 1.If F is further assumed to be an algebraically closed field of characteristic zero,K a finite group,FK the group algebra of K over F,then all local automorphisms of FK are also characterized.
Stability of functional equations in Banach algebras
Cho, Yeol Je; Rassias, Themistocles M; Saadati, Reza
2015-01-01
Some of the most recent and significant results on homomorphisms and derivations in Banach algebras, quasi-Banach algebras, C*-algebras, C*-ternary algebras, non-Archimedean Banach algebras and multi-normed algebras are presented in this book. A brief introduction for functional equations and their stability is provided with historical remarks. Since the homomorphisms and derivations in Banach algebras are additive and R-linear or C-linear, the stability problems for additive functional equations and additive mappings are studied in detail. The latest results are discussed and examined in stability theory for new functional equations and functional inequalities in Banach algebras and C*-algebras, non-Archimedean Banach algebras, non-Archimedean C*-algebras, multi-Banach algebras and multi-C*-algebras. Graduate students with an understanding of operator theory, functional analysis, functional equations and analytic inequalities will find this book useful for furthering their understanding and discovering the l...
Blyth, T S
2002-01-01
Most of the introductory courses on linear algebra develop the basic theory of finite dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num ber of illustrative and worked examples, as well as many exercises that are strategi cally placed throughout the text. Solutions to the ex...
Energy Technology Data Exchange (ETDEWEB)
Palmkvist, Jakob, E-mail: palmkvist@ihes.fr [Institut des Hautes Etudes Scientifiques, 35 Route de Chartres, FR-91440 Bures-sur-Yvette (France)
2014-01-15
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras
Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent; Kato La, V.
2016-10-01
We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.
DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA
Institute of Scientific and Technical Information of China (English)
CHENCAOYU
1996-01-01
Let L be an n-dimensional nilpotent Lie algebra with a basis{x1…,xn),and every xi acts as a locally nilpotent derivation on algebra A. This paper shows that there exists a set of derivations{y1,…,yn}on U(L) such that (A#U(L))#k{y,1,…,yn] is ismorphic to the Weyl algebra An(A).The author also uses the de4rivations to obtain a necessary and sufficient condition for a finite dimesional Lie algebra to be nilpotent.
On the cohomology of Leibniz conformal algebras
Zhang, Jiao
2015-04-01
We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.
Assessing Algebraic Solving Ability: A Theoretical Framework
Lian, Lim Hooi; Yew, Wun Thiam
2012-01-01
Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.
Cardinal invariants on Boolean algebras
Monk, J Donald
2014-01-01
This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the...
Algebraic Quantum Mechanics and Pregeometry
Hiley, D J B P G D B J
2006-01-01
We discuss the relation between the q-number approach to quantum mechanics suggested by Dirac and the notion of "pregeometry" introduced by Wheeler. By associating the q-numbers with the elements of an algebra and regarding the primitive idempotents as "generalized points" we suggest an approach that may make it possible to dispense with an a priori given space manifold. In this approach the algebra itself would carry the symmetries of translation, rotation, etc. Our suggestion is illustrated in a preliminary way by using a particular generalized Clifford Algebra proposed originally by Weyl, which approaches the ordinary Heisenberg algebra in a suitable limit. We thus obtain a certain insight into how quantum mechanics may be regarded as a purely algebraic theory, provided that we further introduce a new set of "neighbourhood operators", which remove an important kind of arbitrariness that has thus far been present in the attempt to treat quantum mechanics solely in terms of a Heisenberg algebra.
Novotna, Jarmila; Hoch, Maureen
2008-01-01
Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…
NON-COMMUTATIVE POISSON ALGEBRA STRUCTURES ON LIE ALGEBRA sln(fCq) WITH NULLITY M
Institute of Scientific and Technical Information of China (English)
Jie TONG; Quanqin JIN
2013-01-01
Non-commutative Poisson algebras are the algebras having both an associa-tive algebra structure and a Lie algebra structure together with the Leibniz law. In this paper, the non-commutative poisson algebra structures on the Lie algebras sln(fCq) are determined.
Applications of algebraic grid generation
Eiseman, Peter R.; Smith, Robert E.
1990-01-01
Techniques and applications of algebraic grid generation are described. The techniques are univariate interpolations and transfinite assemblies of univariate interpolations. Because algebraic grid generation is computationally efficient, the use of interactive graphics in conjunction with the techniques is advocated. A flexible approach, which works extremely well in an interactive environment, called the control point form of algebraic grid generation is described. The applications discussed are three-dimensional grids constructed about airplane and submarine configurations.
Linear algebra and projective geometry
Baer, Reinhold
2005-01-01
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. These focus on the representation of projective geometries by linear manifolds, of projectivities by semilinear transformations, of collineations by linear transformations, and of dualities by semilinear forms. These theorems lead to a reconstruction of the geometry that constituted the discussion's starting point, within algebra
COCLEFT EXTENSIONS OF HOPF ALGEBRAS
Institute of Scientific and Technical Information of China (English)
祝家贵
2006-01-01
Let B and H be finitely generated projective Hopf algebras over a commutative ring R,with B cocommutative and H commutative. In this paper we investigate cocleft extensions of Hopf algebras, and prove that the isomorphism classes of cocleft Hopf algebras extensions of B by H are determined uniquely by the group C(B, H) = ZC(B, H)/d(B, H) .
Categorical Algebra and its Applications
1988-01-01
Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences. The volume contains 28 carefully selected and refereed papers, out of 96 talks delivered, and illustrates the usefulness of category theory today as a powerful tool of investigation in many other areas.
ALGEBRAIC EXTENSION OF *-A OPERATOR
Institute of Scientific and Technical Information of China (English)
左红亮; 左飞
2014-01-01
In this paper, we study various properties of algebraic extension of∗-A operator. Specifically, we show that every algebraic extension of∗-A operator has SVEP and is isoloid. And if T is an algebraic extension of∗-A operator, then Weyl’s theorem holds for f (T ), where f is an analytic functions on some neighborhood of σ(T ) and not constant on each of the components of its domain.
Differential Equations with Linear Algebra
Boelkins, Matthew R; Potter, Merle C
2009-01-01
Linearity plays a critical role in the study of elementary differential equations; linear differential equations, especially systems thereof, demonstrate a fundamental application of linear algebra. In Differential Equations with Linear Algebra, we explore this interplay between linear algebra and differential equations and examine introductory and important ideas in each, usually through the lens of important problems that involve differential equations. Written at a sophomore level, the text is accessible to students who have completed multivariable calculus. With a systems-first approach, t
Notes on noncommutative algebraic topology
Nikolaev, Igor
2010-01-01
An operator (AF-) algebra A_f is assigned to each Anosov diffeomorphism f of a manifold M. The assignment is a functor on the category of (mapping tori of) all such diffeomorphisms, which sends continuous maps between the manifolds to the stable homomorphisms of the corresponding AF-algebras. We use the functor to prove non-existence of continuous maps between the hyperbolic torus bundles, an obstruction being the so-called Galois group of algebra A_f.
Algebraic geometric codes with applications
Institute of Scientific and Technical Information of China (English)
CHEN Hao
2007-01-01
The theory of linear error-correcting codes from algebraic geomet-ric curves (algebraic geometric (AG) codes or geometric Goppa codes) has been well-developed since the work of Goppa and Tsfasman, Vladut, and Zink in 1981-1982. In this paper we introduce to readers some recent progress in algebraic geometric codes and their applications in quantum error-correcting codes, secure multi-party computation and the construction of good binary codes.
Kleene Algebra and Bytecode Verification
2016-04-27
Bytecode 2005 Preliminary Version Kleene Algebra and Bytecode Verification Lucja Kot 1 Dexter Kozen 2 Department of Computer Science Cornell...first-order methods that inductively annotate program points with abstract values. In [6] we introduced a second-order approach based on Kleene algebra ...form a left-handed Kleene algebra . The dataflow labeling is not achieved by inductively labeling the program with abstract values, but rather by
A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.
DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J
2016-12-01
Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions.
Algebra I Essentials For Dummies
Sterling, Mary Jane
2010-01-01
With its use of multiple variables, functions, and formulas algebra can be confusing and overwhelming to learn and easy to forget. Perfect for students who need to review or reference critical concepts, Algebra I Essentials For Dummies provides content focused on key topics only, with discrete explanations of critical concepts taught in a typical Algebra I course, from functions and FOILs to quadratic and linear equations. This guide is also a perfect reference for parents who need to review critical algebra concepts as they help students with homework assignments, as well as for adult learner
Applications of Computer Algebra Conference
Martínez-Moro, Edgar
2017-01-01
The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.
Introduction to algebraic independence theory
Philippon, Patrice
2001-01-01
In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.
REPETITIVE CLUSTER-TILTED ALGEBRAS
Institute of Scientific and Technical Information of China (English)
Zhang Shunhua; Zhang Yuehui
2012-01-01
Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1.We investigate the properties of cluster tilting objects in CFm and the structure of repetitive clustertilted algebras.Moreover,we generalize Theorem 4.2 in [12](Buan A,Marsh R,Reiten I.Cluster-tilted algebra,Trans.Amer.Math.Soc.,359(1)(2007),323-332.) to the situation of CFm,and prove that the tilting graph KCFm of CFm is connected.
The Algebra of Conformal Blocks
Manon, Christopher A
2009-01-01
We study and generalize the connection between the phylogenetic Hilbert functions of Buczynska and Wisniewski \\cite{BW} and the Verlinde formula, as discovered by Sturmfels and Xu in \\cite{StXu}. In order to accomplish this we introduce deformations of algebras of non-abelian theta functions for a general simple complex Lie algebra $\\mathfrak{g}$ structured on the moduli stack of stable punctured curves. We also study the relationship between these algebras and branching algebras, coming from the representation theory of the associated reductive group $G.$
Planar Para Algebras, Reflection Positivity
Jaffe, Arthur
2016-01-01
We define the notion of a planar para algebra, which arises naturally from combining planar algebras with the idea of $\\Z_{N}$ para symmetry in physics. A subfactor planar para algebra is a Hilbert space representation of planar tangles with parafermionic defects, that are invariant under isotopy. For each $\\Z_{N}$, we construct a family of subfactor planar para algebras which play the role of Temperley-Lieb-Jones planar algebras. The first example in this family is the parafermion planar para algebra. Based on this example, we introduce parafermion Pauli matrices, quaternion relations, and braided relations for parafermion algebras which one can use in the study of quantum information. Two different reflections play an important role in the theory of planar para algebras. One is the adjoint operator; the other is the modular conjugation in Tomita-Takesaki theory. We use the latter one to define the double algebra and to introduce reflection positivity. We give a new and geometric proof of reflection positivi...