WorldWideScience

Sample records for lengths mathematically unique

  1. On the non-uniqueness of the nodal mathematical adjoint

    International Nuclear Information System (INIS)

    Müller, Erwin

    2014-01-01

    Highlights: • We evaluate three CMFD schemes for computing the nodal mathematical adjoint. • The nodal mathematical adjoint is not unique and can be non-positive (nonphysical). • Adjoint and forward eigenmodes are compatible if produced by the same CMFD method. • In nodal applications the excited eigenmodes are purely mathematical entities. - Abstract: Computation of the neutron adjoint flux within the framework of modern nodal diffusion methods is often facilitated by reducing the nodal equation system for the forward flux into a simpler coarse-mesh finite-difference form and then transposing the resultant matrix equations. The solution to the transposed problem is known as the nodal mathematical adjoint. Since the coarse-mesh finite-difference reduction of a given nodal formulation can be obtained in a number of ways, different nodal mathematical adjoint solutions can be computed. This non-uniqueness of the nodal mathematical adjoint challenges the credibility of the reduction strategy and demands a verdict as to its suitability in practical applications. This is the matter under consideration in this paper. A selected number of coarse-mesh finite-difference reduction schemes are described and compared. Numerical calculations are utilised to illustrate the differences in the adjoint solutions as well as to appraise the impact on such common applications as the computation of core point kinetics parameters. Recommendations are made for the proper application of the coarse-mesh finite-difference reduction approach to the nodal mathematical adjoint problem

  2. Uniquely Precise: Importance of Conceptual Knowledge and Mathematical Language

    Science.gov (United States)

    Shockey, Tod; Pindiprolu, Sekhar

    2015-01-01

    The importance of mathematical concept development and language is recognized early in children's schooling as they mature through shape and counting experiences. The reader may recall instances of a youngster referring to a "corner" of a shape before the reader has the language of vertex. This language precision needs to continue to…

  3. Sensitivity to numerosity is not a unique visuospatial psychophysical predictor of mathematical ability.

    Science.gov (United States)

    Tibber, Marc S; Manasseh, Gemma S L; Clarke, Richard C; Gagin, Galina; Swanbeck, Sonja N; Butterworth, Brian; Lotto, R Beau; Dakin, Steven C

    2013-08-30

    Sensitivity to visual numerosity has previously been shown to predict human mathematical performance. However, it is not clear whether it is discrimination of numerosity per se that is predictive of mathematical ability, or whether the association is driven by more general task demands. To test this notion we had over 300 participants (ranging in age from 6 to 73 years) perform a symbolic mathematics test and 4 different visuospatial matching tasks. The visual tasks involved matching 2 clusters of Gabor elements for their numerosity, density, size or orientation by a method of adjustment. Partial correlation and regression analyses showed that sensitivity to visual numerosity, sensitivity to visual orientation and mathematical education level predict a significant proportion of shared as well as unique variance in mathematics scores. These findings suggest that sensitivity to visual numerosity is not a unique visual psychophysical predictor of mathematical ability. Instead, the data are consistent with mathematics representing a multi-factorial process that shares resources with a number of visuospatial tasks. Copyright © 2013 The Authors. Published by Elsevier Ltd.. All rights reserved.

  4. Sensitivity to numerosity is not a unique visuospatial psychophysical predictor of mathematical ability☆

    Science.gov (United States)

    Tibber, Marc S.; Manasseh, Gemma S.L.; Clarke, Richard C.; Gagin, Galina; Swanbeck, Sonja N.; Butterworth, Brian; Lotto, R. Beau; Dakin, Steven C.

    2013-01-01

    Sensitivity to visual numerosity has previously been shown to predict human mathematical performance. However, it is not clear whether it is discrimination of numerosity per se that is predictive of mathematical ability, or whether the association is driven by more general task demands. To test this notion we had over 300 participants (ranging in age from 6 to 73 years) perform a symbolic mathematics test and 4 different visuospatial matching tasks. The visual tasks involved matching 2 clusters of Gabor elements for their numerosity, density, size or orientation by a method of adjustment. Partial correlation and regression analyses showed that sensitivity to visual numerosity, sensitivity to visual orientation and mathematical education level predict a significant proportion of shared as well as unique variance in mathematics scores. These findings suggest that sensitivity to visual numerosity is not a unique visual psychophysical predictor of mathematical ability. Instead, the data are consistent with mathematics representing a multi-factorial process that shares resources with a number of visuospatial tasks. PMID:23820087

  5. The short and long of adolescent sleep: the unique impact of day length.

    Science.gov (United States)

    Bartel, Kate; van Maanen, Annette; Cassoff, Jamie; Friborg, Oddgeir; Meijer, Anne Marie; Oort, Frans; Williamson, Paul; Gruber, Reut; Knäuper, Bärbel; Gradisar, Michael

    2017-10-01

    Variation in day length is proposed to impact sleep, yet it is unknown whether this is above the influence of behavioural factors. Day length, sleep hygiene, and parent-set bedtime were simultaneously explored, to investigate the relative importance of each on adolescents' sleep. An online survey was distributed in four countries at varying latitudes/longitudes (Australia, The Netherlands, Canada, Norway). Overall, 711 (242 male; age M = 15.7 ± 1.6, range = 12-19 yrs) adolescents contributed data. Hierarchical regression analyses showed good sleep hygiene was associated with earlier bedtime, shorter sleep latency, and longer sleep (β = -0.34; -0.30; 0.32, p sleep latency (β = -0.21, p sleep (β = -0.14, p = 0.001). Longer day length predicted earlier bedtimes (β = -0.11, p = 0.004), and longer sleep (β = 0.10, p = 0.011). Sleep hygiene had the most clinical relevance for improving sleep, thus should be considered when implementing adolescent sleep interventions, particularly as small negative effects of shorter day length may be minimised through sleep hygiene techniques. Copyright © 2017 Elsevier B.V. All rights reserved.

  6. Why Learning Common Fractions Is Uncommonly Difficult: Unique Challenges Faced by Students With Mathematical Disabilities.

    Science.gov (United States)

    Berch, Daniel B

    In this commentary, I examine some of the distinctive, foundational difficulties in learning fractions and other types of rational numbers encountered by students with a mathematical learning disability and how these differ from the struggles experienced by students classified as low achieving in math. I discuss evidence indicating that students with math disabilities exhibit a significant delay or deficit in the numerical transcoding of decimal fractions, and I further maintain that they may face unique challenges in developing the ability to effectively translate between different types of fractions and other rational number notational formats-what I call conceptual transcoding. I also argue that characterizing this level of comprehensive understanding of rational numbers as rational number sense is irrational, as it misrepresents this flexible and adaptive collection of skills as a biologically based percept rather than a convergence of higher-order competencies that require intensive, formal instruction.

  7. The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement.

    Science.gov (United States)

    Wong, Terry Tin-Yau

    2017-12-01

    The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning. Copyright © 2017 Elsevier Inc. All rights reserved.

  8. Unique effects of the chain lengths and anions of tetra-alkylammonium salts on quenching pyrene excimer.

    Science.gov (United States)

    Jang, Hyun-Sook; Zhao, Jing; Lei, Yu; Nieh, Mu-Ping

    2014-09-10

    Pyrene (Py) excimer, through its unique fluorescence quenching, exhibits high sensitivity and high selectivity in detecting specific electron-deficient molecules, providing a potential platform for sensing technology, optical switch, and probing hydrophobicity of molecular environment. In solution state, its quenching mechanism has been well-studied. However, there remain many unknown properties regarding the quenching mechanism of the solid-state Py excimer. In this paper, the effects of a series of tetra-alkylammonium salts (with a variety of chain lengths and anions) on Py excimer quenching are investigated to identify the controlling parameters of the fluorescence quenching in the binary system. Several experimental approaches including steady-state fluorescence spectroscopy, UV absorption, (13)C-nuclear magnetic resonance (NMR) spectra, X-ray diffraction, scanning electron microscopy, and time-dependent fluorescence decay are employed to seek for the fundamental understanding of the quenching mechanism. The result indicates a unique quenching effect of tetrabutylammonium cation on the pyrene excimer, and which is not observed in the other cations with different chain lengths (the same associated hexafluorophosphate anions). Meanwhile, hexafluorophosphate anion (in the presence of tetrabutylammonium) is able to effectively retain Py excimer fluorescence when the system is prepared by evaporating solvent at high temperature. It is also confirmed that dynamic quenching is involved in the process. Hydrophobic environment around Py molecules shows strong correlation with the formation of Py excimer. The knowledge obtained in this study provides the insights to how the interaction between salt and Py molecule affects the excimer fluorescence.

  9. Seedling length in wheat determined by image processing using mathematical tools

    Directory of Open Access Journals (Sweden)

    André Pich Brunes

    2016-06-01

    Full Text Available ABSTRACT Seed vigour is determined by a series of laboratory tests, many of these laborious and time-consuming. In view of this, the present study aimed to compare the determination of seedling length in wheat using image processing, with the traditional method, as well as the ability of the method to determine seed vigour. The experimental design was completely randomised, with five replications comprising a single-factor experimental scheme. The data were analysed for normality by the Shapiro-Wilk test and variance analysis using ANOVA at 5% probability. The response variables were correlated using Pearson's test, and the methodologies for determining the length of the shoots and roots, by measuring with a graduated rule and by image processing, were compared using the F-test at 5% probability. To compare mean values between cultivars, Tukey's test at 5% probability was used. The length of the shoots and roots of wheat seedlings, determined by image processing using the Matlab® mathematical tool, is efficient in separating the cultivars into levels of vigour in a similar way to evaluations used routinely for this purpose.

  10. A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic-Axiomatic (Matrix Approach ‡

    Directory of Open Access Journals (Sweden)

    Ramin Zahedi

    2017-09-01

    Full Text Available In this article, as a new mathematical approach to origin of the laws of nature, using a new basic algebraic axiomatic (matrix formalism based on the ring theory and Clifford algebras (presented in Section 2, “it is shown that certain mathematical forms of fundamental laws of nature, including laws governing the fundamental forces of nature (represented by a set of two definite classes of general covariant massive field equations, with new matrix formalisms, are derived uniquely from only a very few axioms.” In agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. In essence, the main scheme of this new mathematical axiomatic approach to the fundamental laws of nature is as follows: First, based on the assumption of the rationality of D-momentum and by linearization (along with a parameterization procedure of the Lorentz invariant energy-momentum quadratic relation, a unique set of Lorentz invariant systems of homogeneous linear equations (with matrix formalisms compatible with certain Clifford and symmetric algebras is derived. Then by an initial quantization (followed by a basic procedure of minimal coupling to space-time geometry of these determined systems of linear equations, a set of two classes of general covariant massive (tensor field equations (with matrix formalisms compatible with certain Clifford, and Weyl algebras is derived uniquely as well.

  11. Shared and Unique Risk Factors Underlying Mathematical Disability and Reading and Spelling Disability

    NARCIS (Netherlands)

    Slot, E.M.; van Viersen, S.; de Bree, E.H.; Kroesbergen, E.H.

    2016-01-01

    High comorbidity rates have been reported between mathematical learning disabilities (MD) and reading and spelling disabilities (RSD). Research has identified skills related to math, such as number sense (NS) and visuospatial working memory (visuospatial WM), as well as to literacy, such as

  12. Why Learning Common Fractions Is Uncommonly Difficult: Unique Challenges Faced by Students with Mathematical Disabilities

    Science.gov (United States)

    Berch, Daniel B.

    2017-01-01

    In this commentary, I examine some of the distinctive, foundational difficulties in learning fractions and other types of rational numbers encountered by students with a mathematical learning disability and how these differ from the struggles experienced by students classified as low achieving in math. I discuss evidence indicating that students…

  13. Contributions from specific and general factors to unique deficits: two cases of mathematics learning difficulties

    Directory of Open Access Journals (Sweden)

    Vitor Geraldi Haase

    2014-02-01

    Full Text Available Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties.

  14. Contributions from specific and general factors to unique deficits: two cases of mathematics learning difficulties.

    Science.gov (United States)

    Haase, Vitor G; Júlio-Costa, Annelise; Lopes-Silva, Júlia B; Starling-Alves, Isabella; Antunes, Andressa M; Pinheiro-Chagas, Pedro; Wood, Guilherme

    2014-01-01

    Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties.

  15. Specific Preschool Executive Functions Predict Unique Aspects of Mathematics Development: A 3-Year Longitudinal Study.

    Science.gov (United States)

    Simanowski, Stefanie; Krajewski, Kristin

    2017-08-10

    This study assessed the extent to which executive functions (EF), according to their factor structure in 5-year-olds (N = 244), influenced early quantity-number competencies, arithmetic fluency, and mathematics school achievement throughout first and second grades. A confirmatory factor analysis resulted in updating as a first, and inhibition and shifting as a combined second factor. In the structural equation model, updating significantly affected knowledge of the number word sequence, suggesting a facilitatory effect on basic encoding processes in numerical materials that can be learnt purely by rote. Shifting and inhibition significantly influenced quantity to number word linkages, indicating that these processes promote developing a profound understanding of numbers. These results show the supportive role of specific EF for specific aspects of a numerical foundation. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.

  16. The Analysis on the Length and Content Changes on Secondary Mathematics Textbooks in North Korea

    Science.gov (United States)

    Cho, Hoyun

    2010-01-01

    North Korea is one of the most closed nations in the world. It is difficult to access information about their education system. North Korea's economic system was reorganized on July 1, 2002, as well as the education system. This change has impacted North Korea's mathematics education. With limited information on North Korean mathematics textbooks,…

  17. Mathematical model of fructan biosynthesis and polymer length distribution in plants

    DEFF Research Database (Denmark)

    Rasmussen, Gitte Susanne; Thornley, John H. M.; Parsons, Anthony J.

    2013-01-01

    Background and Aims There are many unresolved issues concerning the biochemistry of fructan biosynthesis. The aim of this paper is to address some of these by means of modelling mathematically the biochemical processes.Methods A model has been constructed for the step-by-step synthesis of fructan...... adjustments.Conclusions Mathematical modelling of fructan biosynthesis can provide a useful tool for helping elucidate the details of the biosynthetic processes....

  18. Distinct Domains of CheA Confer Unique Functions in Chemotaxis and Cell Length in Azospirillum brasilense Sp7.

    Science.gov (United States)

    Gullett, Jessica M; Bible, Amber; Alexandre, Gladys

    2017-07-01

    Chemotaxis is the movement of cells in response to gradients of diverse chemical cues. Motile bacteria utilize a conserved chemotaxis signal transduction system to bias their motility and navigate through a gradient. A central regulator of chemotaxis is the histidine kinase CheA. This cytoplasmic protein interacts with membrane-bound receptors, which assemble into large polar arrays, to propagate the signal. In the alphaproteobacterium Azospirillum brasilense , Che1 controls transient increases in swimming speed during chemotaxis, but it also biases the cell length at division. However, the exact underlying molecular mechanisms for Che1-dependent control of multiple cellular behaviors are not known. Here, we identify specific domains of the CheA1 histidine kinase implicated in modulating each of these functions. We show that CheA1 is produced in two isoforms: a membrane-anchored isoform produced as a fusion with a conserved seven-transmembrane domain of unknown function (TMX) at the N terminus and a soluble isoform similar to prototypical CheA. Site-directed and deletion mutagenesis combined with behavioral assays confirm the role of CheA1 in chemotaxis and implicate the TMX domain in mediating changes in cell length. Fluorescence microscopy further reveals that the membrane-anchored isoform is distributed around the cell surface while the soluble isoform localizes at the cell poles. Together, the data provide a mechanism for the role of Che1 in controlling multiple unrelated cellular behaviors via acquisition of a new domain in CheA1 and production of distinct functional isoforms. IMPORTANCE Chemotaxis provides a significant competitive advantage to bacteria in the environment, and this function has been transferred laterally multiple times, with evidence of functional divergence in different genomic contexts. The molecular principles that underlie functional diversification of chemotaxis in various genomic contexts are unknown. Here, we provide a molecular

  19. Uniquely identifying cell orientation and sarcomere length in the intact rodent heart with oblique plane remote focussing microscopy

    Science.gov (United States)

    Corbett, A. D.; Burton, R. A. B.; Bub, G.; Wilson, T.

    2015-07-01

    In cardiac imaging, the spacing between sub-cellular sarcomere structures is of great importance to physiologists in understanding muscle design and performance. Making accurate measurements of the sarcomere length (SL) presents a significant imaging challenge owing to the size of the SL (~2μm) and its naturally low variability (pathological models of chronic hypertension. As well as improving measurement precision, the distribution of α across the field of view provides additional structural information which can be related to disease morphology. To validate this new imaging protocol, the value of α calculated from the oblique planes provided the input to a rigid model cell which was used to predict the appearance of the cell in the conventional focal plane. The comparison of the model to the image data provided a confidence metric for our measurements. Finally, by considering the optical transfer function, the range of cell orientations for which the method is valid could be calculated.

  20. Expression cloning screening of a unique and full-length set of cDNA clones is an efficient method for identifying genes involved in Xenopus neurogenesis.

    Science.gov (United States)

    Voigt, Jana; Chen, Jun-An; Gilchrist, Mike; Amaya, Enrique; Papalopulu, Nancy

    2005-03-01

    Functional screens, where a large numbers of cDNA clones are assayed for certain biological activity, are a useful tool in elucidating gene function. In Xenopus, gain of function screens are performed by pool screening, whereby RNA transcribed in vitro from groups of cDNA clones, ranging from thousands to a hundred, are injected into early embryos. Once an activity is detected in a pool, the active clone is identified by sib-selection. Such screens are intrinsically biased towards potent genes, whose RNA is active at low quantities. To improve the sensitivity and efficiency of a gain of function screen we have bioinformatically processed an arrayed and EST sequenced set of 100,000 gastrula and neurula cDNA clones, to create a unique and full-length set of approximately 2500 clones. Reducing the redundancy and excluding truncated clones from the starting clone set reduced the total number of clones to be screened, in turn allowing us to reduce the pool size to just eight clones per pool. We report that the efficiency of screening this clone set is five-fold higher compared to a redundant set derived from the same libraries. We have screened 960 cDNA clones from this set, for genes that are involved in neurogenesis. We describe the overexpression phenotypes of 18 single clones, the majority of which show a previously uncharacterised phenotype and some of which are completely novel. In situ hybridisation analysis shows that a large number of these genes are specifically expressed in neural tissue. These results demonstrate the effectiveness of a unique full-length set of cDNA clones for uncovering players in a developmental pathway.

  1. A Unique Primer with an Inosine Chain at the 5'-Terminus Improves the Reliability of SNP Analysis Using the PCR-Amplified Product Length Polymorphism Method.

    Directory of Open Access Journals (Sweden)

    Hideki Shojo

    Full Text Available Polymerase chain reaction-amplified product length polymorphism (PCR-APLP is one of the most convenient and reliable methods for single nucleotide polymorphism (SNP analysis. This method is based on PCR, but uses allele-specific primers containing SNP sites at the 3'-terminus of each primer. To use this method at least two allele-specific primers and one "counter-primer", which serves as a common forward or reverse primer of the allele-specific primers, are required. The allele-specific primers have SNP sites at the 3'-terminus, and another primer should have a few non-complementary flaps at the 5'-terminus to detect SNPs by determining the difference of amplicon length by PCR and subsequent electrophoresis. A major disadvantage of the addition of a non-complementary flap is the non-specific annealing of the primer with non-complementary flaps. However, a design principle for avoiding this undesired annealing has not been fully established, therefore, it is often difficult to design effective APLP primers. Here, we report allele-specific primers with an inosine chain at the 5'-terminus for PCR-APLP analysis. This unique design improves the competitiveness of allele-specific primers and the reliability of SNP analysis when using the PCR-APLP method.

  2. The Influence of Length of School Day on Grade 4 and Grade 5 Language Arts and Mathematics Performance in the State of New Jersey

    Science.gov (United States)

    Plevier, Meghan M.

    2016-01-01

    The purpose of this relational, non-experimental, explanatory, cross sectional study with quantitative methods was to explain the influence of length of school day, if any, on Grade 4 and Grade 5 student achievement in Language Arts and Mathematics as measured by the high-stakes New Jersey standardized test entitled New Jersey Assessment of Skills…

  3. Predicting long-term growth in students' mathematics achievement: the unique contributions of motivation and cognitive strategies.

    Science.gov (United States)

    Murayama, Kou; Pekrun, Reinhard; Lichtenfeld, Stephanie; Vom Hofe, Rudolf

    2013-01-01

    This research examined how motivation (perceived control, intrinsic motivation, and extrinsic motivation), cognitive learning strategies (deep and surface strategies), and intelligence jointly predict long-term growth in students' mathematics achievement over 5 years. Using longitudinal data from six annual waves (Grades 5 through 10; Mage  = 11.7 years at baseline; N = 3,530), latent growth curve modeling was employed to analyze growth in achievement. Results showed that the initial level of achievement was strongly related to intelligence, with motivation and cognitive strategies explaining additional variance. In contrast, intelligence had no relation with the growth of achievement over years, whereas motivation and learning strategies were predictors of growth. These findings highlight the importance of motivation and learning strategies in facilitating adolescents' development of mathematical competencies. © 2012 The Authors. Child Development © 2012 Society for Research in Child Development, Inc.

  4. A unique large-scale undergraduate research experience in molecular systems biology for non-mathematics majors.

    Science.gov (United States)

    Kappler, Ulrike; Rowland, Susan L; Pedwell, Rhianna K

    2017-05-01

    Systems biology is frequently taught with an emphasis on mathematical modeling approaches. This focus effectively excludes most biology, biochemistry, and molecular biology students, who are not mathematics majors. The mathematical focus can also present a misleading picture of systems biology, which is a multi-disciplinary pursuit requiring collaboration between biochemists, bioinformaticians, and mathematicians. This article describes an authentic large-scale undergraduate research experience (ALURE) in systems biology that incorporates proteomics, bacterial genomics, and bioinformatics in the one exercise. This project is designed to engage students who have a basic grounding in protein chemistry and metabolism and no mathematical modeling skills. The pedagogy around the research experience is designed to help students attack complex datasets and use their emergent metabolic knowledge to make meaning from large amounts of raw data. On completing the ALURE, participants reported a significant increase in their confidence around analyzing large datasets, while the majority of the cohort reported good or great gains in a variety of skills including "analysing data for patterns" and "conducting database or internet searches." An environmental scan shows that this ALURE is the only undergraduate-level system-biology research project offered on a large-scale in Australia; this speaks to the perceived difficulty of implementing such an opportunity for students. We argue however, that based on the student feedback, allowing undergraduate students to complete a systems-biology project is both feasible and desirable, even if the students are not maths and computing majors. © 2016 by The International Union of Biochemistry and Molecular Biology, 45(3):235-248, 2017. © 2016 The International Union of Biochemistry and Molecular Biology.

  5. Multiple aspects of self-regulation uniquely predict mathematics but not letter-word knowledge in the early elementary grades.

    Science.gov (United States)

    Blair, Clancy; Ursache, Alexandra; Greenberg, Mark; Vernon-Feagans, Lynne

    2015-04-01

    The relation of self-regulation measured prior to school entry to developing math and reading ability in prekindergarten through the second grade was examined in a prospective longitudinal sample of 1,292 children and families in predominantly rural and low-income communities in 2 regions of high poverty in the United States. Direct assessments of executive function, effortful control, and stress response physiology (indexed by resting levels of cortisol and alpha amylase obtained from saliva) were measured at child age 48 months and parents and teachers reported on children's effortful control using temperament rating scales at child age approximately 60 months. Math and reading ability, as measured by the Woodcock-Johnson III applied problems and letter-word subtests, respectively, were measured at prekindergarten through the second grade. Effects for self-regulation measures were seen primarily for initial level and to some extent growth in both mathematics and reading, even when controlling for family demographic characteristics that represent relevant selection factors into higher levels of both self-regulation and academic achievement. These effects persisted for mathematics but not for reading with the inclusion of child cognitive abilities, vocabulary, and speed of processing measured in prekindergarten, concurrent with the first time point for the academic measures. Results are interpreted as indicating a role for self-regulation in learning ability generally, likely through support for attention and reasoning abilities that are most specific to the assessment of mathematics in this analysis. Implications for instruction and for assessment and the best ways to support the development of early math and reading ability for children at risk for school failure are discussed. (c) 2015 APA, all rights reserved).

  6. Mathematics

    CERN Document Server

    Stein, Sherman K

    2010-01-01

    Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi

  7. Mathematics

    International Nuclear Information System (INIS)

    Demazure, M.

    1988-01-01

    The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr

  8. Optimization of healthcare supply chain in context of macro-ergonomics factors by a unique mathematical programming approach.

    Science.gov (United States)

    Azadeh, A; Motevali Haghighi, S; Gaeini, Z; Shabanpour, N

    2016-07-01

    This study presents an integrated approach for analyzing the impact of macro-ergonomics factors in healthcare supply chain (HCSC) by data envelopment analysis (DEA). The case of this study is the supply chain (SC) of a real hospital. Thus, healthcare standards and macro-ergonomics factors are considered to be modeled by the mathematical programming approach. Over 28 subsidiary SC divisions with parallel missions and objectives are evaluated by analyzing inputs and outputs through DEA. Each division in this HCSC is considered as decision making unit (DMU). This approach can analyze the impact of macro-ergonomics factors on supply chain management (SCM) in healthcare sector. Also, this method ranks the relevant performance efficiencies of each HCSC. In this study by using proposed method, the most effective macro-ergonomics factor on HCSC is identified as "teamwork" issue. Also, this study would help managers to identify the areas of weaknesses in their SCM system and set improvement target plan for the related SCM system in healthcare industry. To the best of our knowledge, this is the first study for macro-ergonomics optimization of HCSC. Copyright © 2016 Elsevier Ltd and The Ergonomics Society. All rights reserved.

  9. Ovarian tumor attachment, invasion and vascularization reflect unique microenvironments in the peritoneum:Insights from xenograft and mathematical models

    Directory of Open Access Journals (Sweden)

    Mara P. Steinkamp

    2013-05-01

    Full Text Available Ovarian cancer relapse is often characterized by metastatic spread throughout the peritoneal cavity with tumors attached to multiple organs. In this study, interaction of ovarian tumor cells with the peritoneal tumor microenvironment was evaluated in a xenograft model based on intraperitoneal injection of fluorescent SKOV3.ip1 ovarian cancer cells. Intra-vital microscopy of mixed GFP-RFP cell populations injected into the peritoneum demonstrated that tumor cells aggregate and attach as mixed spheroids, emphasizing the importance of homotypic adhesion in tumor formation. Electron microscopy provided high resolution structural information about local attachment sites. Experimental measurements from the mouse model were used to build a three-dimensional cellular Potts ovarian tumor model (OvTM that examines ovarian tumor cell attachment, chemotaxis, growth and vascularization. OvTM simulations provide insight into the relative influence of tumor cell-cell adhesion, oxygen availability, and local architecture on tumor growth and morphology. Notably, tumors on the mesentery, omentum or spleen readily invade the open architecture, while tumors attached to the gut encounter barriers that restrict invasion and instead rapidly expand into the peritoneal space. Simulations suggest that rapid neovascularization of SKOV3.ip1 tumors is triggered by constitutive release of angiogenic factors in the absence of hypoxia. This research highlights the importance of cellular adhesion and tumor microenvironment in the seeding of secondary ovarian tumors on diverse organs within the peritoneal cavity. Results of the OvTM simulations indicate that invasion is strongly influenced by features underlying the mesothelial lining at different sites, but is also affected by local production of chemotactic factors. The integrated in vivo mouse model and computer simulations provide a unique platform for evaluating targeted therapies for ovarian cancer relapse.

  10. Normal telomere lengths in naive and memory CD4+ T cells in HIV type 1 infection: a mathematical interpretation

    NARCIS (Netherlands)

    Wolthers, K. C.; Noest, A. J.; Otto, S. A.; Miedema, F.; de Boer, R. J.

    1999-01-01

    To study CD4+ T cell productivity during HIV-1 infection, CD4+ T cell telomere lengths were measured. Cross-sectional and longitudinal analysis of HIV-1-infected individuals with CD4+ T cells counts >300 cells/mm3 showed normal average telomeric restriction fragment (TRF) length and normal

  11. Normal telomere lengths in naive and memory CD4 T cells in HIV type 1 infection : a mathematical interpretation

    NARCIS (Netherlands)

    Wolthers, K.C.; Noest, A.J.; Otto, S.A.; Miedema, F.; Boer, R.J. de

    1999-01-01

    To study CD4+ T cell productivity during HIV-1 infection, CD4+ T cell telomere lengths were measured. Cross-sectional and longitudinal analysis of HIV-1-infected individuals with CD4+ T cells counts >300 cells/mm3 showed normal average telomeric restriction fragment (TRF) length and normal

  12. A statistical approach designed for finding mathematically defined repeats in shotgun data and determining the length distribution of clone-inserts

    DEFF Research Database (Denmark)

    Zhong, Lan; Zhang, Kunlin; Huang, Xiangang

    2003-01-01

    that repeats of different copy number have different probabilities of appearance in shotgun data, so based on this principle, we constructed a statistical model and inferred criteria for mathematically defined repeats (MDRs) at different shotgun coverages. According to these criteria, we developed software...... MDRmasker to identify and mask MDRs in shotgun data. With repeats masked prior to assembly, the speed of assembly was increased with lower error probability. In addition, clone-insert size affect the accuracy of repeat assembly and scaffold construction, we also designed length distribution of clone...

  13. Uniqueness in the determination of vibration sources in rectangular Germain–Lagrange plates using displacement measurements over line segments with arbitrary small length

    International Nuclear Information System (INIS)

    Kawano, Alexandre

    2013-01-01

    The theme of this work is related to the field of vibration and source detection, which is important in naval, aerospace and civil engineering industries. The detection of unexpected vibration sources, in general, signals malfunctioning, or even an undesired presence in the case of defense systems. The focus will be on thin plates, which are among the basic building blocks of large complex structures. Here, we consider loads acting on a rectangular plate R of the product form g(t)Q(x), where the function of time g has a continuous first derivative and the spatial load distribution Q is a square-integrable function over R. We prove that the observation of the displacement of a line segment with arbitrary length parallel to one of the sides of the plate is enough for the determination of Q, provided that the interval of time is long enough. We also prove that the normal derivative along a side of the rectangle measured for an arbitrarily small interval of time is sufficient to determine the spatial load distribution Q. The method used to obtain the results is based on the series decomposition of the dynamic response and an analysis of the almost periodic distribution that arises from it. (paper)

  14. CBM Reading, Mathematics, and Written Expression at the Secondary Level: Examining Latent Composite Relations Among Indices and Unique Predictions With a State Achievement Test

    Science.gov (United States)

    Codding, Robin S.; Petscher, Yaacov; Truckenmiller, Adrea

    2015-01-01

    A paucity of research has examined the utility of curriculum-based measurement (CBM) for data-based decision making at the secondary level. As schools move to multitiered systems of service delivery, it is conceivable that multiple screening measures will be used that address various academic subject areas. The value of including different CBM indices measures is not well understood. The purpose of this study was to (a) examine the relationship among a variety of reading, writing, and mathematics CBM indices administered to 249 seventh-grade students; (b) investigate amount and patterns of growth; and (c) examine predictive validity to a high-stakes state test using latent factor analysis and multiple indicator growth models. Results indicated strong correspondence among CBM types for fall static scores but weak relationships among slopes. Different patterns of growth were yielded for CBM writing than for CBM reading and mathematics. Findings from this study suggested that although reading, mathematics, and writing CBM were independently and moderately related to both English Language Arts and Math test scores, reading was the strongest predictor when all 3 CBM constructs were considered jointly. PMID:26347201

  15. Mathematics everywhere

    CERN Document Server

    Aigner, Martin; Spain, Philip G

    2010-01-01

    Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" unde

  16. Plutonium uniqueness

    International Nuclear Information System (INIS)

    Silver, G.L.

    1984-01-01

    A standard is suggested against which the putative uniqueness of plutonium may be tested. It is common folklore that plutonium is unique among the chemical elements because its four common oxidation states can coexist in the same solution. Whether this putative uniqueness appears only during transit to equilibrium, or only at equilibrium, or all of the time, is not generally made clear. But while the folklore may contain some truth, it cannot be put to test until some measure of 'uniqueness' is agreed upon so that quantitative comparisons are possible. One way of measuring uniqueness is as the magnitude of the product of the mole fractions of the element at equilibrium. A 'coexistence index' is defined and discussed. (author)

  17. Dimensional analysis yields the general second-order differential equation underlying many natural phenomena: the mathematical properties of a phenomenon's data plot then specify a unique differential equation for it.

    Science.gov (United States)

    Kepner, Gordon R

    2014-08-27

    This study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot's mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon. A practical example of each function is analyzed using the general form of the underlying differential equation and the observable unique mathematical properties of each data plot, including boundary conditions. This yields a differential equation that describes the relationship among the physical variables governing the phenomenon's behavior. Complex phenomena such as the Standard Normal Distribution, the Logistic Growth Function, and Hill Ligand binding, which are characterized by data plots of distinctly different sigmoidal character, are readily analyzed by this approach. It provides an alternative, simple, unifying basis for analyzing each of these varied phenomena from a common perspective that ties them together and offers new insights into the appropriate empirical constants for describing each phenomenon.

  18. Mathematics revealed

    CERN Document Server

    Berman, Elizabeth

    1979-01-01

    Mathematics Revealed focuses on the principles, processes, operations, and exercises in mathematics.The book first offers information on whole numbers, fractions, and decimals and percents. Discussions focus on measuring length, percent, decimals, numbers as products, addition and subtraction of fractions, mixed numbers and ratios, division of fractions, addition, subtraction, multiplication, and division. The text then examines positive and negative numbers and powers and computation. Topics include division and averages, multiplication, ratios, and measurements, scientific notation and estim

  19. 'Length'at Length

    Indian Academy of Sciences (India)

    Admin

    He was interested to know how `large' is the set of numbers x for which the series is convergent. Here large refers to its length. But his set is not in the class ♢. Here is another problem discussed by Borel. Consider .... have an infinite collection of pairs of new shoes and want to choose one shoe from each pair. We have an ...

  20. Mathematical psychology.

    Science.gov (United States)

    Batchelder, William H

    2010-09-01

    Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.

  1. Philosophical dimensions in mathematics education

    CERN Document Server

    Francois, Karen

    2007-01-01

    This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.

  2. Physical mathematics

    CERN Document Server

    Cahill, Kevin

    2013-01-01

    Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.

  3. Genetic variation in pea (Pisum sativum L.) demonstrates the importance of root but not shoot C/N ratios in the control of plant morphology and reveals a unique relationship between shoot length and nodulation intensity.

    Science.gov (United States)

    Ludidi, Ndiko N; Pellny, Till K; Kiddle, Guy; Dutilleul, Christelle; Groten, Karin; VAN Heerden, Philippus D R; Dutt, Som; Powers, Stephen J; Römer, Peter; Foyer, Christine H

    2007-10-01

    Nodule numbers are regulated through systemic auto-regulatory signals produced by shoots and roots. The relative effects of shoot and root genotype on nodule numbers together with relationships to organ biomass, carbon (C) and nitrogen (N) status, and related parameters were measured in pea (Pisum sativum) exploiting natural genetic variation in maturity and apparent nodulation intensity. Reciprocal grafting experiments between the early (Athos), intermediate (Phönix) and late (S00182) maturity phenotypes were performed and Pearson's correlation coefficients for the parameters were calculated. No significant correlations were found between shoot C/N ratios and plant morphology parameters, but the root C/N ratio showed a strong correlation with root fresh and dry weights as well as with shoot fresh weight with less significant interactions with leaf number. Hence, the root C/N ratio rather than shoot C/N had a predominant influence on plant morphology when pea plants are grown under conditions of symbiotic nitrogen supply. The only phenotypic characteristic that showed a statistically significant correlation with nodulation intensity was shoot length, which accounted for 68.5% of the variation. A strong linear relationship was demonstrated between shoot length and nodule numbers. Hence, pea nodule numbers are controlled by factors related to shoot extension, but not by shoot or root biomass accumulation, total C or total N. The relationship between shoot length and nodule numbers persisted under field conditions. These results suggest that stem height could be used as a breeding marker for the selection of pea cultivars with high nodule numbers and high seed N contents.

  4. The Uniqueness of Milton Friedman

    OpenAIRE

    J. Daniel Hammond

    2013-01-01

    That there is no Milton Friedman today is not a mystery; the mystery is how Milton Friedman could have been. The facts of Friedman’s biography make him unique among twentieth-century public figures. He had extensive knowledge and expertise in mathematics and statistics. Yet he became a critic of ‘formal’ theory, exemplified by mathematical economics, that failed to engage with real-world facts and data, and of econometric modeling that presumed more knowledge of economic structure than Friedm...

  5. Is Life Unique?

    Science.gov (United States)

    Abel, David L.

    2011-01-01

    Is life physicochemically unique? No. Is life unique? Yes. Life manifests innumerable formalisms that cannot be generated or explained by physicodynamics alone. Life pursues thousands of biofunctional goals, not the least of which is staying alive. Neither physicodynamics, nor evolution, pursue goals. Life is largely directed by linear digital programming and by the Prescriptive Information (PI) instantiated particularly into physicodynamically indeterminate nucleotide sequencing. Epigenomic controls only compound the sophistication of these formalisms. Life employs representationalism through the use of symbol systems. Life manifests autonomy, homeostasis far from equilibrium in the harshest of environments, positive and negative feedback mechanisms, prevention and correction of its own errors, and organization of its components into Sustained Functional Systems (SFS). Chance and necessity—heat agitation and the cause-and-effect determinism of nature’s orderliness—cannot spawn formalisms such as mathematics, language, symbol systems, coding, decoding, logic, organization (not to be confused with mere self-ordering), integration of circuits, computational success, and the pursuit of functionality. All of these characteristics of life are formal, not physical. PMID:25382119

  6. Finite mathematics models and applications

    CERN Document Server

    Morris, Carla C

    2015-01-01

    Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.

  7. Fundamental length and relativistic length

    International Nuclear Information System (INIS)

    Strel'tsov, V.N.

    1988-01-01

    It si noted that the introduction of fundamental length contradicts the conventional representations concerning the contraction of the longitudinal size of fast-moving objects. The use of the concept of relativistic length and the following ''elongation formula'' permits one to solve this problem

  8. Flame Length

    Data.gov (United States)

    Earth Data Analysis Center, University of New Mexico — Flame length was modeled using FlamMap, an interagency fire behavior mapping and analysis program that computes potential fire behavior characteristics. The tool...

  9. Mathematical quantization

    CERN Document Server

    Weaver, Nik

    2001-01-01

    With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics.Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras.In the first half of the book, the author quickly builds the operator algebra setting. He uses this ...

  10. Fundamental length

    International Nuclear Information System (INIS)

    Pradhan, T.

    1975-01-01

    The concept of fundamental length was first put forward by Heisenberg from purely dimensional reasons. From a study of the observed masses of the elementary particles known at that time, it is sumrised that this length should be of the order of magnitude 1 approximately 10 -13 cm. It was Heisenberg's belief that introduction of such a fundamental length would eliminate the divergence difficulties from relativistic quantum field theory by cutting off the high energy regions of the 'proper fields'. Since the divergence difficulties arise primarily due to infinite number of degrees of freedom, one simple remedy would be the introduction of a principle that limits these degrees of freedom by removing the effectiveness of the waves with a frequency exceeding a certain limit without destroying the relativistic invariance of the theory. The principle can be stated as follows: It is in principle impossible to invent an experiment of any kind that will permit a distintion between the positions of two particles at rest, the distance between which is below a certain limit. A more elegant way of introducing fundamental length into quantum theory is through commutation relations between two position operators. In quantum field theory such as quantum electrodynamics, it can be introduced through the commutation relation between two interpolating photon fields (vector potentials). (K.B.)

  11. Mathematical Competences

    DEFF Research Database (Denmark)

    Westphael, Henning; Mogensen, Arne

    2013-01-01

    In this article we present the notion of Mathematical competences as a tool to describe the mathematically gifted students.......In this article we present the notion of Mathematical competences as a tool to describe the mathematically gifted students....

  12. Open problems in mathematics

    CERN Document Server

    Nash, Jr, John Forbes

    2016-01-01

    The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer sc...

  13. Length of excitable knots

    Science.gov (United States)

    Maucher, Fabian; Sutcliffe, Paul

    2017-07-01

    In this paper, we present extensive numerical simulations of an excitable medium to study the long-term dynamics of knotted vortex strings for all torus knots up to crossing number 11. We demonstrate that FitzHugh-Nagumo evolution preserves the knot topology for all the examples presented, thereby providing a field theory approach to the study of knots. Furthermore, the evolution yields a well-defined minimal length for each knot that is comparable to the ropelength of ideal knots. We highlight the role of the medium boundary in stabilizing the length of the knot and discuss the implications beyond torus knots. We also show that there is not a unique attractor within a given knot topology.

  14. Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

    Directory of Open Access Journals (Sweden)

    María F. Ayllón

    2016-04-01

    Full Text Available This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas, flexibility (range of ideas, novelty (unique idea and elaboration (idea development. These factors contribute, among others, to the fact that schoolchildren are competent in mathematics. The problem solving and posing are a very powerful evaluation tool that shows the mathematical reasoning and creative level of a person. Creativity is part of the mathematics education and is a necessary ingredient to perform mathematical assignments. This contribution presents some important research works about problem posing and solving related to the development of mathematical knowledge and creativity. To that end, it is based on various beliefs reflected in the literature with respect to notions of creativity, problem solving and posing.

  15. Endocrinology in Thailand: Unique challenges, unique solutions

    Directory of Open Access Journals (Sweden)

    Viroj Wiwanitkit

    2011-01-01

    Full Text Available Thailand is a developing country in Southeast Asia with a nationally acknowledged requirement for improvement of the medical system. At present, endocrinology is a specific branch of medicine that is taught in few medical schools. There are very few endocrinologists in Thailand, who are unable to cope with the large number of patients with endocrinology problems. Primary care for common endocrine disorders, such as diabetes mellitus and thyroid disease, is still the domain of general practitioners. In this article, the author will present unique challenges and unique solutions of endocrinology practice in Thailand.

  16. On uniqueness in evolution quasivariational inequalities

    Czech Academy of Sciences Publication Activity Database

    Brokate, M.; Krejčí, Pavel; Schnabel, H.

    2004-01-01

    Roč. 11, č. 1 (2004), s. 111-130 ISSN 0944-6532 Institutional research plan: CEZ:AV0Z1019905 Keywords : evolution quasivariational inequality * uniqueness * sweeping process Subject RIV: BA - General Mathematics Impact factor: 0.425, year: 2004 http://www.heldermann-verlag.de/jca/jca11/jca0386.pdf

  17. Mathematical Footprints Discovering Mathematics Everywhere

    CERN Document Server

    Pappas, Theoni

    1999-01-01

    MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent

  18. Mathematical people profiles and interviews

    CERN Document Server

    Albers, Donald

    2008-01-01

    This unique collection contains extensive and in-depth interviews with mathematicians who have shaped the field of mathematics in the twentieth century. Collected by two mathematicians respected in the community for their skill in communicating mathematical topics to a broader audience, the book is also rich with photographs and includes an introduction by Philip J. Davis.

  19. Mathematical Adventures with Harry Potter

    Science.gov (United States)

    Wagner, Meaghan M.; Lachance, Andrea

    2004-01-01

    The current popularity of the Harry Potter books (Rowling 1998, 1999a, 1999b, 2000, 2003) gives teachers a new and unique opportunity to integrate literature with mathematics. Often, books that are connected to mathematical explorations are picture books, which teachers can read easily in one sitting to a group of children. The books in the Harry…

  20. Novice Mathematics Teachers Create Themselves

    Science.gov (United States)

    Schatz Oppenheimer, Orna; Dvir, Nurit

    2018-01-01

    This study presents a qualitative research based on three narratives written by novice mathematics teachers. We examine their unique professional world during their first year of work. The methodology of narrative framework, on which this article is based, helps to gain better understanding of the need for novice mathematics teachers to have…

  1. Persian architecture and mathematics

    CERN Document Server

    2012-01-01

    This volulme features eight original papers dedicated to the theme “Persian Architecture and Mathematics,” guest edited by Reza Sarhangi. All papers were approved through a rigorous process of blind peer review and edited by an interdisciplinary scientific editorial committee. Topics range from symmetry in ancient Persian architecture to the elaborate geometric patterns and complex three-dimensional structures of standing monuments of historical periods, from the expression of mathematical ideas to architectonic structures, and from decorative ornament to the representation of modern group theory and quasi-crystalline patterns. The articles discuss unique monuments Persia, including domed structures and two-dimensional patterns, which have received significant scholarly attention in recent years. This book is a unique contribution to studies of Persian architecture in relation to mathematics.

  2. Mathematical bridges

    CERN Document Server

    Andreescu, Titu; Tetiva, Marian

    2017-01-01

    Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...

  3. Estimation of papaya leaf area using the central vein length

    Directory of Open Access Journals (Sweden)

    Campostrini Eliemar

    2001-01-01

    Full Text Available Four genotypes of papaya (Carica papaya L. two from the 'Solo' group (Sunrise Solo and Improved Sunrise Solo line 72/12 and two from the 'Formosa' group (Tainung 02 and Known-You 01, grown in Macaé, RJ, Brazil (lat. 22(0 24' S, long. 41(0 42' W, were used in this study. Twenty-five mature leaves from each genotype were sampled four and five months after seedling transplant to the field to determine the length of the leaf central vein (LLCV and the leaf area (LA. According to covariance analyses there were no significant differences in the slope and intercept of the mathematical models calculated for each genotype. Thus, a single mathematical model (Log LA = 0.315 + 1.85 Log LLCV, R²=0.898 was adjusted to estimate the LA using the length of LLCV for the four genotypes. An unique model can be applied to estimate the LA for the four papaya genotypes using LLCV in the range from 0.25 to 0.60 m, and for papaya trees 150 to 180 days after transplanting.

  4. Influence of the Alkyl Side Chain Length on the Thermophysical Properties of Chiral Ionic Liquids with a (1R,2S,5R)-(–)-Menthol Substituent and Data Treatment by Means of Mathematical Gnostics.

    Czech Academy of Sciences Publication Activity Database

    Andresová, Adéla; Bendová, Magdalena; Schwarz, Jaroslav; Wagner, Zdeněk; Feder-Kubis, J.

    2017-01-01

    Roč. 242, SEP 2017 (2017), s. 336-348 ISSN 0167-7322 R&D Projects: GA MŠk(CZ) 7AMB14PL005 Grant - others:NSC(PL) 2011/01/B/ST5/06659 Institutional support: RVO:67985858 Keywords : chiral ionic liquid s * thermophysical properties * mathematical gnostics Subject RIV: CF - Physical ; Theoretical Chemistry OBOR OECD: Physical chemistry Impact factor: 3.648, year: 2016

  5. Influence of the Alkyl Side Chain Length on the Thermophysical Properties of Chiral Ionic Liquids with a (1R,2S,5R)-(–)-Menthol Substituent and Data Treatment by Means of Mathematical Gnostics.

    Czech Academy of Sciences Publication Activity Database

    Andresová, Adéla; Bendová, Magdalena; Schwarz, Jaroslav; Wagner, Zdeněk; Feder-Kubis, J.

    2017-01-01

    Roč. 242, SEP 2017 (2017), s. 336-348 ISSN 0167-7322 R&D Projects: GA MŠk(CZ) 7AMB14PL005 Grant - others:NSC(PL) 2011/01/B/ST5/06659 Institutional support: RVO:67985858 Keywords : chiral ionic liquids * thermophysical properties * mathematical gnostics Subject RIV: CF - Physical ; Theoretical Chemistry OBOR OECD: Physical chemistry Impact factor: 3.648, year: 2016

  6. Mathematics disorder

    Science.gov (United States)

    ... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...

  7. Mathematical Chemistry

    OpenAIRE

    Trinajstić, Nenad; Gutman, Ivan

    2002-01-01

    A brief description is given of the historical development of mathematics and chemistry. A path leading to the meeting of these two sciences is described. An attempt is made to define mathematical chemistry, and journals containing the term mathematical chemistry in their titles are noted. In conclusion, the statement is made that although chemistry is an experimental science aimed at preparing new compounds and materials, mathematics is very useful in chemistry, among other things, to produc...

  8. Mathematics Connection

    African Journals Online (AJOL)

    ... and JHS teachers toward mathematics, both upper primary and JHS teachers were found to have significantly more positive attitudes toward mathematics than the lower primary teachers. The study recommended the need to encourage lower primary school teachers to develop more positive attitudes toward mathematics.

  9. Mathematics for physicists

    CERN Document Server

    Dennery, Philippe

    1967-01-01

    ""A fine example of how to present 'classical' physical mathematics."" - American ScientistWritten for advanced undergraduate and graduate students, this volume provides a thorough background in the mathematics needed to understand today's more advanced topics in physics and engineering. Without sacrificing rigor, the authors develop the theoretical material at length, in a highly readable, and, wherever possible, in an intuitive manner. Each abstract idea is accompanied by a very simple, concrete example, showing the student that the abstraction is merely a generalization from easily understo

  10. Effective Prime Uniqueness

    OpenAIRE

    Cholak, Peter; McCoy, Charlie

    2014-01-01

    Assuming the obvious definitions (see paper) we show the a decidable model that is effectively prime is also effectively atomic. This implies that two effectively prime (decidable) models are computably isomorphic. This is in contrast to the theorem that there are two atomic decidable models which are not computably isomorphic. The implications of this work in reverse mathematics is that "effectively prime implies effectively atomic" holds in topped models. But due to an observation of David ...

  11. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

  12. Mathematical modelling

    DEFF Research Database (Denmark)

    Blomhøj, Morten

    2004-01-01

    modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive......Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...

  13. Mathematical Modeling and Pure Mathematics

    Science.gov (United States)

    Usiskin, Zalman

    2015-01-01

    Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

  14. Mathematical problems in meteorological modelling

    CERN Document Server

    Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella

    2016-01-01

    This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...

  15. The uniqueness of stable crack growth data

    International Nuclear Information System (INIS)

    Smith, E.

    1981-01-01

    The paper addresses the uniqueness of the stable crack growth relation, with particular reference to creep crack growth and stress corrosion crack growth, where it is the pattern to use laboratory data which relates the stress intensity K to the crack growth rate dc/dt. Simple models are used to define the conditions under which the K versus dc/dt data is unique. Extensive use is made of the Dugdale-Bilby-Cottrell-Swinden (DBCS) model, in which the yield accompanying crack growth is assumed to be confined to an infinitesimal thin strip coplanar with the growing crack. The DBCS model can be modified to give an incremental growth criterion, which is in the form of a differential equation relating the stress intensity to crack length. The conditions under which this equation gives a unique relation between stress intensity and crack length are then investigated. (orig./HP)

  16. Uniqueness of bounded observables

    Energy Technology Data Exchange (ETDEWEB)

    Navara, M. [Czech Technical Univ., Praha (Czech Republic). Dept. of Math.

    1995-09-01

    By an application of a new construction technique we construct a {sigma}-orthomodular lattice with a strongly order-determining set of states and two bounded observables whose expectations are equal at each state. This answers negatively the uniqueness problem for bounded observables, formulated by S. Gudder. (orig.).

  17. Understanding engineering mathematics

    CERN Document Server

    Cox, Bill

    2001-01-01

    * Unique interactive style enables students to diagnose their strengths and weaknesses and focus their efforts where needed* Ideal for self-study and tutorial work, building from an initially supportive approach to the development of independent learning skills * Free website includes solutions to all exercises, additional topics and applications, guide to learning mathematics, and practice materialStudents today enter engineering courses with a wide range of mathematical skills, due to the many different pre-university qualifications studied. Bill Cox''s aim is for students to gain a thorough understanding of the maths they are studying, by first strengthening their background in the essentials of each topic. His approach allows a unique self-paced study style, in which students Review their strengths and weaknesses through self-administered diagnostic tests, then focus on Revision where they need it, to finally Reinforce the skills required.The book is structured around a highly successful ''transition'' ma...

  18. Mathematical scandals

    CERN Document Server

    Pappas, Theoni

    1997-01-01

    In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre ? in short, the human background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics?Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions

  19. Financial mathematics

    CERN Document Server

    Jothi, A Lenin

    2009-01-01

    Financial services, particularly banking and insurance services is the prominent sector for the development of a nation. After the liberalisation of financial sector in India, the scope of getting career opportunities has been widened. It is heartening to note that various universities in India have introduced professional courses on banking and insurance. A new field of applied mathematics has come into prominence under the name of Financial Mathematics. Financial mathematics has attained much importance in the recent years because of the role played by mathematical concepts in decision - m

  20. Experimental Mathematics and Mathematical Physics

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim

    2009-06-26

    One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

  1. Mathematics 2

    CERN Document Server

    Kodaira, Kunihiko

    1996-01-01

    This is the translation from the Japanese textbook for the grade 11 course, "General Mathematics". It is part of the easier of the three elective courses in mathematics offered at this level and is taken by about 40% of students. The book covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.

  2. Mathematical logic

    CERN Document Server

    Kleene, Stephen Cole

    1967-01-01

    Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.

  3. Mathematics unbound

    CERN Document Server

    Parshall, Karen Hunger

    2002-01-01

    Although today's mathematical research community takes its international character very much for granted, this "global nature" is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians and mathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only develo...

  4. VEDIC MATHEMATICS

    Directory of Open Access Journals (Sweden)

    Sead Rešić

    2015-09-01

    Full Text Available It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.

  5. NASA's unique networking environment

    Science.gov (United States)

    Johnson, Marjory J.

    1988-01-01

    Networking is an infrastructure technology; it is a tool for NASA to support its space and aeronautics missions. Some of NASA's networking problems are shared by the commercial and/or military communities, and can be solved by working with these communities. However, some of NASA's networking problems are unique and will not be addressed by these other communities. Individual characteristics of NASA's space-mission networking enviroment are examined, the combination of all these characteristics that distinguish NASA's networking systems from either commercial or military systems is explained, and some research areas that are important for NASA to pursue are outlined.

  6. Applied mathematics

    CERN Document Server

    Logan, J David

    2013-01-01

    Praise for the Third Edition"Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." -MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and nat

  7. Engineering mathematics

    CERN Document Server

    Bird, John

    2014-01-01

    A practical introduction to the core mathematics required for engineering study and practiceNow in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure

  8. Speed mathematics

    CERN Document Server

    Handley, Bill

    2012-01-01

    This new, revised edition of the bestselling Speed Mathematics features new chapters on memorising numbers and general information, calculating statistics and compound interest, square roots, logarithms and easy trig calculations. Written so anyone can understand, this book teaches simple strategies that will enable readers to make lightning-quick calculations. People who excel at mathematics use better strategies than the rest of us; they are not necessarily more intelligent. With Speed Mathematics you'll discover methods to make maths easy and fun. This book is perfect for stud

  9. Third international handbook of mathematics education

    CERN Document Server

    Bishop, Alan; Keitel, Christine; Kilpatrick, Jeremy; Leung, Frederick

    2013-01-01

    This entirely new Third International Handbook of Mathematics Education comprises 31 chapters which have been written by a total of 84 different authors representing 26 nations, each a recognized expert in the field.   Comprised of four sections: Social, Political and Cultural Dimensions in Mathematics Education; Mathematics Education as a Field of Study; Technology in the Mathematics Curriculum; and International Perspectives on Mathematics Education, this Third Handbook offers essential reading for all persons interested in the future of mathematics education. The authors present challenging international perspectives on the history of mathematics education, current issues, and future directions.   What makes this Handbook unique is its structure. Each section covers past, present and future aspects of mathematics education.   The first chapter in each section identifies and analyzes historical antecedents The “middle” chapters draw attention to present-day key issues and themes The final chapter in ...

  10. Relationship between Mathematics Anxiety and Mathematics ...

    African Journals Online (AJOL)

    Relationship between Mathematics Anxiety and Mathematics Achievement of Junior Secondary School Students in Maiduguri Metropolis, Borno State, Nigeria. ... Journal of Educational Foundations ... Fear of failure in mathematics test and examination was the main reason why students were anxious of mathematics.

  11. Mathematical physiology

    CERN Document Server

    Sneyd, James

    2009-01-01

    There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina. Owing to this extensive coverage, the second edition is published in two volumes. ...

  12. Mathematics Connection

    African Journals Online (AJOL)

    The language barrier education in Africa: The challenge of learning and teaching mathematics in a second language · EMAIL FULL TEXT EMAIL FULL TEXT DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT. J Ibe, K Ekpo, O Akpan, UE Uyoata ...

  13. Mathematical modeling

    CERN Document Server

    Eck, Christof; Knabner, Peter

    2017-01-01

    Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

  14. Mathematical modelling

    CERN Document Server

    2016-01-01

    This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

  15. Algorithmic mathematics

    CERN Document Server

    Hougardy, Stefan

    2016-01-01

    Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.

  16. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2010-01-01

    The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...

  17. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2010-01-01

    The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...

  18. Mathematical statistics

    CERN Document Server

    Pestman, Wiebe R

    2009-01-01

    This textbook provides a broad and solid introduction to mathematical statistics, including the classical subjects hypothesis testing, normal regression analysis, and normal analysis of variance. In addition, non-parametric statistics and vectorial statistics are considered, as well as applications of stochastic analysis in modern statistics, e.g., Kolmogorov-Smirnov testing, smoothing techniques, robustness and density estimation. For students with some elementary mathematical background. With many exercises. Prerequisites from measure theory and linear algebra are presented.

  19. Greek or Not: The Use of Symbols and Abbreviations in Mathematics

    Science.gov (United States)

    Quinnell, Lorna; Carter, Merilyn

    2012-01-01

    The language of mathematics is unique and complex. One feature of the mathematical register is the use of symbols and abbreviations. Whilst it may be possible for a student to think mathematically in the absence of symbols, the written communication of mathematical ideas cannot be achieved concisely without the use of mathematical symbols.…

  20. Mathematical concepts

    CERN Document Server

    Jost, Jürgen

    2015-01-01

    The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: ·         simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure ·         by itself as a first introduction to abstract mathematics ·         together with existing textbooks, to put their results into a more general perspective ·         to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detaile...

  1. The Language of Mathematics Utilizing Math in Practice

    CERN Document Server

    Baber, Robert L

    2011-01-01

    A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process-not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and i

  2. A mathematics sampler topics for the liberal arts

    CERN Document Server

    Berlinghoff, William P; Skrien, Dale

    2001-01-01

    Now in its fifth edition, A Mathematics Sampler presents mathematics as both science and art, focusing on the historical role of mathematics in our culture. It uses selected topics from modern mathematics-including computers, perfect numbers, and four-dimensional geometry-to exemplify the distinctive features of mathematics as an intellectual endeavor, a problem-solving tool, and a way of thinking about the rapidly changing world in which we live. A Mathematics Sampler also includes unique LINK sections throughout the book, each of which connects mathematical concepts with areas of interest th

  3. Mathematical writing

    CERN Document Server

    Vivaldi, Franco

    2014-01-01

    This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.   The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition.   Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...

  4. Mathematical tapas

    CERN Document Server

    Hiriart-Urruty, Jean-Baptiste

    This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something interesting, challenge the reader to solve and learn, and may have surprising results. This first volume of Mathematical Tapas will appeal to mathematicians, motivated undergraduate students from science-based areas, and those generally interested in mathematics.

  5. Mathematical biophysics

    CERN Document Server

    Rubin, Andrew

    2014-01-01

    This book presents concise descriptions and analysis of the classical and modern models used in mathematical biophysics. The authors ask the question "what new information can be provided by the models that cannot be obtained directly from experimental data?" Actively developing fields such as regulatory mechanisms in cells and subcellular systems and electron transport and energy transport in membranes are addressed together with more classical topics such as metabolic processes, nerve conduction and heart activity, chemical kinetics, population dynamics, and photosynthesis. The main approach is to describe biological processes using different mathematical approaches necessary to reveal characteristic features and properties of simulated systems. With the emergence of powerful mathematics software packages such as MAPLE, Mathematica, Mathcad, and MatLab, these methodologies are now accessible to a wide audience. Provides succinct but authoritative coverage of a broad array of biophysical topics and models Wr...

  6. Early predictors of high school mathematics achievement.

    Science.gov (United States)

    Siegler, Robert S; Duncan, Greg J; Davis-Kean, Pamela E; Duckworth, Kathryn; Claessens, Amy; Engel, Mimi; Susperreguy, Maria Ines; Chen, Meichu

    2012-07-01

    Identifying the types of mathematics content knowledge that are most predictive of students' long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students' knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students' knowledge of fractions and of division uniquely predicts those students' knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed.

  7. Mathematical Lives

    CERN Document Server

    Bartocci, Claudio; Guerraggio, Angelo; Lucchetti, Roberto; Williams, Kim

    2011-01-01

    Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the soci

  8. Mathematical papers

    CERN Document Server

    Green, George

    2005-01-01

    An almost entirely self-taught mathematical genius, George Green (1793 -1841) is best known for Green's theorem, which is used in almost all computer codes that solve partial differential equations. He also published influential essays, or papers, in the fields of hydrodynamics, electricity, and magnetism. This collection comprises his most significant works.The first paper, ""An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism,"" which is also the longest and perhaps the most Important, appeared In 1828. It introduced the term potential as desig

  9. Discrete Mathematics

    DEFF Research Database (Denmark)

    Sørensen, John Aasted

    2011-01-01

    The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able....... Having completed this the student is able to carry out the following: Expressions and sets: Define a set; define a logic expression; negate a logic expression; combine logic expressions; construct a truth table for a logic expression; apply reduction rules for logic expressions. Apply these concepts...

  10. Motivated Mathematics

    OpenAIRE

    Aubin, J.-P.

    1983-01-01

    Mathematics seems to be treated at IIASA as if it were some sort of shameful disease, carefully hidden away in departments labelled with trendy but unrevealing names. Any debate about the role of mathematics and mathematicians at IIASA appears fated to be confused by the introduction of many seemingly unrelated issues, by the fact that many of the protagonists have their own vested interests to protect, and by the fact--why not admit it--that there are many dark fears of the more "esoteric" s...

  11. IGCSE core mathematics

    CERN Document Server

    Wall, Terry

    2013-01-01

    Give your core level students the support and framework they require to get their best grades with this book dedicated to the core level content of the revised syllabus and written specifically to ensure a more appropriate pace. This title has been written for Core content of the revised Cambridge IGCSE Mathematics (0580) syllabus for first teaching from 2013. ? Gives students the practice they require to deepen their understanding through plenty of practice questions. ? Consolidates learning with unique digital resources on the CD, included free with every book. We are working with Cambridge

  12. Uniqueness of inverse scattering problem in local quantum physics

    Energy Technology Data Exchange (ETDEWEB)

    Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: schroer@cbpf.br

    2001-06-01

    It is shown that the a Bisognano-Wichmann-Unruh inspired formulation of local quantum physics which starts from wedge-localized algebras, leads to a uniqueness proof for the scattering problem. The important mathematical tool is the thermal KMS aspect of localization and its strengthening by the requirement of crossing symmetry for generalized formfactors. (author)

  13. Zeros and uniqueness of Q-difference polynomials of meromorphic ...

    Indian Academy of Sciences (India)

    Vol. 124, No. 4, November 2014, pp. 533–549. c Indian Academy of Sciences. Zeros and uniqueness of Q-difference polynomials of meromorphic functions with zero order. TING-BIN CAO. ∗. , KAI LIU and NA XU. Department of Mathematics, Nanchang University, Nanchang,. Jiangxi 330031, People's Republic of China.

  14. Mathematical stereochemistry

    CERN Document Server

    Fujita, Shinsaku

    2015-01-01

    Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. A new stereoisogram approach, developed by the author, is introduced in this book, providing a theoretical framework for mathematical aspects of modern stereochemistry. The discussion covers point-groups and permutation symmetry and exemplifies the concepts using organic molecules and inorganic complexes.

  15. Outdoor Mathematics

    Science.gov (United States)

    Kennard, Jackie

    2007-01-01

    One of the most interesting developments in teaching has been the growing importance of the outdoor environment. Whether it be playground, garden or field, the outdoors offers a range of challenging experiences, especially in the delivery of early mathematics. Oral feedback to parents, together with photographic displays, can show them that…

  16. The language of mathematics telling mathematical tales

    CERN Document Server

    Barton, Bill

    2008-01-01

    Everyday mathematical ideas are expressed differently in different languages. This book probes those differences and explores their implications for mathematics education, arguing for alternatives to how we teach and learn mathematics.

  17. Telomere length analysis.

    Science.gov (United States)

    Canela, Andrés; Klatt, Peter; Blasco, María A

    2007-01-01

    Most somatic cells of long-lived species undergo telomere shortening throughout life. Critically short telomeres trigger loss of cell viability in tissues, which has been related to alteration of tissue function and loss of regenerative capabilities in aging and aging-related diseases. Hence, telomere length is an important biomarker for aging and can be used in the prognosis of aging diseases. These facts highlight the importance of developing methods for telomere length determination that can be employed to evaluate telomere length during the human aging process. Telomere length quantification methods have improved greatly in accuracy and sensitivity since the development of the conventional telomeric Southern blot. Here, we describe the different methodologies recently developed for telomere length quantification, as well as their potential applications for human aging studies.

  18. Understanding in mathematics

    CERN Document Server

    Sierpinska, Anna

    1994-01-01

    The concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students'' understanding of the mathematics being taught.

  19. Applied mathematics

    International Nuclear Information System (INIS)

    Nedelec, J.C.

    1988-01-01

    The 1988 progress report of the Applied Mathematics center (Polytechnic School, France), is presented. The research fields of the Center are the scientific calculus, the probabilities and statistics and the video image synthesis. The research topics developed are: the analysis of numerical methods, the mathematical analysis of the physics and mechanics fundamental models, the numerical solution of complex models related to the industrial problems, the stochastic calculus and the brownian movement, the stochastic partial differential equations, the identification of the adaptive filtering parameters, the discrete element systems, statistics, the stochastic control and the development, the image synthesis techniques for education and research programs. The published papers, the congress communications and the thesis are listed [fr

  20. Mathematical epidemiology

    CERN Document Server

    Driessche, Pauline; Wu, Jianhong

    2008-01-01

    Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downlo...

  1. Integrating Non-Mathematical Domains into Mathematical Development: Key Factors to Consider in Constructing Effective Interventions

    Science.gov (United States)

    Purpura, David J.; Ganley, Colleen

    2013-01-01

    The successful acquisition and development of mathematics skills and concepts is a critical aspect of children's early academic growth. The purpose of this study was to systematically evaluate the unique relations of working memory and language to a range of specific early mathematics skills in a sample of preschool and kindergarten age children.…

  2. Dilemma in Teaching Mathematics

    Science.gov (United States)

    Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain

    2012-01-01

    The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…

  3. Telomere length and depression

    DEFF Research Database (Denmark)

    Wium-Andersen, Marie Kim; Ørsted, David Dynnes; Rode, Line

    2017-01-01

    BACKGROUND: Depression has been cross-sectionally associated with short telomeres as a measure of biological age. However, the direction and nature of the association is currently unclear. AIMS: We examined whether short telomere length is associated with depression cross-sectionally as well...... as prospectively and genetically. METHOD: Telomere length and three polymorphisms, TERT, TERC and OBFC1, were measured in 67 306 individuals aged 20-100 years from the Danish general population and associated with register-based attendance at hospital for depression and purchase of antidepressant medication....... RESULTS: Attendance at hospital for depression was associated with short telomere length cross-sectionally, but not prospectively. Further, purchase of antidepressant medication was not associated with short telomere length cross-sectionally or prospectively. Mean follow-up was 7.6 years (range 0...

  4. Myofilament length dependent activation

    Energy Technology Data Exchange (ETDEWEB)

    de Tombe, Pieter P.; Mateja, Ryan D.; Tachampa, Kittipong; Mou, Younss Ait; Farman, Gerrie P.; Irving, Thomas C. (IIT); (Loyola)

    2010-05-25

    The Frank-Starling law of the heart describes the interrelationship between end-diastolic volume and cardiac ejection volume, a regulatory system that operates on a beat-to-beat basis. The main cellular mechanism that underlies this phenomenon is an increase in the responsiveness of cardiac myofilaments to activating Ca{sup 2+} ions at a longer sarcomere length, commonly referred to as myofilament length-dependent activation. This review focuses on what molecular mechanisms may underlie myofilament length dependency. Specifically, the roles of inter-filament spacing, thick and thin filament based regulation, as well as sarcomeric regulatory proteins are discussed. Although the 'Frank-Starling law of the heart' constitutes a fundamental cardiac property that has been appreciated for well over a century, it is still not known in muscle how the contractile apparatus transduces the information concerning sarcomere length to modulate ventricular pressure development.

  5. Upper Extremity Length Equalization

    OpenAIRE

    DeCoster, Thomas A.; Ritterbusch, John; Crawford, Mark

    1992-01-01

    Significant upper extremity length inequality is uncommon but can cause major functional problems. The ability to position and use the hand may be impaired by shortness of any of the long bones of the upper extremity. In many respects upper and lower extremity length problems are similar. They most commonly occur after injury to a growing bone and the treatment modalities utilized in the lower extremity may be applied to the upper extremity. These treatment options include epiphysiodesis, sho...

  6. Ethnomathematics: the cultural aspects of mathematics

    Directory of Open Access Journals (Sweden)

    Milton Rosa

    2011-01-01

    Full Text Available Ethnomathematics studies the cultural aspects of mathematics. It presents mathematical concepts of the school curriculum in a way in which these concepts are related to the students¿ cultural and daily experiences, thereby enhancing their abilities to elaborate meaningful connections and deepening their understanding of mathematics. Ethnomathematical approaches to mathematics curriculum are intended to make school mathematics more relevant and meaningful for students and to promote the overall quality of their education. In this context, the implementation of an ethnomathematical perspective in the school mathematics curriculum helps to develop students' intellectual, social, emotional, and political learning by using their own unique cultural referents to impart their knowledge, skills, and attitudes. This kind of curriculum provides ways for students to maintain their identity while succeeding academically.

  7. Mathematics for natural scientists fundamentals and basics

    CERN Document Server

    Kantorovich, Lev

    2016-01-01

    This book, the first in a two part series, covers a course of mathematics tailored specifically for physics, engineering and chemistry students at the undergraduate level. It is unique in that it begins with logical concepts of mathematics first encountered at A-level and covers them in thorough detail, filling in the gaps in students' knowledge and reasoning. Then the book aids the leap between A-level and university-level mathematics, with complete proofs provided throughout and all complex mathematical concepts and techniques presented in a clear and transparent manner. Numerous examples and problems (with answers) are given for each section and, where appropriate, mathematical concepts are illustrated in a physics context. This text gives an invaluable foundation to students and a comprehensive aid to lecturers. Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.

  8. Mathematics from the birth of numbers

    CERN Document Server

    Gullberg, Jan

    1997-01-01

    This extraordinary work takes the reader on a long and fascinating journey--from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into mathematical logic, set theory, topology, fractals, probability, and assorted other mathematical byways. The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology. Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous...

  9. Doing Mathematics with Purpose: Mathematical Text Types

    Science.gov (United States)

    Dostal, Hannah M.; Robinson, Richard

    2018-01-01

    Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students'…

  10. Teachers' Mathematics as Mathematics-at-Work

    Science.gov (United States)

    Bednarz, Nadine; Proulx, Jérôme

    2017-01-01

    Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…

  11. Teaching Mathematical Modeling in Mathematics Education

    Science.gov (United States)

    Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

    2016-01-01

    Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

  12. Meeting in mathematics

    DEFF Research Database (Denmark)

    Mogensen, Arne; Georgiev, Vladimir; Ulovec, Andreas

    To encourage many more young people to appreciate the real nature and spirit of mathematics and possibly to be enrolled in mathematics study it is important to involve them in doing mathematics (not just learning about mathematics). This goal could be achieved if mathematics teachers are prepared...... to identify and work with mathematically gifted students (without loosing the rest). The book offers chapters on gifted students, mathematical competences and other issues....

  13. Relativistic Length Agony Continued

    Science.gov (United States)

    Redzic, D. V.

    2014-06-01

    We made an attempt to remedy recent confusing treatments of some basic relativistic concepts and results. Following the argument presented in an earlier paper (Redzic 2008b), we discussed the misconceptions that are recurrent points in the literature devoted to teaching relativity such as: there is no change in the object in Special Relativity, illusory character of relativistic length contraction, stresses and strains induced by Lorentz contraction, and related issues. We gave several examples of the traps of everyday language that lurk in Special Relativity. To remove a possible conceptual and terminological muddle, we made a distinction between the relativistic length reduction and relativistic FitzGerald-Lorentz contraction, corresponding to a passive and an active aspect of length contraction, respectively; we pointed out that both aspects have fundamental dynamical contents. As an illustration of our considerations, we discussed briefly the Dewan-Beran-Bell spaceship paradox and the 'pole in a barn' paradox.

  14. Telomere Length and Mortality

    DEFF Research Database (Denmark)

    Kimura, Masayuki; Hjelmborg, Jacob V B; Gardner, Jeffrey P

    2008-01-01

    Leukocyte telomere length, representing the mean length of all telomeres in leukocytes, is ostensibly a bioindicator of human aging. The authors hypothesized that shorter telomeres might forecast imminent mortality in elderly people better than leukocyte telomere length. They performed mortality...... telomeres predicted the death of the first co-twin better than the mTRFL did (mTRFL: 0.56, 95% confidence interval (CI): 0.49, 0.63; mTRFL(50): 0.59, 95% CI: 0.52, 0.66; mTRFL(25): 0.59, 95% CI: 0.52, 0.66; MTRFL: 0.60, 95% CI: 0.53, 0.67). The telomere-mortality association was stronger in years 3-4 than...

  15. The Non-unique Universe

    Science.gov (United States)

    McCabe, Gordon

    2010-06-01

    The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of Gödel’s incompleteness theorem for theories of everything. Three conclusions are obtained in the final section: (i) the theory of the structure of our universe might be an undecidable theory, and this constitutes a potential epistemological limit for mathematical physics, but because such a theory must be complete, there is no ontological barrier to the existence of a final theory of everything; (ii) in terms of mathematical logic, there are two different types of multiverse: classes of non-isomorphic but elementarily equivalent models, and classes of model which are both non-isomorphic and elementarily inequivalent; (iii) for a hypothetical theory of everything to have only one possible model, and to thereby negate the possible existence of a multiverse, that theory must be such that it admits only a finite model.

  16. Discrete or continuous? the quest for fundamental length in modern physics

    CERN Document Server

    Hagar, Amit

    2014-01-01

    The idea of infinity plays a crucial role in our understanding of the universe, with the infinite spacetime continuum perhaps the best-known example - but is spacetime really continuous? Throughout the history of science, many have felt that the continuum model is an unphysical idealization, and that spacetime should be thought of as 'quantized' at the smallest of scales. Combining novel conceptual analysis, a fresh historical perspective, and concrete physical examples, this unique book tells the story of the search for the fundamental unit of length in modern physics, from early classical electrodynamics to current approaches to quantum gravity. Novel philosophical theses, with direct implications for theoretical physics research, are presented and defended in an accessible format that avoids complex mathematics. Blending history, philosophy, and theoretical physics, this refreshing outlook on the nature of spacetime sheds light on one of the most thought-provoking topics in modern physics.

  17. Mathematics, the Computer, and the Impact on Mathematics Education.

    Science.gov (United States)

    Tooke, D. James

    2001-01-01

    Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)

  18. Quantum Gravity Mathematical Models and Experimental Bounds

    CERN Document Server

    Fauser, Bertfried; Zeidler, Eberhard

    2007-01-01

    The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on ...

  19. Full Length Research Article

    African Journals Online (AJOL)

    Administrator

    Out of the 320 male sheep examined, 87(27.2%) were infected, while 9(19.1%) of the 47 females examined were infected (Table 2). Infection varied from one abattoir to another. Age related distribution of P. cervi is shown in Table 3. Out of 356 adult sheep (>2yrs) examined, 35. Full Length Research Article. 12 ...

  20. Diabetes: Unique to Older Adults

    Science.gov (United States)

    ... Stroke Urinary Incontinence Related Documents PDF Choosing Wisely: Diabetes Tests and Treatments Download Related Video Join our e-newsletter! Aging & Health A to Z Diabetes Unique to Older Adults This section provides information ...

  1. Uniqueness property for quasiharmonic functions

    Directory of Open Access Journals (Sweden)

    Sevdiyor A. Imomkulov

    2014-10-01

    Full Text Available In this paper we consider a class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions.

  2. Authenticity of Mathematical Modeling

    Science.gov (United States)

    Tran, Dung; Dougherty, Barbara J.

    2014-01-01

    Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

  3. Full Length Research Article

    African Journals Online (AJOL)

    MEMUNA

    ABSTRACT. A non cooperative markov game with several unique characteristics was introduced. Some of these characteristics include: the existence of a single phase multi server queuing model and markovian transition matrix/matrices for each game, introduction of virtual situations (virtual reality) or dummies to improve ...

  4. Studies on relaxation length of wood by method of gamma radiation ...

    African Journals Online (AJOL)

    Relaxation lengths of different types of wood were determined using gamma radiation from 60Co source. Results show that oxystigma (Oxystigma spp) has the highest relaxation length of 23.810 cm, while mangrove (Rhizophora spp) has the least relaxation length of 1.247 cm. A mathematical model has been developed ...

  5. Uniqueness of rarefaction waves in multidimensional compressible Euler system

    Czech Academy of Sciences Publication Activity Database

    Feireisl, Eduard; Kreml, Ondřej

    2015-01-01

    Roč. 12, č. 3 (2015), s. 489-499 ISSN 0219-8916 R&D Projects: GA ČR GA13-00522S EU Projects: European Commission(XE) 320078 - MATHEF Institutional support: RVO:67985840 Keywords : compressible Euler system * uniqueness * rarefaction wave * Riemann problem Subject RIV: BA - General Mathematics Impact factor: 0.556, year: 2015 http://www.worldscientific.com/doi/abs/10.1142/S0219891615500149

  6. Cognitive correlates of performance in advanced mathematics.

    Science.gov (United States)

    Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

    2012-03-01

    Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.

  7. Gap length distributions by PEPR

    International Nuclear Information System (INIS)

    Warszawer, T.N.

    1980-01-01

    Conditions guaranteeing exponential gap length distributions are formulated and discussed. Exponential gap length distributions of bubble chamber tracks first obtained on a CRT device are presented. Distributions of resulting average gap lengths and their velocity dependence are discussed. (orig.)

  8. Pion nucleus scattering lengths

    International Nuclear Information System (INIS)

    Huang, W.T.; Levinson, C.A.; Banerjee, M.K.

    1971-09-01

    Soft pion theory and the Fubini-Furlan mass dispersion relations have been used to analyze the pion nucleon scattering lengths and obtain a value for the sigma commutator term. With this value and using the same principles, scattering lengths have been predicted for nuclei with mass number ranging from 6 to 23. Agreement with experiment is very good. For those who believe in the Gell-Mann-Levy sigma model, the evaluation of the commutator yields the value 0.26(m/sub σ//m/sub π/) 2 for the sigma nucleon coupling constant. The large dispersive corrections for the isosymmetric case implies that the basic idea behind many of the soft pion calculations, namely, slow variation of matrix elements from the soft pion limit to the physical pion mass, is not correct. 11 refs., 1 fig., 3 tabs

  9. Figures of thought mathematics and mathematical texts

    CERN Document Server

    Reed, David

    2003-01-01

    Examines the ways in which mathematical works can be read as texts, examines their textual strategiesand demonstrates that such readings provide a rich source of philosophical debate regarding mathematics.

  10. Existence and uniqueness of solution for a system of equations of ...

    African Journals Online (AJOL)

    The existence and uniqueness of solution for a system of equations of microwave heating of biologic issue is discussed. Using the Green function approach we establish the existence and uniqueness of solution. Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 177-180 ...

  11. Ethnomathematics: the cultural aspects of mathematics

    Directory of Open Access Journals (Sweden)

    Milton Rosa

    2011-09-01

    Full Text Available Ethnomathematics studies the cultural aspects of mathematics. It presents mathematical concepts of the school curriculum in a way in which these concepts are related to the students’ cultural and daily experiences, thereby enhancing their abilities to elaborate meaningful connections and deepening their understanding ofmathematics. Ethnomathematical approaches to mathematics curriculum are intended to make school mathematics more relevant and meaningful for students and to promote the overall quality of their education.In this context, the implementation of an ethnomathematical perspective in the school mathematics curriculum helps to develop students’ intellectual, social, emotional, and political learning by using their own unique cultural referents to impart their knowledge, skills, and attitudes. This kind of curriculum providesways for students to maintain their identity while succeeding academically.

  12. University Science and Mathematics Education in Transition

    DEFF Research Database (Denmark)

    Skovsmose, Ole; Valero, Paola; Christensen, Ole Ravn

    of science and mathematics education in the current information society and provides insight essential for developing possibilities to improve science and mathematics education in universities all around the world. The uniquely broad treatment offered by University Science and Mathematics Education...... configuration poses to scientific knowledge, to universities and especially to education in mathematics and science. Traditionally, educational studies in mathematics and science education have looked at change in education from within the scientific disciplines and in the closed context of the classroom....... Although educational change is ultimately implemented in everyday teaching and learning situations, other parallel dimensions influencing these situations cannot be forgotten. An understanding of the actual potentialities and limitations of educational transformations are highly dependent on the network...

  13. Length-weight and length-length relationships of freshwater wild ...

    African Journals Online (AJOL)

    Length-weight and length-length relationships of freshwater wild catfish Mystus bleekeri from Nala Daik, Sialkot, Pakistan. ... Linear regression analysis was used, first to compute the degree of relationship between length and weight and then among total (TL), standard (SL) and fork lengths (FL). LWR exhibited a highly ...

  14. Relativistic length agony continued

    Directory of Open Access Journals (Sweden)

    Redžić D.V.

    2014-01-01

    Full Text Available We made an attempt to remedy recent confusing treatments of some basic relativistic concepts and results. Following the argument presented in an earlier paper (Redžić 2008b, we discussed the misconceptions that are recurrent points in the literature devoted to teaching relativity such as: there is no change in the object in Special Relativity, illusory character of relativistic length contraction, stresses and strains induced by Lorentz contraction, and related issues. We gave several examples of the traps of everyday language that lurk in Special Relativity. To remove a possible conceptual and terminological muddle, we made a distinction between the relativistic length reduction and relativistic FitzGerald-Lorentz contraction, corresponding to a passive and an active aspect of length contraction, respectively; we pointed out that both aspects have fundamental dynamical contents. As an illustration of our considerations, we discussed briefly the Dewan-Beran-Bell spaceship paradox and the ‘pole in a barn’ paradox. [Projekat Ministarstva nauke Republike Srbije, br. 171028

  15. Unity and disunity and other mathematical essays

    CERN Document Server

    Davis, Philip J

    2015-01-01

    This book is a mathematical potpourri. Its material originated in classroom presentations, formal lectures, sections of earlier books, book reviews, or just things written by the author for his own pleasure. Written in a nontechnical fashion, this book expresses the unique vision and attitude of the author towards the role of mathematics in society. It contains observations or incidental remarks on mathematics, its nature, its impacts on education and science and technology, its personalities and philosophies. The book is directed towards the math buffs of the world and, more generally, toward

  16. European Success Stories in Industrial Mathematics

    CERN Document Server

    Esteban, Maria J; Lery, Thibaut; Maday, Yvon

    2011-01-01

    This unique book presents real world success stories of collaboration between mathematicians and industrial partners, showcasing first-hand case studies, and lessons learned from the experiences, technologies, and business challenges that led to the successful development of industrial solutions based on mathematics. It shows the crucial contribution of mathematics to innovation and to the industrial creation of value, and the key position of mathematics in the handling of complex systems, amplifying innovation. Each story describes the challenge that led to the industrial cooperation, how the

  17. Introducing philosophy of mathematics

    CERN Document Server

    Friend, Michele

    2014-01-01

    What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual acc

  18. Mathematics for Life: Sustainable Mathematics Education

    Science.gov (United States)

    Renert, Moshe

    2011-01-01

    Ecological sustainability has not been a major focus of mathematics education research, even though it has attracted considerable attention in other areas of educational research in the past decade. The connections between mathematics education and ecological sustainability are not readily apparent. This paper explores how mathematics educators…

  19. Mathematical Modelling Approach in Mathematics Education

    Science.gov (United States)

    Arseven, Ayla

    2015-01-01

    The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

  20. The probability density function of completed length of service (CLS ...

    African Journals Online (AJOL)

    ... functions this paper estimates the functions for some secondary schools in Enugu State. Wastage probabilities are calculated, survivor functions estimated. The accompanying standard errors are also obtained. Key words: Manpower Planning, Length of Service, Modelling, Survivor Functions. [Global Jnl Mathematical Sci ...

  1. Mathematical modelling in science and mathematics education

    Science.gov (United States)

    Teodoro, Vítor Duarte; Neves, Rui Gomes

    2011-01-01

    Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high school and university curricula in science and mathematics. In this paper, it is discussed the relevance of mathematical modelling and illustrated how a computer modelling tool (Modellus, a free tool available on the Internet and developed at FCTUNL) can be used to embed modelling in high school and undergraduate courses. Modellus allows students to create and explore mathematical models using functions, differential and iterative equations, and visualize the behaviour of mathematical objects.

  2. Short cervical length dilemma.

    Science.gov (United States)

    Suhag, Anju; Berghella, Vincenzo

    2015-06-01

    Preterm birth (PTB) is a leading cause of neonatal morbidity and mortality. With research efforts, the rate of PTB decreased to 11.4% in 2013. Transvaginal ultrasound (TVU) cervical length (CL) screening predicts PTB. In asymptomatic singletons without prior spontaneous PTB (sPTB), TVU CL screening should be done. If the cervix is 20 mm or less, vaginal progesterone is indicated. In asymptomatic singletons with prior sPTB, serial CL screening is indicated. In multiple gestations, routine cervical screening is not indicated. In symptomatic women with preterm labor, TVU CL screening and fetal fibronectin testing is recommended. Copyright © 2015 Elsevier Inc. All rights reserved.

  3. discouraged by queue length

    Directory of Open Access Journals (Sweden)

    P. R. Parthasarathy

    2001-01-01

    Full Text Available The transient solution is obtained analytically using continued fractions for a state-dependent birth-death queue in which potential customers are discouraged by the queue length. This queueing system is then compared with the well-known infinite server queueing system which has the same steady state solution as the model under consideration, whereas their transient solutions are different. A natural measure of speed of convergence of the mean number in the system to its stationarity is also computed.

  4. Primary length standard adjustment

    Science.gov (United States)

    Ševčík, Robert; Guttenová, Jana

    2007-04-01

    This paper deals with problems and techniques connected with primary length standard adjusting, which includes disassembling of the device and by use of the secondary laser with collimated beam and diffraction laws successively reassembling of the laser. In the reassembling process the device was enhanced with substituting the thermal grease cooling of cold finger by copper socket cooler. This improved external cooling system enables more effective cooling of molecular iodine in the cell, which allows better pressure stability of iodine vapor and easier readjustment of the system.

  5. Analysis of unique beta transitions

    DEFF Research Database (Denmark)

    Eman, B.; Krmpotic, F.; Tadic, D

    1967-01-01

    The Heidelberg group measurements [For abstr. see Phys. Rev. Nucl. Sci. Vol. 15 (1965)] of unique forbidden transitions have been analysed. It has been found that experimental shape factors can be reproduced only with the induced pseudoscalar form factor d <0, and/or with the induced G-non-conser...

  6. Rufus Choate: A Unique Orator.

    Science.gov (United States)

    Markham, Reed

    Rufus Choate, a Massachusetts lawyer and orator, has been described as a "unique and romantic phenomenon" in America's history. Born in 1799 in Essex, Massachusetts, Choate graduated from Dartmouth College and attended Harvard Law School. Choate's goal was to be the top in his profession. Daniel Webster was Choate's hero. Choate became…

  7. Unique properties of Drosophila spermatocyte primary cilia

    Directory of Open Access Journals (Sweden)

    Maria Giovanna Riparbelli

    2013-09-01

    The primary cilium is an essential organelle required for animal development and adult homeostasis that is found on most animal cells. The primary cilium contains a microtubule-based axoneme cytoskeleton that typically grows from the mother centriole in G0/G1 phase of the cell cycle as a membrane-bound compartment that protrudes from the cell surface. A unique system of bidirectional transport, intraflagellar transport (IFT, maintains the structure and function of cilia. While the axoneme is dynamic, growing and shrinking at its tip, at the same time it is very stable to the effects of microtubule-targeting drugs. The primary cilia found on Drosophila spermatocytes diverge from the general rules of primary cilium biology in several respects. Among these unique attributes, spermatocyte cilia assemble from all four centrioles in an IFT-independent manner in G2 phase, and persist continuously through two cell divisions. Here, we show that Drosophila spermatocyte primary cilia are extremely sensitive to microtubule-targeting drugs, unlike their mammalian counterparts. Spermatocyte cilia and their axonemes fail to assemble or be maintained upon nocodazole treatment, while centriole replication appears unperturbed. On the other hand, paclitaxel (Taxol, a microtubule-stabilizing drug, disrupted transition zone assembly and anchoring to the plasma membrane while causing spermatocyte primary cilia to grow extensively long during the assembly/elongation phase, but did not overtly affect the centrioles. However, once assembled to their mature length, spermatocyte cilia appeared unaffected by Taxol. The effects of these drugs on axoneme dynamics further demonstrate that spermatocyte primary cilia are endowed with unique assembly properties.

  8. Mathematics Connection: Editorial Policies

    African Journals Online (AJOL)

    MATHEMATICS CONNECTION aims at providing a forum to promote the development of Mathematics Education in Ghana. Articles that seek to enhance the teaching and/or learning of mathematics ... Faculty of Social Sciences, Methodist University, Accra Prof. B. K. Gordor, Department of Mathematics (UCC), Cape Coast ...

  9. Mathematics through Millenia

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    2005-01-01

    A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....

  10. Mathematics through millenia

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard

    A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations.......A brief tour through the history of mathematics from the very beginnings to modern times, with an emphasis on the main contributions and important periods of mathematics in various civilizations....

  11. World Mathematical Year 2000

    Indian Academy of Sciences (India)

    2001-08-10

    World Mathematical Year 2000. (July 23 to August 10, 2001) at Indian Institute of Science, Bangalore 560 012 sponsored by National Board for Higher Mathematics, organised by Department of Mathematics and. TIFR Centre, Indian Institute of Science. Prof. J L Bona, Department of Mathematics, University of Texas at ...

  12. Chanting as mathematical enculturation

    Directory of Open Access Journals (Sweden)

    Anne Watson

    2004-10-01

    Full Text Available Unison response is a major teaching strategy in mathematics throughout the world. The spoken word is the dominant source of mathematical stimulus, the dominant shaper of the mathematical environment in which school learners construct mathematical meaning. The teachers’ utterances are intended to be expert, and the creation of learner responses is intended to involve learning of some kind.

  13. It's all just mathematics

    Science.gov (United States)

    Tegmark, Max

    2014-02-01

    The world can be described using mathematical equations and numbers, but why does maths do it so well? In his new book Our Mathematical Universe, a section of which is abridged and edited here, Max Tegmark makes the radical proposal that our reality isn't just described by mathematics - it is mathematics.

  14. Length expectation values in quantum Regge calculus

    International Nuclear Information System (INIS)

    Khatsymovsky, V.M.

    2004-01-01

    Regge calculus configuration superspace can be embedded into a more general superspace where the length of any edge is defined ambiguously depending on the 4-tetrahedron containing the edge. Moreover, the latter superspace can be extended further so that even edge lengths in each the 4-tetrahedron are not defined, only area tensors of the 2-faces in it are. We make use of our previous result concerning quantization of the area tensor Regge calculus which gives finite expectation values for areas. Also our result is used showing that quantum measure in the Regge calculus can be uniquely fixed once we know quantum measure on (the space of the functionals on) the superspace of the theory with ambiguously defined edge lengths. We find that in this framework quantization of the usual Regge calculus is defined up to a parameter. The theory may possess nonzero (of the order of Planck scale) or zero length expectation values depending on whether this parameter is larger or smaller than a certain value. Vanishing length expectation values means that the theory is becoming continuous, here dynamically in the originally discrete framework

  15. Influence of Difficulty with Language of Mathematics on Perceived Self-Efficacy in Learning Mathematics among Upper Primary Students of Kerala

    Science.gov (United States)

    Sarabi, M. K.; Gafoor, K. Abdul

    2017-01-01

    There is increasing realization that mathematics-related self-efficacy expectations are a strong predictor of an array of significant mathematics outcomes. It is also evident that the curricular practice in schools largely neglects development of a student understanding in the unique language of mathematics. Consequently, this study probes how…

  16. Renormalization Group in the uniqueness region weak Gibbsianity and convergence.

    CERN Document Server

    Bertini, L; Olivieri, E

    2004-01-01

    We analyze the block averaging transformation applied to lattice gas models with short range interaction in the uniqueness region below the critical temperature. %We discuss the %Gibbs property of the renormalized measure and the convergence of %renormalized potential under iteration of the map. We prove weak Gibbsianity of the renormalized measure and convergence of the renormalized potential in a weak sense. Since we are arbitrarily close to the coexistence region we have a diverging characteristic length of the system: the correlation length or the critical length for metastability, or both. Thus, to perturbatively treat the problem we have to use a scale--adapted expansion. Moreover, such a model below the critical temperature resembles a disordered system in presence of Griffiths' singularity. Then the cluster expansion that we use must be graded with its minimal scale length diverging when the coexistence line is approached.

  17. Kosovo case: A unique arbitrariness

    Directory of Open Access Journals (Sweden)

    Nakarada Radmila

    2007-01-01

    Full Text Available The end of Cold war, contrary to expectations has brought new conflicts and forms of violence, new divisions and new relativizations of the international legal order. Taking as an example the endeavors to resolve the Kosovo conflict, the author attempts to indicate the broader implications of the international efforts to constitute an independent state on part of the territory of an existing sovereign state. The arguments used to justify the redefinition of the borders of the Serbian state without its consent, the moral, democratic, peace arguments, are reviewed. Particular attention is paid to the argument that Kosovo is a unique case and therefore unique rules should be applied. The author seeks to understand the deeper significance of these efforts, concluding that dismantling the present international legal order is not only a potential danger but a possible aim.

  18. Uniqueness theorems in linear elasticity

    CERN Document Server

    Knops, Robin John

    1971-01-01

    The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...

  19. Special Educators and Mathematics Phobia: An Initial Qualitative Investigation

    Science.gov (United States)

    Humphrey, Michael; Hourcade, Jack J.

    2010-01-01

    Special educators are uniquely challenged to be content experts in all curricular areas, including mathematics, because students in their caseloads may require academic instruction in any area. However, special educators with math phobia may be limited in their ability to provide effective instruction to their students with mathematical deficits…

  20. Mathematical modeling in realistic mathematics education

    Science.gov (United States)

    Riyanto, B.; Zulkardi; Putri, R. I. I.; Darmawijoyo

    2017-12-01

    The purpose of this paper is to produce Mathematical modelling in Realistics Mathematics Education of Junior High School. This study used development research consisting of 3 stages, namely analysis, design and evaluation. The success criteria of this study were obtained in the form of local instruction theory for school mathematical modelling learning which was valid and practical for students. The data were analyzed using descriptive analysis method as follows: (1) walk through, analysis based on the expert comments in the expert review to get Hypothetical Learning Trajectory for valid mathematical modelling learning; (2) analyzing the results of the review in one to one and small group to gain practicality. Based on the expert validation and students’ opinion and answers, the obtained mathematical modeling problem in Realistics Mathematics Education was valid and practical.

  1. The Stages of Student Mathematical Imagination in Solving Mathematical Problems

    Science.gov (United States)

    Wibowo, Teguh; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Sulandra, I. Made

    2017-01-01

    This research is a qualitative study that aimed to describe the stages of students mathematical imagination in solving mathematical problems. There are three kinds of mathematical imagination in solving mathematical problems, namely sensory mathematical imagination, creative mathematical imagination and recreative mathematical imagination.…

  2. Mathematics without boundaries surveys in pure mathematics

    CERN Document Server

    Pardalos, Panos

    2014-01-01

    The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the  latest information.

  3. Correlation lengths of electrostatic turbulence

    International Nuclear Information System (INIS)

    Guiziou, L.; Garbet, X.

    1995-01-01

    This document deals with correlation length of electrostatic turbulence. First, the model of drift waves turbulence is presented. Then, the radial correlation length is determined analytically with toroidal coupling and non linear coupling. (TEC). 5 refs

  4. Correlation lengths of electrostatic turbulence

    International Nuclear Information System (INIS)

    Guiziou, L.; Garbet, X.

    1995-01-01

    In this paper, the radial correlation length of an electrostatic drift wave turbulence is analytically determined in various regimes. The analysis relies on the calculation of a range of mode non linear interaction, which is an instantaneous correlation length. The link with the usual correlation length has not been investigated yet. (TEC). 5 refs

  5. Universal and uniquely human factors in spontaneous number perception.

    Science.gov (United States)

    Ferrigno, Stephen; Jara-Ettinger, Julian; Piantadosi, Steven T; Cantlon, Jessica F

    2017-01-16

    A capacity for nonverbal numerical estimation is widespread among humans and animals. However, it is currently unclear whether numerical percepts are spontaneously extracted from the environment and whether nonverbal perception is influenced by human exposure to formal mathematics. We tested US adults and children, non-human primates, and numerate and innumerate Tsimane' adults on a quantity task in which they could choose to categorize sets of dots on the basis of number alone, surface area alone or a combination of the two. Despite differences in age, species and education, subjects are universally biased to base their judgments on number as opposed to the alternatives. Numerical biases are uniquely enhanced in humans compared to non-human primates, and correlated with degree of mathematics experience in both the US and Tsimane' groups. We conclude that humans universally and spontaneously extract numerical information, and that human nonverbal numerical perception is enhanced by symbolic numeracy.

  6. Mathematical Foundations of Forty Years of Research on Conservation in Geneva. Revised Edition.

    Science.gov (United States)

    Easley, J. A., Jr.

    The question of how Piaget selects mathematical concepts for his theory is addressed as a problem which may have contributed to a misinterpretation of the relevance of conservation studies for mathematics education. A new form of pseudo-conservation is discussed in which nonconservers of length are able to pick out strips of equal length from an…

  7. Non-uniqueness of admissible weak solutions to the Riemann problem for the isentropic Euler equations

    Czech Academy of Sciences Publication Activity Database

    Chiodaroli, E.; Kreml, Ondřej

    2018-01-01

    Roč. 31, č. 4 (2018), s. 1441-1460 ISSN 0951-7715 R&D Projects: GA ČR(CZ) GJ17-01694Y Institutional support: RVO:67985840 Keywords : Riemann problem * non-uniqueness * weak solutions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.767, year: 2016 http://iopscience.iop.org/ article /10.1088/1361-6544/aaa10d/meta

  8. Mathematics for Language, Language for Mathematics

    Science.gov (United States)

    Prochazkova, Lenka Tejkalova

    2013-01-01

    The author discusses the balance and mutual influence of the language of instruction and mathematics in the context of CLIL, Content and Language Integrated Learning. Different aspects of the relationship of language and Mathematics teaching and learning are discussed: the benefits of using a foreign language of instruction, as well as the…

  9. Differences in pupils' mathematics self-concept by class level and ...

    African Journals Online (AJOL)

    The knowledge of mathematics is of great value in scientific and technological fields. Mathematics is widely recognised as an important qualification for employment and further studies. It provides a unique type of experience in problem solving which is an essential component of a complete education. Though mathematics ...

  10. Mathematical model of temperature rise in three-layer skin during ...

    African Journals Online (AJOL)

    We discuss the existence and uniqueness of solution of mathematical model of multi-layered human skin exposed to microwave heating during cancer therapy. We show that our model has a solution and the solution is unique.215-216. Journal of the Nigerian Association of Mathematical Physics Vol. 9 2005: pp.

  11. Mathematical Modeling Using MATLAB

    National Research Council Canada - National Science Library

    Phillips, Donovan

    1998-01-01

    .... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...

  12. Developing My Mathematics Identity

    Science.gov (United States)

    Gonzalez, Lidia

    2016-01-01

    Assuming the role of storyteller, the author uses her experiences as a graduate student and beginning teacher to reflect critically on issues related to mathematics, mathematics education, gender, and diversity.

  13. Journal of applied mathematics

    National Research Council Canada - National Science Library

    2001-01-01

    "[The] Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics...

  14. Semiotic Scaffolding in Mathematics

    DEFF Research Database (Denmark)

    Johansen, Mikkel Willum; Misfeldt, Morten

    2015-01-01

    This paper investigates the notion of semiotic scaffolding in relation to mathematics by considering its influence on mathematical activities, and on the evolution of mathematics as a research field. We will do this by analyzing the role different representational forms play in mathematical...... cognition, and more broadly on mathematical activities. In the main part of the paper, we will present and analyze three different cases. For the first case, we investigate the semiotic scaffolding involved in pencil and paper multiplication. For the second case, we investigate how the development of new...... in both mathematical cognition and in the development of mathematics itself, but mathematical cognition cannot itself be reduced to the use of semiotic scaffolding....

  15. The argument of mathematics

    CERN Document Server

    Aberdein, Andrew

    2014-01-01

    This book presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. It offers large array of examples ranging from the history of mathematics to formal proof verification.

  16. Mathematical knowledge in teaching

    CERN Document Server

    Rowland, Tim

    2011-01-01

    This book examines issues of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing approaches to characterizing, assessing and developing mathematical knowledge for teaching.

  17. Mathematics for the nonmathematician

    CERN Document Server

    Kline, Morris

    1967-01-01

    Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.

  18. Modern mathematics made simple

    CERN Document Server

    Murphy, Patrick

    1982-01-01

    Modern Mathematics: Made Simple presents topics in modern mathematics, from elementary mathematical logic and switching circuits to multibase arithmetic and finite systems. Sets and relations, vectors and matrices, tesselations, and linear programming are also discussed.Comprised of 12 chapters, this book begins with an introduction to sets and basic operations on sets, as well as solving problems with Venn diagrams. The discussion then turns to elementary mathematical logic, with emphasis on inductive and deductive reasoning; conjunctions and disjunctions; compound statements and conditional

  19. Mathematical modeling using Maple

    OpenAIRE

    Beauchamp, Robert Edward.

    1996-01-01

    The area of higher mathematics begins with successive courses in calculus; however, rarely does the calculus student recognize the applications or impetus for the mathematical skills that are taught. Giordano and Weir produced A First Course in Mathematical Modeling, the first text which addressed this shortcoming in the curriculum of every science and engineering field. With the advent of powerful classroom computers, Fox, Maddox, Giordano and Weir produced Mathematical Modeling With Minitab...

  20. Our Mathematical Universe?

    OpenAIRE

    Butterfield, Jeremy

    2014-01-01

    This is a discussion of some themes in Max Tegmark's recent book, Our Mathematical Universe. It was written as a review for Plus Magazine, the online magazine of the UK's national mathematics education and outreach project, the Mathematics Millennium Project. Since some of the discussion (about symmetry breaking, and Pythagoreanism in the philosophy of mathematics) went beyond reviewing Tegmark's book, the material was divided into three online articles. This version combines those three arti...

  1. Interactions: Mathematics, Physics and Philosophy, 1860-1930

    DEFF Research Database (Denmark)

    The main theme of this anthology is the unique interaction between mathematics, physics and philosophy during the beginning of the 20th century. Seminal theories of modern physics and new fundamental mathematical structures were discovered or formed in this period. Significant physicists...... such as Lorentz and Einstein as well as mathematicians such as Poincare, Minkowski, Hilbert and Weyl contributed to this development. They created the new physical theories and the mathematical disciplines that play such paramount roles in their mathematical formulations. These physicists and mathematicians were...

  2. Interactions: Mathematics, Physics and Philosophy, 1860-1930

    DEFF Research Database (Denmark)

    The main theme of this anthology is the unique interaction between mathematics, physics and philosophy during the beginning of the 20th century. Seminal theories of modern physics and new fundamental mathematical structures were discovered or formed in this period. Significant physicists...... such as Lorentz and Einstein as well as mathematicians such as Poincare, Minkowski, Hilbert and Weyl contributed to this development. They created the new physical theories and the mathematical disciplines that play such paramount roles in their mathematical formulations. These physicists and mathematicians were...... also key figures in the philosophical discussions of nature and science - from philosophical tendencies like logical empiricism via critical rationalism to various neo-Kantian trends....

  3. Utah's New Mathematics Core

    Science.gov (United States)

    Utah State Office of Education, 2011

    2011-01-01

    Utah has adopted more rigorous mathematics standards known as the Utah Mathematics Core Standards. They are the foundation of the mathematics curriculum for the State of Utah. The standards include the skills and understanding students need to succeed in college and careers. They include rigorous content and application of knowledge and reflect…

  4. Learning Environments in Mathematics

    Science.gov (United States)

    Turner, Vanshelle E.

    2017-01-01

    Learning mathematics is problematic for most primary school age children because mathematics is rote and the memorization of steps rather than an approach to seeing relationships that builds inquiry and understanding. Therefore, the traditional "algorithmic" way of teaching mathematics has not fully prepared students to be critical…

  5. Masculinities in mathematics

    CERN Document Server

    Mendick, Heather

    2006-01-01

    The study of mathematics, with other ''gendered'' subjects such as science and engineering, usually attracts more male than female pupils. This book explores this phenomenon, addressing the important question of why more boys than girls choose to study mathematics. It illuminates what studying mathematics means for both students and teachers.

  6. Mathematics of Risk Taking

    Indian Academy of Sciences (India)

    Author Affiliations. K B Athreya1 2 M G Nadkarni3. Department of Mathematics Iowa State University, Ames, Iowa; I M I, Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India. Department of Mathematics, University of Mumbai Kalina, Mumbai, 400098, India.

  7. Mathematical Sciences in Australia

    Science.gov (United States)

    Thomas, Jan; Muchatuta, Michelle; Wood, Leigh

    2009-01-01

    This article investigates enrolment trends in mathematical sciences in Australian universities. Data has been difficult to extract and the coding for mathematical disciplines has made investigation challenging. We show that the number of mathematics major undergraduates in Australia is steadily declining though the number studying…

  8. Students' Mathematical Noticing

    Science.gov (United States)

    Lobato, Joanne; Hohensee, Charles; Rhodehamel, Bohdan

    2013-01-01

    Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…

  9. Mathematics Connection: Contact

    African Journals Online (AJOL)

    Principal Contact. Dr. Kofi Mereku Executive Editor Department of Mathematics Education, UCE Mathematical Association of Ghana, C/o Department of Mathematics Education University College of Education of Winneba P. O. Box 25, Winneba, Ghana Phone: +233244961318. Email: dkmereku@uew.edu.gh ...

  10. Mathematical Discovery: Hadamard Resurected

    Science.gov (United States)

    Liljedahl, Peter

    2004-01-01

    In 1943 Jacques Hadamard gave a series of lectures on mathematical invention at the Ecole Libre des Hautes Etudes in New York City. These talks were subsequently published as The Psychology of Mathematical Invention in the Mathematical Field (Hadamard, 1945). In this article I present a study that mirrors the work of Hadamard. Results both…

  11. Making Mathematics Culturally Relevant.

    Science.gov (United States)

    Moyer, Patricia

    2001-01-01

    Examines three strands of elementary mathematics--numerals and counting, recording and calculating, and mathematics exploration and play--and provides ways to integrate culture and mathematics experiences in each area. Specific topics include Egyptian methods for multiplication, the abacus, and the words for the numbers 1-10 in seven different…

  12. Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations

    Science.gov (United States)

    Darlington, Ellie

    2014-01-01

    This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…

  13. Mathematics and mysticism.

    Science.gov (United States)

    Abraham, Ralph

    2015-12-01

    Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination. Copyright © 2015. Published by Elsevier Ltd.

  14. Teaching Mathematics as Agape

    Science.gov (United States)

    Amidon, Joel C.

    2011-01-01

    What happens when the problem of inequitable access to mathematics is addressed by agape (pronounced agapa) or attending to the relationships students develop with mathematics? To respond to this question, this paper offers a description of the journey towards teaching mathematics as agape. First, I organized examples of equity pedagogy around the…

  15. MATHEMATICS AND MUSIC

    OpenAIRE

    ESİ, Ayten

    2017-01-01

    One of the areas where mathematics and art are related is music. Throughout human history, many mathematicians have been interested in music. In this study, the relations between mathematics and music were examined and tried to be explained with various examples that these two are inseparable parts of the each other, and it was tried to be emphasized that mathematics is in the music

  16. Creating Words in Mathematics

    Science.gov (United States)

    Galligan, Linda

    2016-01-01

    A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…

  17. Defining Mathematical Giftedness

    Science.gov (United States)

    Parish, Linda

    2014-01-01

    This theoretical paper outlines the process of defining "mathematical giftedness" for a present study on how primary school teaching shapes the mindsets of children who are mathematically gifted. Mathematical giftedness is not a badge of honour or some special value attributed to a child who has achieved something exceptional.…

  18. Mathematics Teaching Today

    Science.gov (United States)

    Martin, Tami S.; Speer, William R.

    2009-01-01

    This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…

  19. Mathematics of Risk Taking

    Indian Academy of Sciences (India)

    user

    Mathematics of Risk Taking. K B Athreya and M G Nadkarni. Keywords. Investor, risk taking, fair game, martingale, random walk, gam- bling, population. (left) K B Athreya is a visiting professor at IMI,. Mathematics Department,. IISc, Bangalore and is also a professor of mathematics and statistics at Iowa State. University ...

  20. Unique features in the ARIES glovebox line

    International Nuclear Information System (INIS)

    Martinez, H.E.; Brown, W.G.; Flamm, B.; James, C.A.; Laskie, R.; Nelson, T.O.; Wedman, D.E.

    1998-01-01

    A series of unique features have been incorporated into the Advanced Recovery and Integrated Extraction System (ARIES) at the Los Alamos National Laboratory, TA-55 Plutonium Facility. The features enhance the material handling in the process of the dismantlement of nuclear weapon primaries in the glovebox line. Incorporated into these features are the various plutonium process module's different ventilation zone requirements that the material handling systems must meet. These features include a conveyor system that consists of a remotely controlled cart that transverses the length of the conveyor glovebox, can be operated from a remote location and can deliver process components to the entrance of any selected module glovebox. Within the modules there exists linear motion material handling systems with lifting hoist, which are controlled via an Allen Bradley control panel or local control panels. To remove the packaged products from the hot process line, the package is processed through an air lock/electrolytic decontamination process that removes the radioactive contamination from the outside of the package container and allows the package to be removed from the process line

  1. Modeling wildland fire containment with uncertain flame length and fireline width

    Science.gov (United States)

    Romain Mees; David Strauss; Richard Chase

    1993-01-01

    We describe a mathematical model for the probability that a fireline succeeds in containing a fire. The probability increases as the fireline width increases, and also as the fire's flame length decreases. More interestingly, uncertainties in width and flame length affect the computed containment probabilities, and can thus indirectly affect the optimum allocation...

  2. Accounting for primitive terms in mathematics

    Directory of Open Access Journals (Sweden)

    D.F.M. Strauss

    2005-07-01

    Full Text Available The philosophical problem of unity and diversity entails a challenge to the rationalist aim to define everything. Definitions of this kind surface in various academic disciplines in formulations like uniqueness, irreducibility, and what has acquired the designation “primitive terms”. Not even the most “exact” disciplines, such as mathematics, can avoid the implications entailed in giving an account of such primitive terms. A mere look at the historical development of mathematics highlights the fact that alternative perspectives prevailed – from the arithmeticism of Pythagoreanism, the eventual geometrisation of mathematics after the discovery of incommensurability up to the revival of arithmeticism in the mathematics of Cauchy, Weierstrass, Dedekind and Cantor (with the later orientation of Frege, who completed the circle by returning to the view that mathematics essentially is geometry. An assessment of logicism and axiomatic formalism is followed by looking at the primitive meaning of wholeness (and the whole-parts relation. With reference to the views of Hilbert, Weyl and Bernays the article concludes by suggesting that in opposition to arithmeticism and geometricism an alternative option ought to be pursued – one in which both the uniqueness and mutual coherence between the aspects of number and space are acknowledged.

  3. A Technique for Mapping Mathematics Content to Game Design

    Directory of Open Access Journals (Sweden)

    Vani Kalloo

    2015-12-01

    Full Text Available Research has shown that games can be valuable tools for learning mathematics. In this paper, we explain how we tackled the challenge of mapping mathematics content to games in the design of mathematics learning games. We present a unique technique for mapping mathematics content to game design. The technique can be used to improve the game design process by guiding the designer through one of the more challenging stages of the design process, namely, that of incorporating mathematics content into a game. The technique is based on several factors such as mathematics learning pedagogy, game type categorization, the mathematics curriculum, and past research experience. The technique is unique since it focuses on guiding the game designer through the process of mapping the mathematics content to the game idea. Additionally, the technique incorporates several important game design principles. A preliminary evaluation of the technique was conducted with several amateur game designers. Although there are several limitations of the technique, the evaluation shows that it was useful in helping the game designers to design suitable mathematics learning games. 

  4. The nature of mathematics

    CERN Document Server

    Jourdain, Philip E B

    2007-01-01

    Anyone with an interest in mathematics will welcome the republication of this little volume by a remarkable mathematician who was also a logician, a philosopher, and an occasional writer of fiction and poetry. Originally published in 1913, and later included in the acclaimed anthology The World of Mathematics, Jourdain's survey shows how and why the methods of mathematics were developed, traces the development of mathematical science from the earliest to modern times, and chronicles the application of mathematics to natural science.Starting with the ancient Egyptians and Greeks, the author p

  5. Mathematics for the imagination

    CERN Document Server

    Higgins, Peter

    2002-01-01

    Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun new book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind.This is a follow-up to the popular Mathematics for the Curious, Peter Higgins's first investigation into real-life mathematical problems.A highly involving book which encourages the reader to enter into the spirit of mathematical ex

  6. Introductory discrete mathematics

    CERN Document Server

    Balakrishnan, V K

    2010-01-01

    This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv

  7. The development of mathematics

    CERN Document Server

    Bell, Eric Temple

    1945-01-01

    ""This important book . . . presents a broad account of the part played by mathematics in the evolution of civilization, describing clearly the main principles, methods, and theories of mathematics that have survived from about 4000 BC to 1940.""― BooklistIn this time-honored study, one of the 20th century's foremost scholars and interpreters of the history and meaning of mathematics masterfully outlines the development of its leading ideas, and clearly explains the mathematics involved in each. According to the author, a professor of mathematics at the California Institute of Technology from

  8. Fundamental concepts of mathematics

    CERN Document Server

    Goodstein, R L

    Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people

  9. Mathematics in ancient Greece

    CERN Document Server

    Dantzig, Tobias

    2006-01-01

    More than a history of mathematics, this lively book traces mathematical ideas and processes to their sources, stressing the methods used by the masters of the ancient world. Author Tobias Dantzig portrays the human story behind mathematics, showing how flashes of insight in the minds of certain gifted individuals helped mathematics take enormous forward strides. Dantzig demonstrates how the Greeks organized their precursors' melange of geometric maxims into an elegantly abstract deductive system. He also explains the ways in which some of the famous mathematical brainteasers of antiquity led

  10. Philosophy of mathematics

    CERN Document Server

    Gabbay, Dov M; Woods, John

    2009-01-01

    One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mat

  11. What is mathematical logic?

    CERN Document Server

    Crossley, J N; Brickhill, CJ; Stillwell, JC

    2010-01-01

    Although mathematical logic can be a formidably abstruse topic, even for mathematicians, this concise book presents the subject in a lively and approachable fashion. It deals with the very important ideas in modern mathematical logic without the detailed mathematical work required of those with a professional interest in logic.The book begins with a historical survey of the development of mathematical logic from two parallel streams: formal deduction, which originated with Aristotle, Euclid, and others; and mathematical analysis, which dates back to Archimedes in the same era. The streams beg

  12. Travelling Mathematics - The Fate of Diophantos' Arithmetic

    CERN Document Server

    Meskens, Ad

    2010-01-01

    In this book the author presents a comprehensive study of Diophantos' monumental work known as "Arithmetika", a highly acclaimed and unique set of books within the known Greek mathematical corpus. Its author, Diophantos, is an enigmatic figure of whom we know virtually nothing. Starting with Egyptian, Babylonian and early Greek mathematics the author paints a picture of the sources the Arithmetika may have had. Life in Alexandria, where Diophantos lived, is described and, on the basis of the limited available evidence, his biography is outlined. Of Arithmetika's 13 books only 6 survi

  13. Logic and discrete mathematics a concise introduction

    CERN Document Server

    Conradie, Willem

    2015-01-01

    A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade.  The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy

  14. The Ellipse A Historical and Mathematical Journey

    CERN Document Server

    Mazer, Arthur

    2011-01-01

    Explores the development of the ellipse and presents mathematical concepts within a rich, historical context The Ellipse features a unique, narrative approach when presenting the development of this mathematical fixture, revealing its parallels to mankind's advancement from the Counter-Reformation to the Enlightenment. Incorporating illuminating historical background and examples, the author brings together basic concepts from geometry, algebra, trigonometry, and calculus to uncover the ellipse as the shape of a planet's orbit around the sun. The book begins with a discussion that tells the st

  15. Meaning in mathematics education

    CERN Document Server

    Valero, Paola; Hoyles, Celia; Skovsmose, Ole

    2005-01-01

    What does it mean to know mathematics? How does meaning in mathematics education connect to common sense or to the meaning of mathematics itself? How are meanings constructed and communicated and what are the dilemmas related to these processes? There are many answers to these questions, some of which might appear to be contradictory. Thus understanding the complexity of meaning in mathematics education is a matter of huge importance. There are twin directions in which discussions have developed - theoretical and practical - and this book seeks to move the debate forward along both dimensions while seeking to relate them where appropriate. A discussion of meaning can start from a theoretical examination of mathematics and how mathematicians over time have made sense of their work. However, from a more practical perspective, anybody involved in teaching mathematics is faced with the need to orchestrate the myriad of meanings derived from multiple sources that students develop of mathematical knowledge.

  16. The History of Mathematics and Mathematical Education

    Science.gov (United States)

    Grattan-Guinness, I.

    1977-01-01

    Answers to questions which were asked after the author's various lectures in Australia are gathered here. Topics touched upon include "new" mathematics, unknown constants and free variables, propositional functions, linear algebra, arithmetic and geometry, and student assessment. (MN)

  17. Unique immunologic patterns in fibromyalgia.

    Science.gov (United States)

    Behm, Frederick G; Gavin, Igor M; Karpenko, Oleksiy; Lindgren, Valerie; Gaitonde, Sujata; Gashkoff, Peter A; Gillis, Bruce S

    2012-12-17

    Fibromyalgia (FM) is a clinical syndrome characterized by chronic pain and allodynia. The diagnosis of FM has been one of exclusion as a test to confirm the diagnosis is lacking. Recent data highlight the role of the immune system in FM. Aberrant expressions of immune mediators, such as cytokines, have been linked to the pathogenesis and traits of FM. We therefore determined whether cytokine production by immune cells is altered in FM patients by comparing the cellular responses to mitogenic activators of stimulated blood mononuclear cells of a large number of patients with FM to those of healthy matched individuals. Plasma and peripheral blood mononuclear cells (PBMC) were collected from 110 patients with the clinical diagnosis of FM and 91 healthy donors. Parallel samples of PBMC were cultured overnight in medium alone or in the presence of mitogenic activators; PHA or PMA in combination with ionomycin. The cytokine concentrations of IFN-γ, IL-5, IL-6, IL-8, IL-10, MIP-1β , MCP-1, and MIP1-α in plasma as well as in cultured supernatants were determined using a multiplex immunoassay using bead array technology. Cytokine levels of stimulated PBMC cultures of healthy control subjects were significantly increased as compared to matched non-stimulated PBMC cultures. In contrast, the concentrations of most cytokines were lower in stimulated samples from patients with FM compared to controls. The decreases of cytokine concentrations in patients samples ranged from 1.5-fold for MIP-1β to 10.2-fold for IL-6 in PHA challenges. In PMA challenges, we observed 1.8 to 4-fold decreases in the concentrations of cytokines in patient samples. The cytokine responses to mitogenic activators of PBMC isolated from patients with FM were significantly lower than those of healthy individuals, implying that cell-mediated immunity is impaired in FM patients. This novel cytokine assay reveals unique and valuable immunologic traits, which, when combined with clinical patterns, can offer

  18. Symbols are not uniquely human.

    Science.gov (United States)

    Ribeiro, Sidarta; Loula, Angelo; de Araújo, Ivan; Gudwin, Ricardo; Queiroz, João

    2007-01-01

    Modern semiotics is a branch of logics that formally defines symbol-based communication. In recent years, the semiotic classification of signs has been invoked to support the notion that symbols are uniquely human. Here we show that alarm-calls such as those used by African vervet monkeys (Cercopithecus aethiops), logically satisfy the semiotic definition of symbol. We also show that the acquisition of vocal symbols in vervet monkeys can be successfully simulated by a computer program based on minimal semiotic and neurobiological constraints. The simulations indicate that learning depends on the tutor-predator ratio, and that apprentice-generated auditory mistakes in vocal symbol interpretation have little effect on the learning rates of apprentices (up to 80% of mistakes are tolerated). In contrast, just 10% of apprentice-generated visual mistakes in predator identification will prevent any vocal symbol to be correctly associated with a predator call in a stable manner. Tutor unreliability was also deleterious to vocal symbol learning: a mere 5% of "lying" tutors were able to completely disrupt symbol learning, invariably leading to the acquisition of incorrect associations by apprentices. Our investigation corroborates the existence of vocal symbols in a non-human species, and indicates that symbolic competence emerges spontaneously from classical associative learning mechanisms when the conditioned stimuli are self-generated, arbitrary and socially efficacious. We propose that more exclusive properties of human language, such as syntax, may derive from the evolution of higher-order domains for neural association, more removed from both the sensory input and the motor output, able to support the gradual complexification of grammatical categories into syntax.

  19. Non-selfadjoint operators in quantum physics mathematical aspects

    CERN Document Server

    Gazeau, Jean Pierre; Szafraniec, Franciszek Hugon; Znojil, Miloslav

    2015-01-01

    A unique discussion of mathematical methods with applications to quantum mechanics Non-Selfadjoint Operators in Quantum Physics: Mathematical Aspects presents various mathematical constructions influenced by quantum mechanics and emphasizes the spectral theory of non-adjoint operators. Featuring coverage of functional analysis and algebraic methods in contemporary quantum physics, the book discusses recent emergence of the unboundedness of metric operators, which is a serious issue in the study of parity-time-symmetric quantum mechanics. The book also answers mathematical questions that are currently the subject of rigorous analysis, with potentially significant physical consequences. In addition to prompting a discussion of the role of mathematical methods in the contemporary development of quantum physics, the book features: * Chapter contributions written by well-known mathematical physicists who clarify numerous misunderstandings and misnomers while shedding light on new approaches in this growing area *...

  20. 18th European Conference on Mathematics for Industry

    CERN Document Server

    Capasso, Vincenzo; Nicosia, Giuseppe; Romano, Vittorio

    2016-01-01

    This book presents a collection of papers emphasizing applications of mathematical models and methods to real-world problems of relevance for industry, life science, environment, finance, and so on. The biannual Conference of ECMI (the European Consortium of Mathematics in Industry) held in 2014 focused on various aspects of industrial and applied mathematics. The five main topics addressed at the conference were mathematical models in life science, material science and semiconductors, mathematical methods in the environment, design automation and industrial applications, and computational finance. Several other topics have been treated, such as, among others, optimization and inverse problems, education, numerical methods for stiff pdes, model reduction, imaging processing, multi physics simulation, mathematical models in textile industry. The conference, which brought together applied mathematicians and experts from industry, provided a unique opportunity to exchange ideas, problems and methodologies...

  1. Mathematical theory of compressible viscous fluids analysis and numerics

    CERN Document Server

    Feireisl, Eduard; Pokorný, Milan

    2016-01-01

    This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematic...

  2. An introduction to mathematical modeling a course in mechanics

    CERN Document Server

    Oden, Tinsley J

    2011-01-01

    A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...

  3. 7 Length-weight relationship

    African Journals Online (AJOL)

    Administrator

    Length-weight measurements were taken from well-preserved fish specimens from which stomachs were extracted for the analysis of the food contents, using frequency of occurrence, numerical and gravimetric methods, as well as index of relative importance. The length-frequency analysis showed a size distribution with a ...

  4. Comparison of fiber length analyzers

    Science.gov (United States)

    Don Guay; Nancy Ross Sutherland; Walter Rantanen; Nicole Malandri; Aimee Stephens; Kathleen Mattingly; Matt Schneider

    2005-01-01

    In recent years, several fiber new fiber length analyzers have been developed and brought to market. The new instruments provide faster measurements and the capability of both laboratory and on-line analysis. Do the various fiber analyzers provide the same length, coarseness, width, and fines measurements for a given fiber sample? This paper provides a comparison of...

  5. Unique immunologic patterns in fibromyalgia

    Directory of Open Access Journals (Sweden)

    Behm Frederick G

    2012-12-01

    Full Text Available Abstract Background Fibromyalgia (FM is a clinical syndrome characterized by chronic pain and allodynia. The diagnosis of FM has been one of exclusion as a test to confirm the diagnosis is lacking. Recent data highlight the role of the immune system in FM. Aberrant expressions of immune mediators, such as cytokines, have been linked to the pathogenesis and traits of FM. We therefore determined whether cytokine production by immune cells is altered in FM patients by comparing the cellular responses to mitogenic activators of stimulated blood mononuclear cells of a large number of patients with FM to those of healthy matched individuals. Methods Plasma and peripheral blood mononuclear cells (PBMC were collected from 110 patients with the clinical diagnosis of FM and 91 healthy donors. Parallel samples of PBMC were cultured overnight in medium alone or in the presence of mitogenic activators; PHA or PMA in combination with ionomycin. The cytokine concentrations of IFN-γ, IL-5, IL-6, IL-8, IL-10, MIP-1β , MCP-1, and MIP1-α in plasma as well as in cultured supernatants were determined using a multiplex immunoassay using bead array technology. Results Cytokine levels of stimulated PBMC cultures of healthy control subjects were significantly increased as compared to matched non-stimulated PBMC cultures. In contrast, the concentrations of most cytokines were lower in stimulated samples from patients with FM compared to controls. The decreases of cytokine concentrations in patients samples ranged from 1.5-fold for MIP-1β to 10.2-fold for IL-6 in PHA challenges. In PMA challenges, we observed 1.8 to 4-fold decreases in the concentrations of cytokines in patient samples. Conclusion The cytokine responses to mitogenic activators of PBMC isolated from patients with FM were significantly lower than those of healthy individuals, implying that cell-mediated immunity is impaired in FM patients. This novel cytokine assay reveals unique and valuable

  6. A mathematical approach to research problems of science and technology theoretical basis and developments in mathematical modeling

    CERN Document Server

    Ei, Shin-ichiro; Koiso, Miyuki; Ochiai, Hiroyuki; Okada, Kanzo; Saito, Shingo; Shirai, Tomoyuki

    2014-01-01

    This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.

  7. Mathematical Sciences Institute Workshop

    CERN Document Server

    Scott, Philip

    1990-01-01

    A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions ...

  8. Global existence and uniqueness result for the diffusive Peterlin viscoelastic model

    Czech Academy of Sciences Publication Activity Database

    Medviďová-Lukáčová, M.; Mizerová, H.; Nečasová, Šárka

    2015-01-01

    Roč. 120, June (2015), s. 154-170 ISSN 0362-546X R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : Peterlin viscoelastic model * existence * uniqueness Subject RIV: BA - General Mathematics Impact factor: 1.125, year: 2015 http://www.sciencedirect.com/science/article/pii/S0362546X1500070X

  9. Existence and uniqueness of a periodic solution to an indefinite attractive singular equation

    Czech Academy of Sciences Publication Activity Database

    Hakl, Robert; Zamora, M.

    2016-01-01

    Roč. 195, č. 3 (2016), s. 995-1009 ISSN 0373-3114 Institutional support: RVO:67985840 Keywords : singular differential equation * periodic solution * uniqueness Subject RIV: BA - General Mathematics Impact factor: 0.864, year: 2016 http://link.springer.com/article/10.1007%2Fs10231-015-0501-3

  10. Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence.

    Science.gov (United States)

    Lourenco, Stella F; Bonny, Justin W; Fernandez, Edmund P; Rao, Sonia

    2012-11-13

    Humans and nonhuman animals share the capacity to estimate, without counting, the number of objects in a set by relying on an approximate number system (ANS). Only humans, however, learn the concepts and operations of symbolic mathematics. Despite vast differences between these two systems of quantification, neural and behavioral findings suggest functional connections. Another line of research suggests that the ANS is part of a larger, more general system of magnitude representation. Reports of cognitive interactions and common neural coding for number and other magnitudes such as spatial extent led us to ask whether, and how, nonnumerical magnitude interfaces with mathematical competence. On two magnitude comparison tasks, college students estimated (without counting or explicit calculation) which of two arrays was greater in number or cumulative area. They also completed a battery of standardized math tests. Individual differences in both number and cumulative area precision (measured by accuracy on the magnitude comparison tasks) correlated with interindividual variability in math competence, particularly advanced arithmetic and geometry, even after accounting for general aspects of intelligence. Moreover, analyses revealed that whereas number precision contributed unique variance to advanced arithmetic, cumulative area precision contributed unique variance to geometry. Taken together, these results provide evidence for shared and unique contributions of nonsymbolic number and cumulative area representations to formally taught mathematics. More broadly, they suggest that uniquely human branches of mathematics interface with an evolutionarily primitive general magnitude system, which includes partially overlapping representations of numerical and nonnumerical magnitude.

  11. Mathematical Properties Relevant to Geomagnetic Field Modeling

    DEFF Research Database (Denmark)

    Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

    2010-01-01

    Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers.......The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...... be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered...

  12. Interfacial Fluid Mechanics A Mathematical Modeling Approach

    CERN Document Server

    Ajaev, Vladimir S

    2012-01-01

    Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail.  Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also:  Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...

  13. Advances in mathematical economics

    CERN Document Server

    Maruyama, Toru

    2017-01-01

    The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

  14. Advances in mathematical economics

    CERN Document Server

    Maruyama, Toru

    2016-01-01

    The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

  15. Advances in mathematical economics

    CERN Document Server

    Yamazaki, Akira

    2006-01-01

    A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.

  16. Advances in mathematical economics

    CERN Document Server

    Yamazaki, Akira

    2006-01-01

    A lot of economic problems can formulated as constrained optimizations and equilibration of their solutions.Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who were seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking for effective mathematical tools for their researchers.

  17. International Mathematical Internet Olympiad

    Directory of Open Access Journals (Sweden)

    Alexander Domoshnitsky

    2012-10-01

    Full Text Available Modern Internet technologies open new possibilities in wide spectrum of traditional methods used in mathematical education. One of the areas, where these technologies can be efficiently used, is an organization of mathematical competitions. Contestants can stay at their schools or universities and try to solve as many mathematical problems as possible and then submit their solutions through Internet. Simple Internet technologies supply audio and video connection between participants and organizers.

  18. Interactive Mathematics Textbooks

    DEFF Research Database (Denmark)

    Sinclair, Robert

    1999-01-01

    We claim that important considerations have been overlooked in designinginteractive mathematics educational software in the past.In particular,most previous work has concentrated on how to make use ofpre-existing software in mathematics education, rather than firstasking the more...... fundamentalquestion of which requirements mathematics education puts on software, and thendesigning software to fulfil these requirements.We present a working prototype system which takes a script defining an interactivemathematicaldocument and then provides a reader with an interactive realization of thatdocument....

  19. Learning Mathematics through Programming

    DEFF Research Database (Denmark)

    Misfeldt, Morten; Ejsing-Duun, Stine

    2015-01-01

    In this paper we explore the potentials for learning mathematics through programming by a combination of theoretically derived potentials and cases of practical pedagogical work. We propose a model with three interdependent learning potentials as programming which can: (1) help reframe the students...... to mathematics is paramount. Analyzing two cases, we suggest a number of ways in which didactical attention to epistemic mediation can support learning mathematics....

  20. Advances in mathematical economics

    CERN Document Server

    Maruyama, Toru

    2015-01-01

    The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

  1. Mathematics in Engineering

    OpenAIRE

    Chatterjee, Anindya

    2005-01-01

    I try to convey some of the variety and excitement involved in the application of mathematics to engineering problems; to provide a taste of some actual mathematical calculations that engineers do; and finally, to make clear the distinctions between the applied subject of engineering and its purer parents, which include mathematics and the physical sciences. Two main points of this article are that in engineering it is approximation, and not truth, that reigns; and that an engineer carries a ...

  2. Educating mathematics teacher educators

    DEFF Research Database (Denmark)

    Højgaard, Tomas; Jankvist, Uffe Thomas

    2014-01-01

    The paper argues for a three-dimensional course design structure for future mathematics teacher educators. More precisely we describe the design and implementation of a course basing itself on: the two mathematical competencies of modelling and problem tackling, this being the first dimension......; the two mathematical topics of differential equations and stochastics, this being the second dimension; and finally a third dimension the purpose of which is to deepen the two others by means of a didactical perspective....

  3. Ideation in mathematical writing

    DEFF Research Database (Denmark)

    Misfeldt, Morten

    2007-01-01

    This paper considers idea generation during the mathematical writing process. Two contrasting explanations of the creative potential in connection to writing is presented; writing as a process of setting and obtaining rhetorical goals and writing as a process of discovery. These views...... are then related to two empirically found categories of functions that writing serves researchers in the field of mathematics, concluding that both views contributes to understanding the creative potential in relation to mathematical writing....

  4. Handbook of mathematics

    CERN Document Server

    Kuipers, L

    1969-01-01

    International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examp

  5. Mathematical mind-benders

    CERN Document Server

    Winkler, Peter

    2007-01-01

    Peter Winkler is at it again. Following the enthusiastic reaction to Mathematical Puzzles: A Connoisseur's Collection, Peter has compiled a new collection of elegant mathematical puzzles to challenge and entertain the reader. The original puzzle connoisseur shares these puzzles, old and new, so that you can add them to your own anthology. This book is for lovers of mathematics, lovers of puzzles, lovers of a challenge. Most of all, it is for those who think that the world of mathematics is orderly, logical, and intuitive-and are ready to learn otherwise! A pdf with errata is updated by the aut

  6. Mathematics at University

    DEFF Research Database (Denmark)

    Winsløw, Carl

    2015-01-01

    Mathematics is studied in universities by a large number of students. At the same time it is a field of research for a (smaller) number of university teachers. What relations, if any, exist between university research and teaching of mathematics? Can research “support” teaching? What research...... and what teaching? In this presentation we propose a theoretical framework to study these questions more precisely, based on the anthropological theory of didactics. As a main application, the links between the practices of mathematical research and university mathematics teaching are examined...

  7. Mathematics in India

    CERN Document Server

    Plofker, Kim

    2009-01-01

    Based on extensive research in Sanskrit sources, Mathematics in India chronicles the development of mathematical techniques and texts in South Asia from antiquity to the early modern period. Kim Plofker reexamines the few facts about Indian mathematics that have become common knowledge--such as the Indian origin of Arabic numerals--and she sets them in a larger textual and cultural framework. The book details aspects of the subject that have been largely passed over in the past, including the relationships between Indian mathematics and astronomy, and their cross-fertilizations with Islamic sc

  8. Mathematical fallacies and paradoxes

    CERN Document Server

    Bunch, Bryan

    1982-01-01

    Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.

  9. Philosophy and mathematics: interactions.

    Science.gov (United States)

    Rashed, Roshdi

    From Plato to the beginnings of the last century, mathematics provided philosophers with methods of exposition, procedures of demonstration, and instruments of analysis. The unprecedented development of mathematics on the one hand, and the mathematicians' appropriation of Logic from the philosophers on the other hand, have given rise to two problems with which the philosophers have to contend: (1) Is there still a place for the philosophy of mathematics? and (2) To what extent is a philosophy of mathematics still possible? This article offers some reflections on these questions, which have preoccupied a good many philosophers and continue to do so.

  10. Teaching secondary mathematics

    CERN Document Server

    Rock, David

    2013-01-01

    Solidly grounded in up-to-date research, theory and technology,?Teaching Secondary Mathematics?is a practical, student-friendly, and popular text for secondary mathematics methods courses. It provides clear and useful approaches for mathematics teachers, and shows how concepts typically found in a secondary mathematics curriculum can be taught in a positive and encouraging way. The thoroughly revised fourth edition combines this pragmatic approach with truly innovative and integrated technology content throughout. Synthesized content between the book and comprehensive companion websi

  11. Sixth form pure mathematics

    CERN Document Server

    Plumpton, C

    1968-01-01

    Sixth Form Pure Mathematics, Volume 1, Second Edition, is the first of a series of volumes on Pure Mathematics and Theoretical Mechanics for Sixth Form students whose aim is entrance into British and Commonwealth Universities or Technical Colleges. A knowledge of Pure Mathematics up to G.C.E. O-level is assumed and the subject is developed by a concentric treatment in which each new topic is used to illustrate ideas already treated. The major topics of Algebra, Calculus, Coordinate Geometry, and Trigonometry are developed together. This volume covers most of the Pure Mathematics required for t

  12. Journal of applied mathematics

    National Research Council Canada - National Science Library

    2001-01-01

    .... Subject areas include (but are not limited to) approximation theory, computing, control and systems, differential equations and dynamical systems, financial mathematics, fluid mechanics and solid mechanics, fractional calculus...

  13. Mathematics, Mathematicians, and Desire

    OpenAIRE

    Roodal Persad, Veda

    2014-01-01

    This thesis is about mapping the landscape of engagement with mathematics, including elucidating aspects of who we are, as human beings, when we do mathematics and of what mathematics calls us to do if we are to engage with it. Using the concept of desire in the psychoanalytic theory of Jacques Lacan and the forms of desire as elucidated by the Lacanian theorist, Mark Bracher, I seek to find out what the mathematical encounter takes (the demands and costs) and what it gives (the offers and re...

  14. Mathematics in civilization

    CERN Document Server

    Resnikoff, Howard L

    2015-01-01

    Space flight, computers, lasers, and information technology ― these are but a few examples of the spectacular growth, development, and far-reaching applications of mathematics. But what of the field's past? Upon which intellectual milestones were the foundations of modern mathematics constructed? How has our comprehension of the physical universe, language, and the nature of thought itself been influenced and informed by the developments of mathematics through the ages?This lucid presentation examines how mathematics shaped and was shaped by the course of human events. In a format suited to co

  15. Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics

    Science.gov (United States)

    Wang, Youjun

    2009-01-01

    In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…

  16. Using Mathematics Literature with Prospective Secondary Mathematics Teachers

    Science.gov (United States)

    Jett, Christopher C.

    2014-01-01

    Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

  17. On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers

    Science.gov (United States)

    Cai, Jinfa; Ding, Meixia

    2017-01-01

    Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…

  18. Finite Mathematics and Discrete Mathematics: Is There a Difference?

    Science.gov (United States)

    Johnson, Marvin L.

    Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

  19. Ethnomathematics study: uncovering units of length, area, and volume in Kampung Naga Society

    Science.gov (United States)

    Septianawati, T.; Turmudi; Puspita, E.

    2017-02-01

    During this time, mathematics is considered as something neutral and not associated with culture. It can be seen from mathematics learning in the school which adopt many of foreign mathematics learning are considered more advanced (western). In fact, Indonesia is a rich country in cultural diversity. In the cultural activities, there are mathematical ideas that were considered a important thing in the mathematics learning. A study that examines the idea or mathematical practices in a variety of cultural activities are known as ethnomathematics. In Indonesia, there are some ethnic maintain their ancestral traditions, one of them is Kampung Naga. Therefore, this study was conducted in Kampung Naga. This study aims to uncover units of length, area, and volume used by Kampung Naga society. This study used a qualitative approach and ethnography methods. In this research, data collection is done through the principles of ethnography such as observation, interviews, documentation, and field notes. The results of this study are units of length, area, and volume used by Kampung Naga society and its conversion into standard units. This research is expected to give information to the public that mathematics has a relationship with culture and become recommendation to mathematics curriculum in Indonesia.

  20. The Relation Between Inattentive and Hyperactive/Impulsive Behaviors and Early Mathematics Skills.

    Science.gov (United States)

    Sims, Darcey M; Purpura, David J; Lonigan, Christopher J

    2016-08-01

    Despite strong evidence that inattentive and hyperactive/impulsive behaviors are associated with mathematical difficulties in school-age children, little research has been conducted to examine the link between these constructs before the start of formal education. The purpose of this study was to examine how different manifestations of inattentive and hyperactive/impulsive behaviors, as measured by different assessment tools, are related to early mathematics skills in preschoolers. Eighty-two preschool children completed a measure of early mathematics and the Continuous Performance Test (CPT). Teachers rated children's behaviors using the Conners' Teacher Rating Scale-15 Item. Sixty-five of these children completed mathematics assessments 1 year later. Teacher ratings of inattention were uniquely related to concurrent early mathematics skills, whereas CPT errors were uniquely predictive of early mathematics skills 1 year later. Findings have implications for the understanding and assessment of behavior problems that are associated with early mathematics difficulties. © The Author(s) 2012.

  1. Neurocognitive mechanisms of mathematical giftedness: A literature review.

    Science.gov (United States)

    Zhang, Li; Gan, John Q; Wang, Haixian

    2017-01-01

    Mathematically gifted children/adolescents have demonstrated exceptional abilities and traits in logical reasoning, mental imagery, and creative thinking. In the field of cognitive neuroscience, the past studies on mathematically gifted brains have concentrated on investigating event-related brain activation regions, cerebral laterality of cognitive functions, functional specialization that is uniquely dedicated for specific cognitive purposes, and functional interactions among discrete brain regions. From structural and functional perspectives, these studies have witnessed both "general" and "unique" neural characteristics of mathematically gifted brains. In this article, the theoretical background, empirical studies, and neurocognitive mechanisms of mathematically gifted children/adolescents are reviewed. Based on the integration of the findings, some potential directions for the future research are identified and discussed.

  2. [Length growth of tunny (Thunnus thynnus) according to Sella's data].

    Science.gov (United States)

    Sager, G; Sammler, R

    1982-01-01

    The dates of Sella (1929) for the length of the mediterranean tunny (Thunnus thynnus) already treated by Krüger (1973) are taken as a basis for mathematical approximations by 19 growth functions. For this purpose some functions had to be modified to allow for a non-horizontal tangent at the beginning. As the available length values cease with 14 years of age, there is much room for the theoretical final length giving a good insight into the characteristics of the different approximations. Surprisingly the functions with final growth time yield values with only small deviations from each other except for one calculation thus hinting to a theoretical growth duration of about 25 +/- 2 years.

  3. Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching

    OpenAIRE

    Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

    2017-01-01

    The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...

  4. Proof and knowledge in mathematics

    CERN Document Server

    Detlefsen, Michael

    2005-01-01

    These questions arise from any attempt to discover an epistemology for mathematics. This collection of essays considers various questions concerning the nature of justification in mathematics and possible sources of that justification. Among these are the question of whether mathematical justification is a priori or a posteriori in character, whether logical and mathematical differ, and if formalization plays a significant role in mathematical justification,

  5. The mathematics companion mathematical methods for physicists and engineers

    CERN Document Server

    Fischer-Cripps, Anthony C

    2014-01-01

    Part 1 Essential Mathematics: Basic mathematics. Differentiation. Integration. Exponentials and logarithms. Hyperbolic functions. Infinite series. Part 2 Advance Mathematics: Ordinary differential equations. Laplace transforms. Vector analysis. Partial derivatives. Multiple integrals. Fourier series. Special functions. Partial differential equations.

  6. Mathematics in Ancient India

    Indian Academy of Sciences (India)

    In this series of articles, we intend to have a glimpse of some of the landmarks in ancient In- dian mathematics with special emphasis on num- ber theory. This issue features a brief overview of some of the high peaks of mathematics in an- cient India. In the next part we shall describe. Aryabhata's general solution in integers ...

  7. Mathematics. [SITE 2002 Section].

    Science.gov (United States)

    Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.

    This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2002 conference: (1) "Teachers' Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship" (Mara Alagic); (2) "A Fractal Is a Pattern in Your Neighborhood" (Craig N. Bach); (3)…

  8. Dyslexia, Dyspraxia and Mathematics.

    Science.gov (United States)

    Yeo, Dorian

    This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…

  9. Pursuing Mathematics in India

    Indian Academy of Sciences (India)

    Admin

    2012-09-07

    Sep 7, 2012 ... they have to do to bring out their full potential and ii) they establish a rapport with other participants and teachers which helps them shape their career in mathematics. For details on venues, dates and other information please look into: http://www.mtts.org.in/. Advanced Training in Mathematics (ATM) ...

  10. Advanced Mathematical Thinking

    Science.gov (United States)

    Dubinsky, Ed; McDonald, Michael A.; Edwards, Barbara S.

    2005-01-01

    In this article we propose the following definition for advanced mathematical thinking: Thinking that requires deductive and rigorous reasoning about mathematical notions that are not entirely accessible to us through our five senses. We argue that this definition is not necessarily tied to a particular kind of educational experience; nor is it…

  11. Mathematical analysis in India

    Indian Academy of Sciences (India)

    Mathematics being too vast a canvas, this writing has been broken down further into sub-disciplines. More speci- fically, regarding work in mathematical analysis, three people – namely Alladi Sitaram, V S Sunder and M Vanninathan – were entrusted with the task of coming up with something representative, subject to some ...

  12. Mathematics of Risk Taking

    Indian Academy of Sciences (India)

    https://www.ias.ac.in/article/fulltext/reso/014/01/0066-0079. Keywords. Investor; risk taking; fair game; martingale; random walk; gambling; population. Author Affiliations. K B Athreya1 2 M G Nadkarni3. Department of Mathematics Iowa State University, Ames, Iowa; I M I, Department of Mathematics, Indian Institute of Science, ...

  13. Mathematics for computer graphics

    CERN Document Server

    Vince, John

    2006-01-01

    Helps you understand the mathematical ideas used in computer animation, virtual reality, CAD, and other areas of computer graphics. This work also helps you to rediscover the mathematical techniques required to solve problems and design computer programs for computer graphic applications

  14. Elementary Mathematics Leaders

    Science.gov (United States)

    Fennell, Francis; Kobett, Beth McCord; Wray, Jonathan A.

    2013-01-01

    Elementary school mathematics leaders often come to the realization that their position, however titled and determined, although dedicated to addressing needs in math teaching and learning, also entails and directly involves leadership. Elementary school math specialists/instructional leaders (referenced here as elementary mathematics leaders, or…

  15. Problems for Computer Mathematics.

    Science.gov (United States)

    Allison, Ronald; And Others

    This booklet contains some 80 problems in mathematics suitable for computer solution. The problems range from very simple to complex. Problems have been included from most mathematic disciplines, including number theory, analytical geometry, probability and statistics, trigonometry, equations, and sequence and limits. For the most part these…

  16. Mathematics in Ancient India

    Indian Academy of Sciences (India)

    SERIES I ARTICLE. Mathematics in Ancient India. 3. Brahmagupta's Lemma: The Samasabhavana. Amartya Kumar Dutta is an Associate Professor of. Mathematics at the. Indian Statistical. Institute, Kolkata. His research interest is in commutative algebra. Part 1, An overview, Reso- nance, VoL7, No.4, pp.4-19,. 2002. Part 2.

  17. History of Mathematics

    DEFF Research Database (Denmark)

    Hansen, Vagn Lundsgaard; Gray, Jeremy

    Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO.......Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO....

  18. Mathematics Teaching and Inclusion

    DEFF Research Database (Denmark)

    This volume contains the proceedings of the 3rd Nordic Research Conference on Special Needs Education in Mathematics, which took place in Rebild organised by Aalborg University in November 23-25, 2005. The theme of the conference was Mathematics Education and Inclusion. The conference theme...

  19. Archives: Mathematics Connection

    African Journals Online (AJOL)

    Items 1 - 9 of 9 ... Archives: Mathematics Connection. Journal Home > Archives: Mathematics Connection. Log in or Register to get access to full text downloads. Username, Password, Remember me, or Register · Journal Home · ABOUT THIS JOURNAL · Advanced Search · Current Issue · Archives. 1 - 9 of 9 Items. 2011 ...

  20. Revisiting Mathematics Manipulative Materials

    Science.gov (United States)

    Swan, Paul; Marshall, Linda

    2010-01-01

    It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics…

  1. Mathematical Graphic Organizers

    Science.gov (United States)

    Zollman, Alan

    2009-01-01

    As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…

  2. Proceedings - Mathematical Sciences

    Indian Academy of Sciences (India)

    21

    School of Mathematical Sciences,. Universiti Sains Malaysia,. 11800 USM, Malaysia. andy@usm.my. Wen Chean Teh†. School of Mathematical Sciences, ... ones, been met with failure thus far. (Z,−) is a good example of an algebraic system not too remote from a semigroup that turns out not to be a Ramsey algebra. We are ...

  3. CLASSICS On Teaching Mathematics

    Indian Academy of Sciences (India)

    Nowhere was this tradition stronger than in France, and he has especially harsh words for its influence on education. Nevertheless, one must remember that he used many results from this form of mathematics, even contributed to it, and was honoured by the French mathematical community with a lifetime professorship!

  4. Mathematical Education for Geographers

    Science.gov (United States)

    Wilson, Alan

    1978-01-01

    Outlines mathematical topics of use to college geography students identifies teaching methods for mathematical techniques in geography at the University of Leeds; and discusses problem of providing students with a framework for synthesizing all content of geography education. For journal availability, see SO 506 593. (Author/AV)

  5. What is mathematics?

    DEFF Research Database (Denmark)

    Høyrup, Jens

    2017-01-01

    The paper discusses the question “What is mathematics?” from a point of view inspired by anthropology. In this perspective, the character of mathematical thinking and argument is strongly affected - almost essentially determined, indeed - by the dynamics of the specific social, mostly professional...

  6. Computer Aided Mathematics

    DEFF Research Database (Denmark)

    Sinclair, Robert

    1998-01-01

    Course notes of a PhD course held in 1998. The central idea is to introduce students to computational mathematics using object oriented programming in C++.......Course notes of a PhD course held in 1998. The central idea is to introduce students to computational mathematics using object oriented programming in C++....

  7. Mathematics and computing

    Indian Academy of Sciences (India)

    The interaction of computing and mathematics is of course a very longstanding one in that, at some elementary level the words were more or less synonymous. However, mathematics has naturally focussed on abstract concepts and ideas while many scientific fields need and perform much computation. With fast modern ...

  8. Refresher Course in Mathematics

    Indian Academy of Sciences (India)

    Applications are invited. from University/College teachers and Researchers interested in participating in the Academy Refresher Course on Mathematical Analysis and Applications to be held at Departme~t of Mathematics, Berhampur University, Berhampur from December. 1-13, 2003. Prof. V Kannan of University of ...

  9. Experimenting with Mathematical Biology

    Science.gov (United States)

    Sanft, Rebecca; Walter, Anne

    2016-01-01

    St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The lab classes required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs…

  10. Mathematics and Sports

    Indian Academy of Sciences (India)

    nal stereotype of a mathematician is a highly nonathletic, myopic individual with his head buried in books. Reality, of course, is other- wise. One finds many who are proficient in both mathematics and sports, but even so, rarely there's someone who combines the two. Mathematics in sports? Certainly. Tendulkar does not ...

  11. Is This Mathematical?

    Science.gov (United States)

    Dodd, Jennifer

    2010-01-01

    In this article, the author reports on the findings of her research on what her Year 10 students consider to be "mathematical." The class contains thirteen students who will all sit the higher tier IGCSE next year. The author found out that the students considered things she told them to have a higher mathematical status than work they…

  12. Classical and Weak Solutions for Two Models in Mathematical Finance

    Science.gov (United States)

    Gyulov, Tihomir B.; Valkov, Radoslav L.

    2011-12-01

    We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.

  13. Non-unique factorizations algebraic, combinatorial and analytic theory

    CERN Document Server

    Geroldinger, Alfred

    2006-01-01

    From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory offers a look at the present state of the theory in a single, unified resource.Taking a broad look at the algebraic, combinatorial, and analytic fundamentals, this book derives factorization results and applies them in concrete arithmetical situations using appropriate transfer principles. It begins with a basic introduction that can be understood with knowledge of standard basic algebra. The authors then move to the algebraic theory of monoids, arithmetic theory of monoids, the structure of sets of lengths, additive group theory, arithmetical invariants, and the arithmetic of Krull monoids. They also provide a s...

  14. Rethinking the mathematics curriculum

    CERN Document Server

    Hoyles, Celia; Woodhouse, Geoffrey

    1998-01-01

    At a time when political interest in mathematics education is at its highest, this book demonstrates that the issues are far from straightforward. A wide range of international contributors address such questions as: What is mathematics, and what is it for? What skills does mathematics education need to provide as technology advances? What are the implications for teacher education? What can we learn from past attempts to change the mathematics curriculum? Rethinking the Mathematics Curriculum offers stimulating discussions, showing much is to be learnt from the differences in culture, national expectations, and political restraints revealed in the book. This accessible book will be of particular interest to policy makers, curriculum developers, educators, researchers and employers as well as the general reader.

  15. Developing mathematical modelling competence

    DEFF Research Database (Denmark)

    Blomhøj, Morten; Jensen, Tomas Højgaard

    2003-01-01

    In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....

  16. Mathematics of aperiodic order

    CERN Document Server

    Lenz, Daniel; Savinien, Jean

    2015-01-01

    What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomolog...

  17. Canadian Mathematical Congress

    CERN Document Server

    1977-01-01

    For two weeks in August, 1975 more than 140 mathematicians and other scientists gathered at the Universite de Sherbrooke. The occasion was the 15th Biennial Seminar of the Canadian Mathematical Congress, entitled Mathematics and the Life Sciences. Participants in this inter­ disciplinary gathering included researchers and graduate students in mathematics, seven different areas of biological science, physics, chemistry and medical science. Geographically, those present came from the United States and the United Kingdom as well as from academic departments and government agencies scattered across Canada. In choosing this particular interdisciplinary topic the programme committee had two chief objectives. These were to promote Canadian research in mathematical problems of the life sciences, and to encourage co-operation and exchanges between mathematical scientists" biologists and medical re­ searchers. To accomplish these objective the committee assembled a stim­ ulating programme of lectures and talks. Six ...

  18. Mathematics in everyday life

    CERN Document Server

    Haigh, John

    2016-01-01

    How does mathematics impact everyday events? The purpose of this book is to show a range of examples where mathematics can be seen at work in everyday life. From money (APR, mortgage repayments, personal finance), simple first and second order ODEs, sport and games (tennis, rugby, athletics, darts, tournament design, soccer, snooker), business (stock control, linear programming, check digits, promotion policies, investment), the social sciences (voting methods, Simpson’s Paradox, drug testing, measurements of inequality) to TV game shows and even gambling (lotteries, roulette, poker, horse racing), the mathematics behind commonplace events is explored. Fully worked examples illustrate the ideas discussed and each chapter ends with a collection of exercises. Everyday Mathematics supports other first year modules by giving students extra practice in working with calculus, linear algebra, geometry, trigonometry and probability. Secondary/high school level mathematics is all that is required for students to und...

  19. Advanced engineering mathematics

    CERN Document Server

    Jeffrey, Alan

    2001-01-01

    Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) th...

  20. Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

    Science.gov (United States)

    Hebert, Michael A.; Powell, Sarah R.

    2016-01-01

    Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…

  1. Neurodevelopmental pathways to preterm children's specific and general mathematic abilities.

    Science.gov (United States)

    Jaekel, Julia; Bartmann, Peter; Schneider, Wolfgang; Wolke, Dieter

    2014-10-01

    Preterm children have problems with mathematics but knowledge about the predictors of specific mathematic abilities in preterm populations is scarce. This study investigated neurodevelopmental pathways to children's general and specific mathematic abilities across the full gestational age range. Prospective geographically defined longitudinal investigation in Germany. 947 children across the full gestational age range (23-41 weeks). Outcome measures. At 8 years, children's cognitive and mathematic abilities were measured and residuals of a regression predicting mathematic scores by IQ were used to identify specific mathematic abilities. Neurodevelopmental cascade models revealed that adverse effects of preterm birth on mathematic abilities were mediated by neonatal risk. Specific mathematic abilities were uniquely predicted by the duration of hospitalization and ventilation. Prolonged neonatal medical treatment and, in particular, mechanical ventilation may lead to specific impairments in mathematic tasks. These findings have implications for the mode of respiratory support in neonates, routine follow-up and intervention planning as well as research about brain reorganization after preterm birth. Copyright © 2014. Published by Elsevier Ireland Ltd.

  2. Ocular hemodynamics and glaucoma: the role of mathematical modeling.

    Science.gov (United States)

    Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

    2013-01-01

    To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

  3. A practical course in differential equations and mathematical modeling

    CERN Document Server

    Ibragimov , Nail H

    2009-01-01

    A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame

  4. What We Think We Know About Maya Mathematics and Astronomy

    Science.gov (United States)

    Van Stone, M.

    2016-01-01

    In most cultures, mathematics and astronomy are obscure and arcane. Not so to the ancient Maya. Despite what we consider technological “deficiencies”—they lacked both metal tools and the wheel—their public inscriptions paid uniquely sophisticated attention to these sciences. At any given monument, fully half the text is devoted to situating events in time, particularly specifying the precise number of days between events, whether historical or mythological. Often these intervals have numerological significance, and many are precise multiples of the periodicities of heavenly bodies. The Maya apparently were fully aware of the exact length of the tropical year, the sidereal year, the cycles of Venus, and eclipses; and there is evidence that they even celebrated events reflecting the 26,000-year precession cycle. However, Maya illuminati had an agenda quite alien to our way of thinking. Clues to their knowledge are arcane, rare, and often difficult for us to recognize with eyes clouded by our modern worldview. The body of work left to us consists of just a few tantalizing sherds of a once-rich and diverse astromythological tradition. Moreover, there was no single pan-Mayan mythos. An astronomical alignment seen repeatedly in one city will be completely absent in others. Each city-state emphasized specific and often unique features, and they often contradict one another. But we soldier on. The diversity we find so frustrating is simply the fine structure of their worldview. Intellectual historians have for too long been, like Procrustes, trying to force all Maya science and religion into a single universal straitjacket.

  5. Unique Physician Identification Number (UPIN) Directory

    Data.gov (United States)

    U.S. Department of Health & Human Services — The Unique Physician Identification Number (UPIN) Directory contains selected information on physicians, doctors of Osteopathy, limited licensed practitioners and...

  6. CEBAF Upgrade Bunch Length Measurements

    Energy Technology Data Exchange (ETDEWEB)

    Ahmad, Mahmoud [Old Dominion Univ., Norfolk, VA (United States)

    2016-05-01

    Many accelerators use short electron bunches and measuring the bunch length is important for efficient operations. CEBAF needs a suitable bunch length because bunches that are too long will result in beam interruption to the halls due to excessive energy spread and beam loss. In this work, bunch length is measured by invasive and non-invasive techniques at different beam energies. Two new measurement techniques have been commissioned; a harmonic cavity showed good results compared to expectations from simulation, and a real time interferometer is commissioned and first checkouts were performed. Three other techniques were used for measurements and comparison purposes without modifying the old procedures. Two of them can be used when the beam is not compressed longitudinally while the other one, the synchrotron light monitor, can be used with compressed or uncompressed beam.

  7. Continuously variable focal length lens

    Science.gov (United States)

    Adams, Bernhard W; Chollet, Matthieu C

    2013-12-17

    A material preferably in crystal form having a low atomic number such as beryllium (Z=4) provides for the focusing of x-rays in a continuously variable manner. The material is provided with plural spaced curvilinear, optically matched slots and/or recesses through which an x-ray beam is directed. The focal length of the material may be decreased or increased by increasing or decreasing, respectively, the number of slots (or recesses) through which the x-ray beam is directed, while fine tuning of the focal length is accomplished by rotation of the material so as to change the path length of the x-ray beam through the aligned cylindrical slows. X-ray analysis of a fixed point in a solid material may be performed by scanning the energy of the x-ray beam while rotating the material to maintain the beam's focal point at a fixed point in the specimen undergoing analysis.

  8. Mathematics as verbal behavior.

    Science.gov (United States)

    Marr, M Jackson

    2015-04-01

    "Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. Copyright © 2015 Elsevier B.V. All rights reserved.

  9. Overview of bunch length measurements

    International Nuclear Information System (INIS)

    Lumpkin, A. H.

    1999-01-01

    An overview of particle and photon beam bunch length measurements is presented in the context of free-electron laser (FEL) challenges. Particle-beam peak current is a critical factor in obtaining adequate FEL gain for both oscillators and self-amplified spontaneous emission (SASE) devices. Since measurement of charge is a standard measurement, the bunch length becomes the key issue for ultrashort bunches. Both time-domain and frequency-domain techniques are presented in the context of using electromagnetic radiation over eight orders of magnitude in wavelength. In addition, the measurement of microbunching in a micropulse is addressed

  10. Kondo length in bosonic lattices

    Science.gov (United States)

    Giuliano, Domenico; Sodano, Pasquale; Trombettoni, Andrea

    2017-09-01

    Motivated by the fact that the low-energy properties of the Kondo model can be effectively simulated in spin chains, we study the realization of the effect with bond impurities in ultracold bosonic lattices at half filling. After presenting a discussion of the effective theory and of the mapping of the bosonic chain onto a lattice spin Hamiltonian, we provide estimates for the Kondo length as a function of the parameters of the bosonic model. We point out that the Kondo length can be extracted from the integrated real-space correlation functions, which are experimentally accessible quantities in experiments with cold atoms.

  11. The determinants of IPO firm prospectus length in Africa

    Directory of Open Access Journals (Sweden)

    Bruce Hearn

    2013-04-01

    Full Text Available This paper studies the differential impact on IPO firm listing prospectus length from increasing proportions of foreign directors from civil as opposed to common law societies and social elites. Using a unique hand-collected and comprehensive sample of 165 IPO firms from across 18 African countries the evidence suggests that increasing proportions of directors from civil code law countries is associated with shorter prospectuses while the opposite is true for their common law counterparts. Furthermore increasing proportions of directors drawn from elevated social positions in indigenous society is related to increasing prospectus length in North Africa while being insignificant in SSA.

  12. Mathematical methods for physicists

    CERN Document Server

    Arfken, George B

    1985-01-01

    Mathematical Methods for Physicists, Third Edition provides an advanced undergraduate and beginning graduate study in physical science, focusing on the mathematics of theoretical physics. This edition includes sections on the non-Cartesian tensors, dispersion theory, first-order differential equations, numerical application of Chebyshev polynomials, the fast Fourier transform, and transfer functions. Many of the physical examples provided in this book, which are used to illustrate the applications of mathematics, are taken from the fields of electromagnetic theory and quantum mechanics. The He

  13. Equations of mathematical physics

    CERN Document Server

    Tikhonov, A N

    2011-01-01

    Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri

  14. Logic in elementary mathematics

    CERN Document Server

    Exner, Robert M

    2011-01-01

    This applications-related introductory treatment explores facets of modern symbolic logic useful in the exposition of elementary mathematics. The authors convey the material in a manner accessible to those trained in standard elementary mathematics but lacking any formal background in logic. Topics include the statement calculus, proof and demonstration, abstract mathematical systems, and the restricted predicate calculus. The final chapter draws upon the methods of logical reasoning covered in previous chapters to develop solutions of linear and quadratic equations, definitions of order and

  15. First aid in mathematics

    CERN Document Server

    Sulley, Robert

    2014-01-01

    Achieve the best possible standard with this bestselling book of traditional practice and guidance - now in colour!. First Aid in Mathematics provides all the help and support needed for learning and practising Mathematics. It offers comprehensive coverage of core mathematical topics in clear and accessible language. It is suitable for both native English speakers and students of English as a second language and can be used in class, or as a reference and revision book. - Develops a strong basis of understanding with core topics covered in clear and accessible language. - Improves student's ab

  16. Mathematical modelling techniques

    CERN Document Server

    Aris, Rutherford

    1995-01-01

    ""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode

  17. Contemporary mathematical physics

    CERN Document Server

    Dobrushin, R L; Shubin, M A; Vershik, Anatoly M

    1996-01-01

    This first of a two-volume collection is a celebration of the scientific heritage of F. A. Berezin (1931-1980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization, and Grassmannian analysis ("supermathematics"). Collected here are papers by his many of his colleagues and others who worked in related areas, representing a wide spectrum of topics

  18. Applied impulsive mathematical models

    CERN Document Server

    Stamova, Ivanka

    2016-01-01

    Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.

  19. Mathematics year 5 answers

    CERN Document Server

    Alexander, Serena; Poggo, Tammy

    2014-01-01

    Features the complete set of answers to the exercises in Mathematics Year 5, to save you time marking work and enable you to identify areas requiring further attention. The book includes diagrams and workings where necessary, to ensure pupils understand how to present their answers. Also available from Galore Park www.galorepark.co.uk :. - Mathematics Year 5. - Mathematics Year 6. - 11+ Maths Practice Exercises. - 11+ Maths Revision Guide. - 10-Minute Maths Tests Workbook Age 8-10. - 10-Minute Maths Tests Workbook Age 9-11. - Mental Arithmetic Workbook Age 8-10. - Mental Arithmetic Workbook Ag

  20. The Mathematics of Knots

    CERN Document Server

    Banagl, Markus

    2011-01-01

    The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested

  1. Constructivism in mathematics

    CERN Document Server

    Troelstra, AS

    1988-01-01

    Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras.The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The te

  2. Mentoring in mathematics education

    CERN Document Server

    Hyde, Rosalyn

    2013-01-01

    Designed to support both teachers and university-based tutors in mentoring pre-service and newly qualified mathematics teachers at both primary and secondary levels, Mentoring Mathematics Teachers offers straightforward practical advice that is based on practice, underpinned by research, and geared specifically towards this challenging subject area.Developed by members of The Association of Mathematics Education Teachers, the authors draw upon the most up-to-date research and theory to provide evidence-based practical guidance. Themes covered include:

  3. The Greatest Mathematical Discovery?

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, David H.; Borwein, Jonathan M.

    2010-05-12

    What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.

  4. Makers of mathematics

    CERN Document Server

    Hollingdale, S. H

    1989-01-01

    Fascinating and highly readable, this book recounts the history of mathematics as revealed in the lives and writings of the most distinguished practitioners of the art: Archimedes, Descartes, Fermat, Pascal, Newton, Leibniz, Euler, Gauss, Hamilton, Einstein, and many more. Author Stuart Hollingdale introduces and explains the roles of these gifted and often colorful figures in the development of mathematics as well as the ways in which their work relates to mathematics as a whole.Although the emphasis in this absorbing survey is primarily biographical, Hollingdale also discusses major historic

  5. Fundamentals of university mathematics

    CERN Document Server

    McGregor, C M; Stothers, W W

    2010-01-01

    The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differe

  6. Constructing mathematical knowledge

    CERN Document Server

    Ernest, Paul

    2012-01-01

    This book provides a panorama of complimentary and forward looking perspectives on the learning of mathematics and epistemology from some of the leading contributors to the field. It explores constructivist and social theories of learning, and discusses the role of the computer in the light of these theories. It brings analyses from psychoanalysis, Hermeneutics and other perspectives to bear on the issues of mathematics and learning. It enquires into the nature of enquiry itself, and an important emergent theme is the role of language. Finally it relates the history of mathematics to its te

  7. Mathematization in introductory physics

    Science.gov (United States)

    Brahmia, Suzanne M.

    Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in

  8. Mathematics of relativity

    CERN Document Server

    Rainich, George Yuri

    1950-01-01

    Based on the ideas of Einstein and Minkowski, this concise treatment is derived from the author's many years of teaching the mathematics of relativity at the University of Michigan. Geared toward advanced undergraduates and graduate students of physics, the text covers old physics, new geometry, special relativity, curved space, and general relativity. Beginning with a discussion of the inverse square law in terms of simple calculus, the treatment gradually introduces increasingly complicated situations and more sophisticated mathematical tools. Changes in fundamental concepts, which characterize relativity theory, and the refinements of mathematical technique are incorporated as necessary. The presentation thus offers an easier approach without sacrifice of rigor.

  9. Mathematics and biology

    International Nuclear Information System (INIS)

    Khan, I.A.

    1991-06-01

    In India and in so many other countries, the science students are generally separated into two main streams: one opting mathematical sciences, the other studying biological sciences. As a result, medicos and biologists have no adequate knowledge of mathematical sciences. It causes a great drawback to them in order to be perfect and updated in their profession, due to the tremendous application of mathematics in bio-sciences, now-a-days. The main aim of this article is to emphasize on the need of the time to produce the mathematico-biologists in abundance for the better service of mankind. (author)

  10. Higher engineering mathematics

    CERN Document Server

    John Bird

    2014-01-01

    A practical introduction to the core mathematics principles required at higher engineering levelJohn Bird's approach to mathematics, based on numerous worked examples and interactive problems, is ideal for vocational students that require an advanced textbook.Theory is kept to a minimum, with the emphasis firmly placed on problem-solving skills, making this a thoroughly practical introduction to the advanced mathematics engineering that students need to master. The extensive and thorough topic coverage makes this an ideal text for upper level vocational courses. Now in

  11. Constant-Length Random Substitutions and Gibbs Measures

    Science.gov (United States)

    Maldonado, C.; Trejo-Valencia, L.; Ugalde, E.

    2018-04-01

    This work is devoted to the study of processes generated by random substitutions over a finite alphabet. We prove, under mild conditions on the substitution's rule, the existence of a unique process which remains invariant under the substitution, and which exhibits a polynomial decay of correlations. For constant-length substitutions, we go further by proving that the invariant state is precisely a Gibbs measure which can be obtained as the projective limit of its natural Markovian approximations. We end up the paper by studying a class of substitutions whose invariant state is the unique Gibbs measure for a hierarchical two-body interaction.

  12. The elementary school teachers’ ability in the length measurement

    Science.gov (United States)

    Julie, Hongki

    2017-09-01

    The purpose of this study was to describe the elementary school teachers' mathematical ability (1) to develop students’ activities which constructed longer than, shorter than, and as long as concepts, (2) to develop students’ activities which constructed standard unit on the length measurement, and (3) to develop a problem which used by student to construct why a conversion activity on the unit of the length was useful in the daily life after they have participated in the Realistic Mathematics Education (RME) workshops. Curry and Outhread said if teachers knew more about the growth of students’ conceptual understanding of the length, they would be better able to teach that topic [4]. Therefore, in the workshop, teachers were asked to learn more on the stages of the measurement teaching and learning process and why each stage was important. This capability was described by the results of a test which was content of four problems given to teachers after they have attended the workshop. Research subjects in this study were 14 elementary school teachers at Yogyakarta. The results of the study were as follows: (1) only four of 14 teachers who had the first ability; (2) all teachers had the second ability; and (3) all the teachers did not have the third ability.

  13. Mathematics, anxiety, and the brain.

    Science.gov (United States)

    Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

    2017-05-24

    Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.

  14. Mathematics for the liberal arts

    CERN Document Server

    Bindner, Donald; Hemmeter, Joe

    2014-01-01

    Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes workNumerous figures and diagrams as well as hundreds of worked example...

  15. Mathematical omnibus thirty lectures on classic mathematics

    CERN Document Server

    Fuchs, Dmitry; Fuchs, Dmitry

    2007-01-01

    The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an accomplished artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

  16. 77 FR 40735 - Unique Device Identification System

    Science.gov (United States)

    2012-07-10

    ... postmarket surveillance, and better security of devices through more effective detection and removal of... Drug Administration 21 CFR Parts 16, 801, 803, et al. Unique Device Identification System; Proposed..., 806, 810, 814, 820, 821, 822, and 830 [Docket No. FDA-2011-N-0090] RIN 0910-AG31 Unique Device...

  17. Uniqueness of time-independent electromagnetic fields

    DEFF Research Database (Denmark)

    Karlsson, Per W.

    1974-01-01

    As a comment on a recent paper by Steele, a more general uniqueness theorem for time-independent fields is mentioned. ©1974 American Institute of Physics......As a comment on a recent paper by Steele, a more general uniqueness theorem for time-independent fields is mentioned. ©1974 American Institute of Physics...

  18. Constructing Dense Graphs with Unique Hamiltonian Cycles

    Science.gov (United States)

    Lynch, Mark A. M.

    2012-01-01

    It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…

  19. Cyclic codes of length 2

    Indian Academy of Sciences (India)

    Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45

    [X]/〈X2m. − 1〉 are given. Cyclic codes of length 2m over the finite field Fq, of odd characteristic, are defined in terms of their generator polynomials. The exact minimum distance and the dimension of the codes are obtained. Keywords.

  20. Diet, nutrition and telomere length.

    Science.gov (United States)

    Paul, Ligi

    2011-10-01

    The ends of human chromosomes are protected by DNA-protein complexes termed telomeres, which prevent the chromosomes from fusing with each other and from being recognized as a double-strand break by DNA repair proteins. Due to the incomplete replication of linear chromosomes by DNA polymerase, telomeric DNA shortens with repeated cell divisions until the telomeres reach a critical length, at which point the cells enter senescence. Telomere length is an indicator of biological aging, and dysfunction of telomeres is linked to age-related pathologies like cardiovascular disease, Parkinson disease, Alzheimer disease and cancer. Telomere length has been shown to be positively associated with nutritional status in human and animal studies. Various nutrients influence telomere length potentially through mechanisms that reflect their role in cellular functions including inflammation, oxidative stress, DNA integrity, DNA methylation and activity of telomerase, the enzyme that adds the telomeric repeats to the ends of the newly synthesized DNA. Copyright © 2011 Elsevier Inc. All rights reserved.

  1. Fractional baud-length coding

    Directory of Open Access Journals (Sweden)

    J. Vierinen

    2011-06-01

    Full Text Available We present a novel approach for modulating radar transmissions in order to improve target range and Doppler estimation accuracy. This is achieved by using non-uniform baud lengths. With this method it is possible to increase sub-baud range-resolution of phase coded radar measurements while maintaining a narrow transmission bandwidth. We first derive target backscatter amplitude estimation error covariance matrix for arbitrary targets when estimating backscatter in amplitude domain. We define target optimality and discuss different search strategies that can be used to find well performing transmission envelopes. We give several simulated examples of the method showing that fractional baud-length coding results in smaller estimation errors than conventional uniform baud length transmission codes when estimating the target backscatter amplitude at sub-baud range resolution. We also demonstrate the method in practice by analyzing the range resolved power of a low-altitude meteor trail echo that was measured using a fractional baud-length experiment with the EISCAT UHF system.

  2. Femur length and biparietal diameter

    African Journals Online (AJOL)

    2014-12-02

    Dec 2, 2014 ... Shipp TD, Bromley B, Mascola M, Benacerraf B. Variation in fetal femur length with respect to maternal race. J Ultrasound Med 2001;20:141‑4. 25. Deter RL, Harrist RB, Birnholz JC, Hadlock FP. Quantitative Obstetrical. Ultrasonography. New York: Wiley; 1986. 26. Yeh MN, Bracero L, Reilly KB, Murtha L, ...

  3. Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication

    Science.gov (United States)

    Kaya, Defne; Aydin, Hasan

    2016-01-01

    Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…

  4. Using Mathematics in Science: Working with Your Mathematics Department

    Science.gov (United States)

    Lyon, Steve

    2014-01-01

    Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…

  5. Mathematical Intelligence and Mathematical Creativity: A Causal Relationship

    Science.gov (United States)

    Tyagi, Tarun Kumar

    2017-01-01

    This study investigated the causal relationship between mathematical creativity and mathematical intelligence. Four hundred thirty-nine 8th-grade students, age ranged from 11 to 14 years, were included in the sample of this study by random cluster technique on which mathematical creativity and Hindi adaptation of mathematical intelligence test…

  6. Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

    Science.gov (United States)

    Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

    2014-01-01

    Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

  7. Mathematics Curriculum, the Philosophy of Mathematics and its ...

    African Journals Online (AJOL)

    It is my observation that the current school mathematics curriculum in Ethiopia is not producing competent mathematics students. Many mathematicians in Ethiopia and other part of the world have often expressed grief that the majority of students do not understand mathematical concepts, or do not see why mathematical ...

  8. Beyond "Doing" Mathematics: Engaging Talented Students in Mathematically Creative Writing

    Science.gov (United States)

    Firmender, Janine M.; Dilley, Anna; Amspaugh, Christina; Field, Kathryn; LeMay, Steven; Casa, Tutita M.

    2017-01-01

    With recent increased attention to engaging students in written mathematical communication, the Elementary Mathematical Writing Task Force has recommended specific types of and purposes for mathematical writing with the ultimate goals of communicating and reasoning: Exploratory, Informative/Explanatory, Argumentative, and Mathematically Creative.…

  9. Paradoxes in mathematics

    CERN Document Server

    Farlow, Stanley J

    2014-01-01

    Students and puzzle enthusiasts will get plenty of enjoyment plus some painless mathematical instruction from 28 conundrums, including The Curve That Shook the World, Space Travel in a Wineglass, and Through Cantor's Looking Glass.

  10. Mathematics and physics

    CERN Document Server

    Manin, Yu I

    1981-01-01

    A bird's eye view of mathematics ; physical quantities, dimensions and constants : the source of numbers in physics ; a drop of milk : observer, observation, observable and unobservable ; space-time as a physical system ; action and symmetry.

  11. Mathematical analysis II

    CERN Document Server

    Canuto, Claudio

    2015-01-01

    The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, ...

  12. Applied Mathematics Seminar 1982

    International Nuclear Information System (INIS)

    1983-01-01

    This report contains the abstracts of the lectures delivered at 1982 Applied Mathematics Seminar of the DPD/LCC/CNPq and Colloquy on Applied Mathematics of LCC/CNPq. The Seminar comprised 36 conferences. Among these, 30 were presented by researchers associated to brazilian institutions, 9 of them to the LCC/CNPq, and the other 6 were given by visiting lecturers according to the following distribution: 4 from the USA, 1 from England and 1 from Venezuela. The 1981 Applied Mathematics Seminar was organized by Leon R. Sinay and Nelson do Valle Silva. The Colloquy on Applied Mathematics was held from october 1982 on, being organized by Ricardo S. Kubrusly and Leon R. Sinay. (Author) [pt

  13. Fostering Mathematical Curiosity.

    Science.gov (United States)

    Knuth, Eric J.

    2002-01-01

    Demonstrates what it might mean to engage students in problem posing and how teachers might begin to create classroom environments that encourage, develop, and foster mathematical curiosity. (Author/NB)

  14. Fundamentals of scientific mathematics

    CERN Document Server

    Owen, George E

    2003-01-01

    Offering undergraduates a solid mathematical background (and functioning equally well for independent study), this rewarding, beautifully illustrated text covers geometry and matrices, vector algebra, analytic geometry, functions, and differential and integral calculus. 1961 edition.

  15. Handbook of mathematics

    CERN Document Server

    Bronshtein, I N; Musiol, Gerhard; Mühlig, Heiner

    2015-01-01

    This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and  new paragraphs,  new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.

  16. Mathematics for operations research

    CERN Document Server

    1994-01-01

    Effective procedures for mathematical tasks in many fields: resolving linear independence, finding null spaces and factors of matrices; differentiating vectors and matrices by chain rule, many more. Techniques illustrated in examples. 1,300 problems. 1978 edition.

  17. Mathematical games, abstract games

    CERN Document Server

    Neto, Joao Pedro

    2013-01-01

    User-friendly, visually appealing collection offers both new and classic strategic board games. Includes abstract games for two and three players and mathematical games such as Nim and games on graphs.

  18. Visualization and mathematics III

    CERN Document Server

    Polthier, Konrad

    2003-01-01

    This research book on Mathematical Visualization contains state of the art presentations on visualization problems in mathematics, on fundamental mathematical research in computer graphics, and on software frameworks for the application of visualization to real-world problems. All contributions were written by leading experts in the field and peer-refereed by an international editorial team. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin. The themes of the book cover important recent developments on - Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology - Geometric Modelling - Image Based Visualization - Software Environments and Applications - Education and Communication The variety of topics makes the book a suitable resource for researchers, lecturers, and practitioners; http://www-sfb288.math.tu-berlin.de/vismath/

  19. Mathematics for physical chemistry

    CERN Document Server

    Mortimer, Robert G

    2005-01-01

    Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data.* Numerous examples and problems interspersed throughout the presentations * Each extensive chapter contains a preview, objectives, and ...

  20. Mathematical methods for physicists

    CERN Document Server

    Arfken, George B

    2005-01-01

    This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.* Updates the leading graduate-level text in mathematical physics* Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering* Focuses on problem-solving skills and offers a vast array of exercises * Clearly illustrates and proves mathematical relationsNew in the Sixth Edition:* Updated content throughout, based on users'' feedback * More advanced sections, including differential forms and the elegant forms of Maxwell''s equations* A new chapter on probability and statistics* More elementary sections have been deleted

  1. Optimization and simulation of tandem column supercritical fluid chromatography separations using column back pressure as a unique parameter.

    Science.gov (United States)

    Wang, Chunlei; Tymiak, Adrienne A; Zhang, Yingru

    2014-04-15

    Tandem column supercritical fluid chromatography (SFC) has demonstrated to be a useful technique to resolve complex mixtures by serially coupling two columns of different selectivity. The overall selectivity of a tandem column separation is the retention time weighted average of selectivity from each coupled column. Currently, the method development merely relies on extensive screenings and is often a hit-or-miss process. No attention is paid to independently adjust retention and selectivity contributions from individual columns. In this study, we show how tandem column SFC selectivity can be optimized by changing relative dimensions (length or inner diameter) of the coupled columns. Moreover, we apply column back pressure as a unique parameter for SFC optimization. Continuous tuning of tandem column SFC selectivity is illustrated through column back pressure adjustments of the upstream column, for the first time. In addition, we show how and why changing coupling order of the columns can produce dramatically different separations. Using the empirical mathematical equation derived in our previous study, we also demonstrate a simulation of tandem column separations based on a single retention time measurement on each column. The simulation compares well with experimental results and correctly predicts column order and back pressure effects on the separations. Finally, considerations on instrument and column hardware requirements are discussed.

  2. Financial Mathematics Learning

    OpenAIRE

    Pérez Briceño , Juan Carlos; Iñiguez Ortega , Andrea; León Pineda , Sergio Mauricio

    2017-01-01

    International audience; This article is part of learning in financial mathematics students who are studying at the National University of Loja. He made a slight historical review, indicating the necessary application of mathematics in the field of finance and training in this area, carried out an analysis of the current situation, conceptualizes and analyzes the importance to other subjects, a review of the most important contents and formulas it is done, so we can get to conclude why studyin...

  3. Mathematical Optimiation in Economics

    CERN Document Server

    De Finetti, Bruno

    2011-01-01

    Preface by B. de Finetti.- G.Th. Guilbaud: Les equilibres dans les modeles economiques.-H.W. Kuhn: Locational problems and mathematical programming.- M. Morishima: The multi-sectoral theory of economic growth.- B. Martos, J. Kornai: Experiments in Hungary with industry-wide and economy wide programming.- A. Prekopa: Probability distribution problems concerning stochastic programming problems.- R. Frisch: General principles and mathematical techniques of macroeconomic programming.

  4. The reality of Mathematics

    Science.gov (United States)

    Ligomenides, Panos A.

    2009-05-01

    The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.

  5. Mathematics and linguistics

    Energy Technology Data Exchange (ETDEWEB)

    Landauer, C.; Bellman, K.L.

    1996-12-31

    In this paper, we study foundational issues that we believe will help us develop a theoretically sound approach to constructing complex systems. The two theoretical approaches that have helped us understand and develop computational systems in the past are mathematics and linguistics. We describe some differences and strengths of the approaches, and propose a research program to combine the richness of linguistic reasoning with the precision of mathematics.

  6. Mathematics for electronic technology

    CERN Document Server

    Howson, D P

    1975-01-01

    Mathematics for Electronic Technology is a nine-chapter book that begins with the elucidation of the introductory concepts related to use of mathematics in electronic engineering, including differentiation, integration, partial differentiation, infinite series, vectors, vector algebra, and surface, volume and line integrals. Subsequent chapters explore the determinants, differential equations, matrix analysis, complex variable, topography, graph theory, and numerical analysis used in this field. The use of Fourier method for harmonic analysis and the Laplace transform is also described. The ma

  7. Mathematical foundations of thermodynamics

    CERN Document Server

    Giles, R; Stark, M; Ulam, S

    2013-01-01

    Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodyn

  8. Mathematics of Deep Learning

    OpenAIRE

    Vidal, Rene; Bruna, Joan; Giryes, Raja; Soatto, Stefano

    2017-01-01

    Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain elusive. This tutorial will review recent work that aims to provide a mathematical justification for several properties of deep networks, such as global optimality, geometric stability, and invariance of the learned representations.

  9. Learning higher mathematics

    CERN Document Server

    Pontrjagin, Lev Semenovič

    1984-01-01

    Lev Semenovic Pontrjagin (1908) is one of the outstanding figures in 20th century mathematics. In a long career he has made fundamental con­ tributions to many branches of mathematics, both pure and applied. He has received every honor that a grateful government can bestow. Though in no way constrained to do so, he has through the years taught mathematics courses at Moscow State University. In the year 1975 he set himself the task of writing a series of books on secondary school and beginning university mathematics. In his own words, "I wished to set forth the foundations of higher mathematics in a form that would have been accessible to myself as a lad, but making use of all my experience as a scientist and a teacher, ac­ cumulated over many years. " The present volume is a translation of the first two out of four moderately sized volumes on this theme planned by Pro­ fessor Pontrjagin. The book begins at the beginning of modern mathematics, analytic ge­ ometry in the plane and 3-dimensional space. Refin...

  10. New mathematical cuneiform texts

    CERN Document Server

    Friberg, Jöran

    2016-01-01

    This monograph presents in great detail a large number of both unpublished and previously published Babylonian mathematical texts in the cuneiform script. It is a continuation of the work A Remarkable Collection of Babylonian Mathematical Texts (Springer 2007) written by Jöran Friberg, the leading expert on Babylonian mathematics. Focussing on the big picture, Friberg explores in this book several Late Babylonian arithmetical and metro-mathematical table texts from the sites of Babylon, Uruk and Sippar, collections of mathematical exercises from four Old Babylonian sites, as well as a new text from Early Dynastic/Early Sargonic Umma, which is the oldest known collection of mathematical exercises. A table of reciprocals from the end of the third millennium BC, differing radically from well-documented but younger tables of reciprocals from the Neo-Sumerian and Old-Babylonian periods, as well as a fragment of a Neo-Sumerian clay tablet showing a new type of a labyrinth are also discussed. The material is presen...

  11. A history of mathematics

    CERN Document Server

    Boyer, Carl B

    1989-01-01

    "Boyer and Merzbach distill thousands of years of mathematics into this fascinating chronicle. From the Greeks to Godel, the mathematics is brilliant; the cast of characters is distinguished; the ebb and flow of ideas is everywhere evident. And, while tracing the development of European mathematics, the authors do not overlook the contributions of Chinese, Indian, and Arabic civilizations. Without doubt, this is--and will long remain--a classic one-volume history of mathematics and mathematicians who create it." --William Dunham Author, Journey Through Genius, The Great Theorems of Mathematics "When we read a book like A History of Mathematics, we get the picture of a mounting structure, ever taller and broader and more beautiful and magnificent--and with a foundation, moreover, that is as untainted and as functional now as it was when Thales worked out the first geometrical theorems nearly 26 centuries ago." --From the Foreword by Isaac Asimov "One of the most useful and comprehensive general introductions t...

  12. Nuclear medicine and mathematics

    International Nuclear Information System (INIS)

    Pedroso de Lima, J.J.

    1996-01-01

    The purpose of this review is not to present a comprehensive description of all the mathematical tools used in nuclear medicine, but to emphasize the importance of the mathematical method in nuclear medicine and to elucidate some of the mathematical concepts currently used. We can distinguish three different areas in which mathematical support has been offered to nuclear medicine: Physiology, methodology and data processing. Nevertheless, the boundaries between these areas can be indistinct. It is impossible in a single article to give even an idea of the extent and complexity of the procedures currently usede in nuclear medicine, such as image processing, reconstruction from projections and artificial intelligence. These disciplines do not belong to nuclear medicine: They are already branches of engineering, and my interest will reside simply in revealing a little of the elegance and the fantastic potential of these new 'allies' of nuclear medicine. In this review the mathematics of physiological interpretation and methodology are considered together in the same section. General aspects of data-processing methods, including image processing and artificial intelligence, are briefly analysed. The mathematical tools that are most often used to assist the interpretation of biological phenomena in nuclear medicine are considered; these include convolution and deconvolution methods, Fourier analysis, factorial analysis and neural networking. (orig.)

  13. EFFECT OF MATHEMATICS LEARNING ON THE DEVELOPMENT OF MATHEMATICS CREATIVITY

    OpenAIRE

    Dr. Jyoti Sharma

    2017-01-01

    The paper presents an empirical study done in Indian classrooms to understand the effect of mathematics learning experiences on the development of mathematics creativity. The study was designed in two stages, at stage I, it was planned to find out scope, practice and promotion of creative thinking in mathematics classroom; teachers’ own engagements with creative mathematical task and teachers’ attitude towards mathematics creativity. Stage II was designed to find out responses of students and...

  14. Skolem and pessimism about proof in mathematics.

    Science.gov (United States)

    Cohen, Paul J

    2005-10-15

    Attitudes towards formalization and proof have gone through large swings during the last 150 years. We sketch the development from Frege's first formalization, to the debates over intuitionism and other schools, through Hilbert's program and the decisive blow of the Gödel Incompleteness Theorem. A critical role is played by the Skolem-Lowenheim Theorem, which showed that no first-order axiom system can characterize a unique infinite model. Skolem himself regarded this as a body blow to the belief that mathematics can be reliably founded only on formal axiomatic systems. In a remarkably prescient paper, he even sketches the possibility of interesting new models for set theory itself, something later realized by the method of forcing. This is in contrast to Hilbert's belief that mathematics could resolve all its questions. We discuss the role of new axioms for set theory, questions in set theory itself, and their relevance for number theory. We then look in detail at what the methods of the predicate calculus, i.e. mathematical reasoning, really entail. The conclusion is that there is no reasonable basis for Hilbert's assumption. The vast majority of questions even in elementary number theory, of reasonable complexity, are beyond the reach of any such reasoning. Of course this cannot be proved and we present only plausibility arguments. The great success of mathematics comes from considering 'natural problems', those which are related to previous work and offer a good chance of being solved. The great glories of human reasoning, beginning with the Greek discovery of geometry, are in no way diminished by this pessimistic view. We end by wishing good health to present-day mathematics and the mathematics of many centuries to come.

  15. Internationalizing the Mathematical Finance Course

    Science.gov (United States)

    Okonkwo, Zephyrinus C.

    2017-01-01

    About the year 2000, the Department of Mathematics and Computer Science, Albany State University (ASU), Albany, Georgia, USA envisioned the need to have a comprehensive curriculum revision based on recommendations of the Conference Boards of The Mathematical Sciences, the American Mathematical Society, the Mathematical Association of American, and…

  16. Measuring Developmental Students' Mathematics Anxiety

    Science.gov (United States)

    Ding, Yanqing

    2016-01-01

    This study conducted an item-level analysis of mathematics anxiety and examined the dimensionality of mathematics anxiety in a sample of developmental mathematics students (N = 162) by Multi-dimensional Random Coefficients Multinominal Logit Model (MRCMLM). The results indicate a moderately correlated factor structure of mathematics anxiety (r =…

  17. Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

    Science.gov (United States)

    Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

    2017-01-01

    The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

  18. Assessment and realistic mathematics education

    NARCIS (Netherlands)

    Heuvel-Panhuizen, M.H.A.M. van den

    1996-01-01

    This book describes the consequences of Realistic Mathematics Education (RME) for assessing students’ understanding of mathematics in primary school. RME is the Dutch answer to the worldwide need to reform mathematics education. Changed ideas about mathematics as a school subject, its goals,

  19. Mathematical points as didactical ideas

    DEFF Research Database (Denmark)

    Mogensen, Arne

    Mathematics teaching in Denmark was recently recommended better organized in sequences with clear mathematical pedagogical goals and a focus on mathematical points. In this paper I define a mathematical point and inform on coding of transcripts in a video based Danish research study on grade 8...

  20. Mathematical Modeling: A Structured Process

    Science.gov (United States)

    Anhalt, Cynthia Oropesa; Cortez, Ricardo

    2015-01-01

    Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

  1. Celebrating Mathematics All Year 'Round

    Science.gov (United States)

    Daire, Sandra Arguelles

    2010-01-01

    Celebrating mathematics should be a yearlong event in which students in mathematics classes of all levels engage in mathematics activities and competitions that will encourage growth in mathematical knowledge, enthusiasm for the subject, and collaboration among students of different abilities and backgrounds. Pi Day and Pi Week festivities--a good…

  2. Finding Meaning in Mathematical Mnemonics

    Science.gov (United States)

    Miller, Geoffrey; Obara, Samuel

    2017-01-01

    A mathematical mnemonic is a visual cue or verbal strategy that is used to aid initial memorisation and recall of a mathematical concept or procedure. Used wisely, mathematical mnemonics can benefit students' performance and understanding. Explorations into how mathematical mnemonics work can also offer students opportunities to engage in proof…

  3. Mathematical Modeling, Simulation and Optimization for Selected Robotic Processes related to Manufacturing of Unique Concrete Elements

    DEFF Research Database (Denmark)

    Cortsen, Jens

    dobbeltkurvede armerings gitter med to samarbejdende robotter, hvor delprocesserne er bøjning, transportering og binding af ameringsstænger. Robotinstallationen er baseret på et off-line simuleringsprogram med dynamisk simulerings support for stangnedbøjning og samtidigt robot control for at reducere...

  4. Length of a Hanging Cable

    Directory of Open Access Journals (Sweden)

    Eric Costello

    2011-01-01

    Full Text Available The shape of a cable hanging under its own weight and uniform horizontal tension between two power poles is a catenary. The catenary is a curve which has an equation defined by a hyperbolic cosine function and a scaling factor. The scaling factor for power cables hanging under their own weight is equal to the horizontal tension on the cable divided by the weight of the cable. Both of these values are unknown for this problem. Newton's method was used to approximate the scaling factor and the arc length function to determine the length of the cable. A script was written using the Python programming language in order to quickly perform several iterations of Newton's method to get a good approximation for the scaling factor.

  5. Keeping disease at arm's length

    DEFF Research Database (Denmark)

    Lassen, Aske Juul

    2015-01-01

    and physical activities at the activity centre. In this way, keeping disease at arm’s length is analysed as an ambiguous health strategy. The article shows the importance of looking into how active ageing is practised, as active ageing seems to work well in the everyday life of the older people by not giving......Many older people live with a range of chronic diseases. However, these diseases do not necessarily impede an active lifestyle. In this article the author analyses the relation between the active ageing discourse and the way older people at two Danish activity centres handle disease. How does...... active ageing change everyday life with chronic disease, and how do older people combine an active life with a range of chronic diseases? The participants in the study use activities to keep their diseases at arm’s length, and this distancing of disease at the same time enables them to engage in social...

  6. TIME SERIES ANALYSIS USING A UNIQUE MODEL OF TRANSFORMATION

    Directory of Open Access Journals (Sweden)

    Goran Klepac

    2007-12-01

    Full Text Available REFII1 model is an authorial mathematical model for time series data mining. The main purpose of that model is to automate time series analysis, through a unique transformation model of time series. An advantage of this approach of time series analysis is the linkage of different methods for time series analysis, linking traditional data mining tools in time series, and constructing new algorithms for analyzing time series. It is worth mentioning that REFII model is not a closed system, which means that we have a finite set of methods. At first, this is a model for transformation of values of time series, which prepares data used by different sets of methods based on the same model of transformation in a domain of problem space. REFII model gives a new approach in time series analysis based on a unique model of transformation, which is a base for all kind of time series analysis. The advantage of REFII model is its possible application in many different areas such as finance, medicine, voice recognition, face recognition and text mining.

  7. Creativity and technical innovation: spatial ability's unique role.

    Science.gov (United States)

    Kell, Harrison J; Lubinski, David; Benbow, Camilla P; Steiger, James H

    2013-09-01

    In the late 1970s, 563 intellectually talented 13-year-olds (identified by the SAT as in the top 0.5% of ability) were assessed on spatial ability. More than 30 years later, the present study evaluated whether spatial ability provided incremental validity (beyond the SAT's mathematical and verbal reasoning subtests) for differentially predicting which of these individuals had patents and three classes of refereed publications. A two-step discriminant-function analysis revealed that the SAT subtests jointly accounted for 10.8% of the variance among these outcomes (p spatial ability was added, an additional 7.6% was accounted for--a statistically significant increase (p spatial ability has a unique role in the development of creativity, beyond the roles played by the abilities traditionally measured in educational selection, counseling, and industrial-organizational psychology. Spatial ability plays a key and unique role in structuring many important psychological phenomena and should be examined more broadly across the applied and basic psychological sciences.

  8. Systematic perspectives on diverging mathematical orientations

    Directory of Open Access Journals (Sweden)

    D.F.M. Strauss

    2005-07-01

    Full Text Available The popular view that mathematics is “objective” and “neutral” in the sense that it does not know different standpoints is contradicted by the factual state of modern mathematics. In the light of the dominant one-sided trends in the history of mathe-matics, fluctuating between arithmeticism and a geometrisation of this discipline, this article explores some provisional starting-points for a different view. This third option is explored by investigating some features of an acknowledgement of the uniqueness of number and space without neglecting the inter-aspectual connections between these two modal functions. An argument is advanced regarding the inevitability of employing analogical (or elementary basic concepts, and this perspective is articulated in terms of the theory of modal aspects. Numerical and spatial terms are discussed and eventually focused on a deepened understanding of the meaning of infinity. In addition to a brief look at the circularity present in the arithmeticist claim that mathematics could be fully arithmetised (Grünbaum, attention is also asked for the agreement between Aristotle and Cantor regarding the nature of continuity – assessed in terms of the irreducibility of the numerical and spatial aspects of reality. Finally a characterisation is given of the ontological assumpt-ions of intuitionism and axiomatic formalism.

  9. Mathematical structures for computer graphics

    CERN Document Server

    Janke, Steven J

    2014-01-01

    A comprehensive exploration of the mathematics behind the modeling and rendering of computer graphics scenes Mathematical Structures for Computer Graphics presents an accessible and intuitive approach to the mathematical ideas and techniques necessary for two- and three-dimensional computer graphics. Focusing on the significant mathematical results, the book establishes key algorithms used to build complex graphics scenes. Written for readers with various levels of mathematical background, the book develops a solid foundation for graphics techniques and fills in relevant grap

  10. Engaging Life-Sciences Students with Mathematical Models: Does Authenticity Help?

    Science.gov (United States)

    Poladian, Leon

    2013-01-01

    Compulsory mathematics service units for the life sciences present unique challenges: even students who learn some specific skills maintain a negative attitude to mathematics and do not see the relevance of the unit towards their degree. The focus on authentic content and the presentation and teaching of global or qualitative methods before…

  11. Do Advanced Mathematics Skills Predict Success in Biology and Chemistry Degrees?

    Science.gov (United States)

    Adkins, Michael; Noyes, Andrew

    2018-01-01

    The mathematical preparedness of science undergraduates has been a subject of debate for some time. This paper investigates the relationship between school mathematics attainment and degree outcomes in biology and chemistry across England, a much larger scale of analysis than has hitherto been reported in the literature. A unique dataset which…

  12. Learners' Performance in Mathematics: A Case Study of Public High Schools, South Africa

    Science.gov (United States)

    Mapaire, Lawrence

    2016-01-01

    Mathematics is fundamental to national prosperity in providing tools for understanding science, technology, engineering and economics. It is essential in public decision-making and for participation in the knowledge economy. Mathematics equips pupils with uniquely powerful ways to describe, analyse and change the world. It can stimulate moments of…

  13. UNIQUE 28 CM LONG VERMIFORM APPENDIX

    OpenAIRE

    Ravindra Kumar Boddeti; Roopa Kulkarni; Pradeep Kumar H Murudkar

    2013-01-01

    Vermiform appendix is a vestigial organ in human beings and situated at the ileocaecal junction. It opens into the caecum. It is a narrow tube of varying length. The normal, average length is about 5 cm to 10 cm. The longest vermiform appendix has been reported to be measuring about 25 cm. In the present case a long vermiform appendix was observed in female, formalin fixed, adult cadaver during the routine dissection for medical undergraduates. The Vermiform appendix was retrocaecal and exten...

  14. Tattoos and piercings: bodily expressions of uniqueness?

    Science.gov (United States)

    Tiggemann, Marika; Hopkins, Louise A

    2011-06-01

    The study aimed to investigate the motivations underlying the body modification practices of tattooing and piercing. There were 80 participants recruited from an Australian music store, who provided descriptions of their tattoos and piercings and completed measures of need for uniqueness, appearance investment and distinctive appearance investment. It was found that tattooed individuals scored significantly higher on need for uniqueness than non-tattooed individuals. Further, individuals with conventional ear piercings scored significantly lower on need for uniqueness than individuals with no piercings or with facial and body piercings. Neither appearance investment nor distinctive appearance investment differed significantly among tattoo or piercing status groups. Strength of identification with music was significantly correlated with number of tattoos, but not number of piercings. It was concluded that tattooing, but not body piercing, represents a bodily expression of uniqueness. Copyright © 2011 Elsevier Ltd. All rights reserved.

  15. Approximate Uniqueness Estimates for Singular Correlation Matrices.

    Science.gov (United States)

    Finkbeiner, C. T.; Tucker, L. R.

    1982-01-01

    The residual variance is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is presented for the case when the correlation matrix is singular. (Author/JKS)

  16. High Blood Pressure: Unique to Older Adults

    Science.gov (United States)

    ... our e-newsletter! Aging & Health A to Z High Blood Pressure Hypertension Unique to Older Adults This section provides information ... Pressure Targets are Different for Very Old Adults High blood pressure (also called hypertension) increases your chance of having ...

  17. Proceedings – Mathematical Sciences | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    Howard's conjecture, which states that in the linear instability problem of inviscid heterogeneous parallel shear flow growth rate of an arbitrary unstable wave must approach zero as the wave length decreases to zero, is established in a mathematically rigorous fashion for plane parallel heterogeneous shear flows with ...

  18. Matematica 1. Livro do Aluno (Mathematics 1. Student Workbook).

    Science.gov (United States)

    D'Alu, Maria Jose

    Matematica 1 is the first book of a mathematics program in Portuguese "designed for first graders." The book contains 15 chapters dealing with: sets, numeration, place value, numbers from 0 through 99, addition and subtraction, geometric shapes, measurements (money, time, length), fractions, word problems, and commutative and associative…

  19. Proceedings – Mathematical Sciences | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras with involution are studied. ... of an arbitrary unstable wave must approach zero as the wave length decreases to zero, is established in a mathematically rigorous fashion for plane parallel heterogeneous shear flows with ...

  20. A truly Newtonian softening length for disc simulations

    Science.gov (United States)

    Huré, J.-M.; Trova, A.

    2015-02-01

    The softened point mass model is commonly used in simulations of gaseous discs including self-gravity while the value of associated length λ remains, to some degree, controversial. This `parameter' is however fully constrained when, in a discretized disc, all fluid cells are demanded to obey Newton's law. We examine the topology of solutions in this context, focusing on cylindrical cells more or less vertically elongated. We find that not only the nominal length depends critically on the cell's shape (curvature, radial extension, height), but it is either a real or an imaginary number. Setting λ as a fraction of the local disc thickness - as usually done - is indeed not the optimal choice. We then propose a novel prescription valid irrespective of the disc properties and grid spacings. The benefit, which amounts to 2-3 more digits typically, is illustrated in a few concrete cases. A detailed mathematical analysis is in progress.

  1. Quantum kinetic Heisenberg models: a unique dynamics

    International Nuclear Information System (INIS)

    Timonen, J.; Pilling, D.J.; Bullough, R.K.

    1986-01-01

    We suggest that the dynamics Glauber embodied in his kinetic Ising model can be introduced similarly and in an apparently unique way, into the quantum statistical mechanics of the quantum-integrable models like the Heisenberg, sine-Gordon and Massive Thirring models. The latter may suggest an extension of the theory to unique kinetic Ising models in two dimensions. The kinetic repulsive bose gas which is studied in detail in the steady state seems to be a solvable kinetic model. (author)

  2. Mathematics education a spectrum of work in mathematical sciences departments

    CERN Document Server

    Hsu, Pao-sheng; Pollatsek, Harriet

    2016-01-01

    Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its val...

  3. Mathematical models for prediction of safety factors for a simply ...

    African Journals Online (AJOL)

    From the results obtained, mathematical prediction models were developed using a least square regression analysis for bending, shear and deflection modes of failure considered in the study. The results showed that the safety factors for material, dead and live load are not unique, but they are influenced by safety index ...

  4. Learning mathematics concepts in a traditional socio-culture ...

    African Journals Online (AJOL)

    Abstract. This paper argues that each culture has its unique applications of mathematical concepts. It presents this argument by showing how the Great Zimbabwe Monument that was built between the 12th and 14th century applied some geometrical concepts that some secondary school students in Zimbabwe find difficult ...

  5. The Mathematics of Charged Particles interacting with Electromagnetic Fields

    DEFF Research Database (Denmark)

    Petersen, Kim

    In this thesis, we study the mathematics used to describe systems of charged quantum mechanical particles coupled with their classical self-generated electromagnetic field. We prove the existence of a unique local in time solution to the many-body Maxwell-Schrödinger initial value problem expressed...

  6. Constraint theory multidimensional mathematical model management

    CERN Document Server

    Friedman, George J

    2017-01-01

    Packed with new material and research, this second edition of George Friedman’s bestselling Constraint Theory remains an invaluable reference for all engineers, mathematicians, and managers concerned with modeling. As in the first edition, this text analyzes the way Constraint Theory employs bipartite graphs and presents the process of locating the “kernel of constraint” trillions of times faster than brute-force approaches, determining model consistency and computational allowability. Unique in its abundance of topological pictures of the material, this book balances left- and right-brain perceptions to provide a thorough explanation of multidimensional mathematical models. Much of the extended material in this new edition also comes from Phan Phan’s PhD dissertation in 2011, titled “Expanding Constraint Theory to Determine Well-Posedness of Large Mathematical Models.” Praise for the first edition: "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory...

  7. Progress in Industrial Mathematics at ECMI 2000

    CERN Document Server

    Capasso, Vincenzo; Greco, Antonio

    2002-01-01

    The European Consortium for Mathematics in Industry (ECMI) was founded in 1986 by leading groups of mathematicians in Europe for the following scopes: i) direct involvement of mathematicians in R&D activities; ii) international cooperation at a European scale; iii) education of industrial mathematicians to meet the growing demand for such experts. ECMI 2000 shows that ECMI has offered a unique example of effective international cooperation thanks to the financial support of the European Framework programmes. In particular they have helped ECMI establishing a set of Special Interest Groups to favour interaction with industry . This volume includes minisymposia about their activities, in particular microelectronics, glass, polymers, finance, traffic, and textiles. Applied mathematicians and other professionals working in academia or industry will find the book to be a useful and stimulating source of mathematical applications related to industrial problems.

  8. A mathematical medley fifty easy pieces on mathematics

    CERN Document Server

    Szpiro, George G

    2010-01-01

    Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material. -Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years. -Marcus du Sautoy, Oxford University, author

  9. Mathematical olympiad challenges

    CERN Document Server

    Andreescu, Titu

    2000-01-01

    Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory were selected from numerous mathematical competitions and journals. An important feature of the work is the comprehensive background material provided with each grouping of problems. The problems are clustered by topic into self-contained sections with solutions provided separately. All sections start with an essay discussing basic facts and one or two representative examples. A list of carefully chosen problems follows and the reader is invited to take them on. Additionally, historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on encouraging readers to move away from routine exercises and memorized algorithms toward creative solutions to open-e...

  10. Mathematical grammar of biology

    CERN Document Server

    Yamagishi, Michel Eduardo Beleza

    2017-01-01

    This seminal, multidisciplinary book shows how mathematics can be used to study the first principles of DNA. Most importantly, it enriches the so-called “Chargaff’s grammar of biology” by providing the conceptual theoretical framework necessary to generalize Chargaff’s rules. Starting with a simple example of DNA mathematical modeling where human nucleotide frequencies are associated to the Fibonacci sequence and the Golden Ratio through an optimization problem, its breakthrough is showing that the reverse, complement and reverse-complement operators defined over oligonucleotides induce a natural set partition of DNA words of fixed-size. These equivalence classes, when organized into a matrix form, reveal hidden patterns within the DNA sequence of every living organism. Intended for undergraduate and graduate students both in mathematics and in life sciences, it is also a valuable resource for researchers interested in studying invariant genomic properties.

  11. Advances in mathematical economics

    CERN Document Server

    Yamazaki, Akira

    2005-01-01

    A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. The editorial board of this series comprises the following prominent economists and mathematicians: Managing Editors: S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.). Editors: R. Anderson (U.C. Berkeley), C. Castaing (Univ. Montpellier), F.H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeley), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J.-M. Grandmont...

  12. Mathematical methods in engineering

    CERN Document Server

    Machado, José

    2014-01-01

    This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as:  Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control,  Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications,  Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.

  13. Mathematics for sustainability

    CERN Document Server

    Roe, John; Jamshidi, Sara

    2018-01-01

    Designed for the 21st century classroom, this textbook poses, refines, and analyzes questions of sustainability in a quantitative environment. Building mathematical knowledge in the context of issues relevant to every global citizen today, this text takes an approach that empowers students of all disciplines to understand and reason with quantitative information. Whatever conclusions may be reached on a given topic, this book will prepare the reader to think critically about their own and other people’s arguments and to support them with careful, mathematical reasoning. Topics are grouped in themes of measurement, flow, connectivity, change, risk, and decision-making. Mathematical thinking is at the fore throughout, as students learn to model sustainability on local, regional, and global scales. Exercises emphasize concepts, while projects build and challenge communication skills. With no prerequisites beyond high school algebra, instructors will find this book a rich resource for engaging all majors in the...

  14. Mathematical analysis I

    CERN Document Server

    Zorich, Vladimir A

    2015-01-01

    VLADIMIR A. ZORICH is professor of mathematics at Moscow State University. His areas of specialization are analysis, conformal geometry, quasiconformal mappings, and mathematical aspects of thermodynamics. He solved the problem of global homeomorphism for space quasiconformal mappings. He holds a patent in the technology of mechanical engineering, and he is also known by his book Mathematical Analysis of Problems in the Natural Sciences . This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems...

  15. Mathematical models of morphogenesis

    Directory of Open Access Journals (Sweden)

    Dilão Rui

    2015-01-01

    Full Text Available Morphogenesis is the ensemble of phenomena that generates the form and shape of organisms. Organisms are classified according to some of its structural characteristics, to its metabolism and to its form. In particular, the empirical classification associated with the phylum concept is related with the form and shape of organisms. In the first part of this talk, we introduce the class of mathematical models associated the Turing approach to pattern formation. In the Turing approach, morphogenesis models are described by reaction-diffusion parabolic partial differential equations. Based on this formalism, we present a mathematical model describing the first two hours of development of the fruit fly Drosophila. In the second part of this talk, we present results on Pareto optimality to calibrate and validate mathematical models.

  16. Mathematics difficulties & classroom leadership

    DEFF Research Database (Denmark)

    Schmidt, Maria Christina Secher

    2016-01-01

    are presented: 1) descriptions of the teachers’ classroom leadership to include all their students in the learning community, 2) the learning community produced by stated and practiced rules for teaching and learning behavior, 3) the classroom behavior of students who experience difficulties with mathematics....... The findings suggest that the teachers’ pedagogical choices and actions support an active learning environment for students in diverse learning needs, and that the teachers practise dimensions of inclusive classroom leadership that are known to be successful for teaching mathematics to all students. Despite......This article investigates possible links between inclusion, students, for whom mathematics is extensively difficult, and classroom leadership through a case study on teaching strategies and student participation in four classrooms at two different primary schools in Denmark. Three sets of results...

  17. Basic mathematics for biochemists

    CERN Document Server

    Cornish-Bowden, Athel

    1981-01-01

    Some teachers of biochemistry think it positively beneficial for students to struggle with difficult mathematics. I do not number myself among these people, although I have derived much personal pleasure from the study of mathematics and from applying it to problems that interest me in biochemistry. On the contrary, I think that students choose courses in biochemistry out of interest in biochemistry and that they should not be encumbered with more mathematics than is absolutely required for a proper understanding of biochemistry. This of course includes physical chemistry, because a biochemist ignorant of physical chemistry is no biochemist. I have been guided by these beliefs in writing this book. I have laid heavy emphasis on those topics, such as the use of logarithms, that play an important role in biochemistry and often cause problems in teaching; I have ignored others, such as trigonometry, that one can manage without. The proper treatment of statistics has been more difficult to decide. Although it cle...

  18. Basic engineering mathematics

    CERN Document Server

    Bird, John

    2014-01-01

    Introductory mathematics written specifically for students new to engineering Now in its sixth edition, Basic Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams. John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure that readers can relate theory to practice. The extensive and thorough topic coverage makes this an ideal text for introductory level engineering courses. This title is supported by a companion website with resources for both students and lecturers, including lists of essential formulae, multiple choice tests, full solutions for all 1,600 further questions contained within the practice exercises, and biographical information on t...

  19. Engineering mathematics pocket book

    CERN Document Server

    Bird, John

    2008-01-01

    This compendium of essential formulae, definitions, tables and general information provides the mathematical information required by students, technicians, scientists and engineers in day-to-day engineering practice. A practical and versatile reference source, now in its fourth edition, the layout has been changed and the book has been streamlined to ensure the information is even more quickly and readily available - making it a handy companion on-site, in the office as well as for academic study. It also acts as a practical revision guide for those undertaking BTEC Nationals, Higher Nationals and NVQs, where engineering mathematics is an underpinning requirement of the course.All the essentials of engineering mathematics - from algebra, geometry and trigonometry to logic circuits, differential equations and probability - are covered, with clear and succinct explanations and illustrated with over 300 line drawings and 500 worked examples based in real-world application. The emphasis throughout the book is on ...

  20. Principles of mathematical modeling

    CERN Document Server

    Dym, Clive

    2004-01-01

    Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...

  1. Frontiers in mathematical biology

    CERN Document Server

    1994-01-01

    Volume 100, which is the final volume of the LNBM series serves to commemorate the acievements in two decades of this influential collection of books in mathematical biology. The contributions, by the leading mathematical biologists, survey the state of the art in the subject, and offer speculative, philosophical and critical analyses of the key issues confronting the field. The papers address fundamental issues in cell and molecular biology, organismal biology, evolutionary biology, population ecology, community and ecosystem ecology, and applied biology, plus the explicit and implicit mathematical challenges. Cross-cuttting issues involve the problem of variation among units in nonlinear systems, and the related problems of the interactions among phenomena across scales of space, time and organizational complexity.

  2. Non-unique conical and non-conical tangents to rectifiable stationary varifolds in R-4

    Czech Academy of Sciences Publication Activity Database

    Kolář, Jan

    2015-01-01

    Roč. 54, č. 2 (2015), s. 1875-1909 ISSN 0944-2669 R&D Projects: GA AV ČR IAA100190903; GA ČR(CZ) GAP201/12/0290 Institutional support: RVO:67985840 Keywords : minimal surfaces * cones * uniqueness Subject RIV: BA - General Mathematics Impact factor: 1.555, year: 2015 http://link.springer.com/article/10.1007%2Fs00526-015-0847-9

  3. Mathematics for the liberal arts

    CERN Document Server

    Brown, Jason I

    2014-01-01

    The Math in Your Life Health, Safety, and Mathematics Found in Translation The Essentials of Conversion Making Sense of Your World with Statistics Summarizing Data with a Few Good Numbers Estimating Unknowns Leading You Down the Garden Path with Statistics Visualizing with Mathematics Seeing Data A Graph Is Worth a Thousand Words Money and Risk Money - Now or Later Risk Taking and Probability The Life in Your Math! Deciding to Make the Best Decisions Making the Right Choices for You Game Theory - Coming Out on Top Making Joint Decisions Art Imitating Math The Math that Makes the Art Believing What You See (or Not) The Mathematics of Sound (and the Sound of Mathematics) The Mathematics of Listening The Mathematics of Composing Solving Musical Mysteries with MSI (Math Scene Investigations) Late Night Mathematics - Humor and Philosophy Laughing with Mathematics The Limits of Mathematics Bibliography Index Review questions appear at the end of each chapter.

  4. Mathematical control theory

    International Nuclear Information System (INIS)

    Agrachev, A.A.

    2002-01-01

    This volume is based on the lecture notes of the minicourses given in the frame of the school on Mathematical Control Theory held at the Abdus Salam ICTP from 3 to 28 September 2001. Mathematical Control Theory is a rapidly growing field which provides strict theoretical and computational tools for dealing with problems arising in electrical and aerospace engineering, automatics, robotics, applied chemistry, and biology etc. Control methods are also involved in questions pertaining to the development of countries in the South, such as wastewater treatment, agronomy, epidemiology, population dynamics, control of industrial and natural bio-reactors. Since most of these natural processes are highly nonlinear, the tools of nonlinear control are essential for the modelling and control of such processes. At present regular courses in Mathematical Control Theory are rarely included in the curricula of universities, and very few researchers receive enough background in the field. Therefore it is important to organize specific activities in the form of schools to provide the necessary background for those embarking on research in this field. The school at the Abdus Salam ICTP consisted of several minicourses intended to provide an introduction to various topics of Mathematical Control Theory, including Linear Control Theory (finite and infinite-dimensional), Nonlinear Control, and Optimal Control. The last week of the school was concentrated on applications of Mathematical Control Theory, in particular, those which are important for the development of non-industrialized countries. The school was intended primarily for mathematicians and mathematically oriented engineers at the beginning of their career. The typical participant was expected to be a graduate student or young post-doctoral researcher interested in Mathematical Control Theory. It was assumed that participants have sufficient background in Ordinary Differential Equations and Advanced Calculus. The volume

  5. Comprehensive basic mathematics

    CERN Document Server

    Veena, GR

    2005-01-01

    Salient Features As per II PUC Basic Mathematics syllabus of Karnataka. Provides an introduction to various basic mathematical techniques and the situations where these could be usefully employed. The language is simple and the material is self-explanatory with a large number of illustrations. Assists the reader in gaining proficiency to solve diverse variety of problems. A special capsule containing a gist and list of formulae titled ''REMEMBER! Additional chapterwise arranged question bank and 3 model papers in a separate section---''EXAMINATION CORNER''.

  6. The mathematics of games

    CERN Document Server

    Beasley, John D

    2006-01-01

    ""Mind-exercising and thought-provoking.""-New ScientistIf playing games is natural for humans, analyzing games is equally natural for mathematicians. Even the simplest of games involves the fundamentals of mathematics, such as figuring out the best move or the odds of a certain chance event. This entertaining and wide-ranging guide demonstrates how simple mathematical analysis can throw unexpected light on games of every type-games of chance, games of skill, games of chance and skill, and automatic games.Just how random is a card shuffle or a throw of the dice? Is bluffing a valid poker strat

  7. Mathematical modelling of metabolism

    DEFF Research Database (Denmark)

    Gombert, Andreas Karoly; Nielsen, Jens

    2000-01-01

    Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....

  8. CLEP college mathematics

    CERN Document Server

    Friedman, Mel

    2012-01-01

    Earn College Credit with REA's Test Prep for CLEP* College Mathematics Everything you need to pass the exam and get the college credit you deserve.CLEP* is the most popular credit-by-examination program in the country, accepted by more than 2,900 colleges and universities. For over 15 years, REA has helped students pass the CLEP* exam and earn college credit while reducing their tuition costs. Our test prep for CLEP* College Mathematics and the free online tools that come with it, allow you to create a personalized CLEP* study plan that can be customized to fit you: your schedule, your lea

  9. Phenomenology and Mathematics

    CERN Document Server

    Hartimo, Mirja

    2010-01-01

    During Edmund Husserl,s lifetime, modern logic and mathematics rapidly developed toward their current outlook and Husserl,s writings can be fruitfully compared and contrasted with both 19th century figures (Boole, Schroder, Weierstrass) as well as the 20th century characters (Heyting, Zermelo, Godel). Besides the more historical studies, the internal ones on Husserl alone and the external ones attempting to clarify his role in the more general context of the developing mathematics and logic, Husserl,s phenomenology offers also a systematically rich but little researched area of investigation.

  10. Concepts of modern mathematics

    CERN Document Server

    Stewart, Ian

    1995-01-01

    Some years ago, ""new math"" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of ""new math"" have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor an

  11. Mathematics for the environment

    CERN Document Server

    Walter, Martin

    2011-01-01

    MATHEMATICS IS CONNECTED TO EVERYTHING ELSEEarth's Climate and Some Basic Principles One of the Greatest Crimes of the 20th Century Feedback Edison's Algorithm: Listening to Nature's Feedback Fuzzy Logic, Filters, the Bigger Picture Principle Consequences of the Crime: Suburbia's Topology A Toxic Consequence of the Crime Hubbert's Peak and the End of Cheap Oil Resource Wars: Oil and Water The CO2 Greenhouse Law of Svante ArrheniusEconomic Instability: Ongoing Causes Necessary Conditions for Economic Success The Mathematical Structure of Ponzi Schemes Dishonest Assessment of Risk One Reason Why

  12. Mathematical Astronomy in India

    Science.gov (United States)

    Plofker, Kim

    Astronomy in South Asia's Sanskrit tradition, apparently originating in simple calendric computations regulating the timing of ancient ritual practices, expanded over the course of two or three millennia to include detailed spherical models, an endless variety of astrological systems, and academic mathematics in general. Assimilating various technical models, methods, and genres from the astronomy of neighboring cultures, Indian astronomers created new forms that were in turn borrowed by their foreign counterparts. Always recognizably related to the main themes of Eurasian geocentric mathematical astronomy, Indian astral science nonetheless maintained its culturally distinct character until Keplerian heliocentrism and Newtonian mechanics replaced it in colonial South Asia's academic mainstream.

  13. Perspectives on mathematical practices bringing together philosophy of mathematics, sociology of mathematics, and mathematics education

    CERN Document Server

    van Kerkhove, Bart

    2007-01-01

    Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the ""classical"" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the ""products"" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next. The editors of this book felt the urge, first of all, to bring together the widest variety of aut

  14. Concepts of mathematical modeling

    CERN Document Server

    Meyer, Walter J

    2004-01-01

    Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec

  15. Discrete algorithmic mathematics

    CERN Document Server

    Maurer, Stephen B

    2005-01-01

    The exposition is self-contained, complemented by diverse exercises and also accompanied by an introduction to mathematical reasoning … this book is an excellent textbook for a one-semester undergraduate course and it includes a lot of additional material to choose from.-EMS, March 2006In a textbook, it is necessary to select carefully the statements and difficulty of the problems … in this textbook, this is fully achieved … This review considers this book an excellent one.-The Mathematical Gazette, March 2006

  16. A mathematical gallery

    CERN Document Server

    Gaal, Lisl

    2017-01-01

    Embark on a playful mathematical tour, aided by Lisl Gaal's illustrations of familiar scenes and whimsical triggers for the imagination. Along the way, find fruit stands arranged using polynomial multiplication, checkerboard tablecloths sewed with patterns of primes in a two-dimensional number system, and deceptive cats revealing that simple counting is not always so simple. Grasping the mathematics in this book requires only a basic background in algebra and geometry, so while the ideas can be understood and enjoyed at a variety of levels, it is recommended for ages 13-99. Touching on topics in current research, this is a book to read and revisit, gaining new insights each time.

  17. Mathematical foundations of elasticity

    CERN Document Server

    Marsden, Jerrold E

    1994-01-01

    This advanced-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Prerequisites include a solid background in advanced calculus and the basics of geometry and functional analysis.The first two chapters cover the background geometry ― developed as needed ― and use this discussion to obtain the basic results on kinematics and dynamics of con

  18. What is Mathematics?

    DEFF Research Database (Denmark)

    Høyrup, Jens

    The paper discusses the question “what is mathematics” from a point of view inspired by anthropology. In this perspective, the character of mathematical thinking and argument is strongly affected – almost essentially determined, indeed – by the dynamics of the specific social, mostly professional...... classical Greek philosophical quest for causes and general explanations had caused mathematical explanation to become an autonomous endeavour in the shape of explicit proof and deductivity, proof and deductivity presented themselves as options – sometimes exploited, sometimes not – even in the teaching...

  19. Insights into teaching mathematics

    CERN Document Server

    Orton, Anthony

    2004-01-01

    Providing essential guidance and background information about teaching mathematics, this book is intended particularly for teachers who do not regard themselves as specialists in mathematics. It deals with issues of learning and teaching, including the delivery of content and the place of problems and investigations. Difficulties which pupils encounter in connection with language and symbols form important sections of the overall discussion of how to enhance learning. The curriculum is considered in brief under the headings of number, algebra, shape and space, and data handling, and special at

  20. Computer mathematics for programmers

    CERN Document Server

    Abney, Darrell H; Sibrel, Donald W

    1985-01-01

    Computer Mathematics for Programmers presents the Mathematics that is essential to the computer programmer.The book is comprised of 10 chapters. The first chapter introduces several computer number systems. Chapter 2 shows how to perform arithmetic operations using the number systems introduced in Chapter 1. The third chapter covers the way numbers are stored in computers, how the computer performs arithmetic on real numbers and integers, and how round-off errors are generated in computer programs. Chapter 4 details the use of algorithms and flowcharting as problem-solving tools for computer p

  1. Introduction to mathematical logic

    CERN Document Server

    Mendelson, Elliott

    2015-01-01

    The new edition of this classic textbook, Introduction to Mathematical Logic, Sixth Edition explores the principal topics of mathematical logic. It covers propositional logic, first-order logic, first-order number theory, axiomatic set theory, and the theory of computability. The text also discusses the major results of Gödel, Church, Kleene, Rosser, and Turing.The sixth edition incorporates recent work on Gödel's second incompleteness theorem as well as restoring an appendix on consistency proofs for first-order arithmetic. This appendix last appeared in the first edition. It is offered in th

  2. Applied mathematics made simple

    CERN Document Server

    Murphy, Patrick

    1982-01-01

    Applied Mathematics: Made Simple provides an elementary study of the three main branches of classical applied mathematics: statics, hydrostatics, and dynamics. The book begins with discussion of the concepts of mechanics, parallel forces and rigid bodies, kinematics, motion with uniform acceleration in a straight line, and Newton's law of motion. Separate chapters cover vector algebra and coplanar motion, relative motion, projectiles, friction, and rigid bodies in equilibrium under the action of coplanar forces. The final chapters deal with machines and hydrostatics. The standard and conte

  3. 3rd International Conference on Computational Mathematics and Computational Geometry

    CERN Document Server

    Ravindran, Anton

    2016-01-01

    This volume presents original research contributed to the 3rd Annual International Conference on Computational Mathematics and Computational Geometry (CMCGS 2014), organized and administered by Global Science and Technology Forum (GSTF). Computational Mathematics and Computational Geometry are closely related subjects, but are often studied by separate communities and published in different venues. This volume is unique in its combination of these topics. After the conference, which took place in Singapore, selected contributions chosen for this volume and peer-reviewed. The section on Computational Mathematics contains papers that are concerned with developing new and efficient numerical algorithms for mathematical sciences or scientific computing. They also cover analysis of such algorithms to assess accuracy and reliability. The parts of this project that are related to Computational Geometry aim to develop effective and efficient algorithms for geometrical applications such as representation and computati...

  4. Amongst mathematicians teaching and learning mathematics at university level

    CERN Document Server

    Nardi, Elena

    2008-01-01

    "Amongst Mathematicians" offers a unique perspective on the ways in which mathematicians perceive their students' learning, the way they teach and reflect on those teaching practices. Elena Nardi employs fictional characters to create a conversation on these important issues. While personas are created, the facts incorporated into their stories are based on large bodies of data including intense focus groups comprised of mathematicians and mathematics education.This book further develops analyses of the data and demonstrates the pedagogical potential that lies in collaborative research that engages educators, researchers, and students in undergraduate mathematics education. Nardi also addresses the need for action in undergraduate mathematics education by creating discourse for reform and demonstrating the feasibility and potential of collaboration between mathematicians and researchers. "Amongst Mathematicians" is of interest to the entire mathematics community including teacher educators, undergraduate and ...

  5. The general theory of relativity a mathematical exposition

    CERN Document Server

    Das, Anadijiban

    2012-01-01

     The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: • tensor analysis • the special theory of relativity • the general theory of relativity and Einstein’s field equations • spherically symmetric solutions and experimental confirmations • static and stationary space-time domains • black holes • cosmological models • algebraic classifications and the Newman-Penrose equations • the coupled Einstein-Maxwell-Klein-Gordon equations • appendices covering mathematical supplements and special topics Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars. Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Irelan...

  6. Rays, waves, and scattering topics in classical mathematical physics

    CERN Document Server

    Adam, John A

    2017-01-01

    This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technica...

  7. Fundamentals of teaching mathematics at university level

    CERN Document Server

    Baumslag, Benjamin

    2000-01-01

    This unique book presents a personal and global approach to teaching mathematics at university level. It is impressively broad in its scope, and thought-provoking in its advice. The author writes with a love of his subject and the benefit of a long and varied career. He compares and contrasts various educational systems and philosophies. Furthermore, by constantly drawing on his own experiences and those of his colleagues, he offers useful suggestions on how teachers can respond to the problems they face. This book will interest educationalists, policy advisers, administrators, lecturers, and

  8. Expanding your horizons in science and mathematics

    Science.gov (United States)

    1985-01-01

    Through the presentation of its Expanding Your Horizons in Science and Mathematics career education conferences for secondary school young women, the Math/Science Network continues its efforts to remove the educational, psychological, and cultural barriers which prevent women from entering math-and science-based careers. The Expanding Your Horizons conferences were presented on 77 college, university and high school campuses across the United States. This year, these unique one day conferences reached 15,500 students, 3,000 parents and educators, and involved 3,000 career women who volunteered their services as conference planners, workshop leaders, speakers, and role models.

  9. Cambridge IGCSE mathematics core and extended

    CERN Document Server

    Pimentel, Ric

    2013-01-01

    The most cost effective and straightforward way to teach the revised syllabus, with all the core and extended content covered by a single book and accompanying free digital resources.  . This title has been written for the revised Cambridge IGCSE Mathematics (0580) syllabus, for first teaching from 2013.  . ·         Gives students the practice they require to deepen their understanding through plenty of questions. ·         Consolidates learning with unique digital resources on the CD, included free with every Student's Book.  . We are working with Cambridge International Examinations to gain

  10. Implementing a new mathematics curriculum: Mathematics teachers’ beliefs and practices

    OpenAIRE

    Ernest Ampadu

    2013-01-01

    Mathematics has become a ‘critical filter’ in the social, economic and professional development of individuals and forms a core component of the school curriculum in most countries. It is upon this utilitarian nature of mathematics to the individual and the society as a whole that the school mathematics curriculum has been undergoing a number of restructuring over the last three decades. In Ghana, a new mathematics curriculum was introduced in September 2007 which aims at shifting the teachin...

  11. Continental Mathematics League.

    Science.gov (United States)

    Quartararo, Joseph

    2002-01-01

    This article describes the activities of the Continental Mathematics League, which offers a series of meets for children in grades 3 though 9. In addition, a Calculus League and a Computer Contest are offered. The league allows schools to participate by mail so that rural schools can participate. (CR)

  12. Measurement, Mathematics, and Music.

    Science.gov (United States)

    Blackburn, Katie; White, David

    The Greek mathematician, Pythagoras, was among the first to undertake a mathematical study of music. His work, resulted in a scale of notes which can produce beautiful melodies and which is easily reproduced in the elementary classroom. In an age when teachers look for an interdisciplinary connection between various aspects of the curriculum, in a…

  13. Research in Mathematics Education

    Science.gov (United States)

    Schoenfeld, Alan H.

    2016-01-01

    As one of the three Rs, "'rithmetic" has always been central to education and education research. By virtue of that centrality, research in mathematics education has often reflected and at times led trends in education research. This chapter provides some deep background on epistemological and other issues that shape current research,…

  14. Putting Foundations Into Mathematics

    Science.gov (United States)

    Hubbard, G. L.

    1972-01-01

    For meaningful learning of mathematics, a learning set is required which demands that all things accepted as true should be demonstrable in terms of a paradigm appropriate to the child's cognitive development: preparatory, concrete-particular, concrete-general, formal-abstract. Future teachers should experience all paradigms to become aware that…

  15. Elementary School Mathematics Priorities

    Science.gov (United States)

    Wilson, W. Stephen

    2009-01-01

    This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…

  16. Foundations of mathematical logic

    CERN Document Server

    Curry, Haskell B

    2010-01-01

    Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods, including algorithms and epitheory, and offers a brief treatment of Markov's approach to algorithms, explains elementary facts about lattices and similar algebraic systems, and more. 1963 edition.

  17. Relationality and Mathematical Knowing

    Science.gov (United States)

    Maheux, Jean-Francois; Roth, Wolff-Michael

    2011-01-01

    Current conceptualizations of knowing and learning tend to separate the knower from others, the world they know, and themselves. In this article, we offer "relationality" as an alternative to such conceptualizations of mathematical knowing. We begin with the perspective of Maturana and Varela to articulate some of its problems and our alternative.…

  18. Towards mathematical philosophy

    CERN Document Server

    Hendricks, Vincent F

    2008-01-01

    Logical investigations in cognitive science have successfully utilized methods and systems of belief revision, non-monotonic logic and dynamic epistemic logic. This title deals with focal issues of belief revision. It contains a collection of articles applying methods of logic or, more generally, of mathematics to solve problems.

  19. Pursuing Mathematics in India

    Indian Academy of Sciences (India)

    Admin

    2012-09-07

    Sep 7, 2012 ... of public–private partnership in research and education in India. The Institute receives major private funding, side by side with substantial .... We are writing this to say that students who fail to do well in Mathematics Olympiad have no reason to get disheartened and to think that they are not good enough to ...

  20. Mathematics Curriculum Evaluation Framework

    Science.gov (United States)

    Stein, Marcy; Kinder, Diane; Milchick, Sherry

    2004-01-01

    In this paper, we present a framework for evaluating commercially developed mathematics programs. This framework is based on principles of instructional design derived from a Direct Instruction approach to education. Given the role that instructional programs play in the classroom, especially for teachers who have not been well prepared to teach…

  1. Refresher Course in Mathematics

    Indian Academy of Sciences (India)

    T C Panda of Berhampur University the Course Co·ordinator. This Course is intended mainly for those involved with undergraduate/ postgraduate. teaching. Only teachers/re- searchers desirous of devoting full time in the Academic Programme need apply. Course Capsule: Analysis, dynamical systems, mathematical ...

  2. Vision in elementary mathematics

    CERN Document Server

    Sawyer, W W

    2003-01-01

    Sure-fire techniques of visualizing, dramatizing, and analyzing numbers promise to attract and retain students' attention and understanding. Topics include basic multiplication and division, algebra, word problems, graphs, negative numbers, fractions, many other practical applications of elementary mathematics. 1964 ed. Answers to Problems.

  3. Music, Mathematics and Bach

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 3. Music, Mathematics and Bach - Layers of Melody. Rahul Siddharthan. General Article Volume 4 Issue 3 March 1999 pp 8-15. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/004/03/0008-0015 ...

  4. Some Interesting Mathematical Gems

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 11; Issue 9. Some Interesting Mathematical Gems. V G Tikekar. General Article Volume 11 Issue 9 September 2006 pp 29-42 ... Author Affiliations. V G Tikekar1. c/o Thakar New Mahadwar Road Near Padmaraje School Kolhapur 416006, India.

  5. Elementary Mathematics with PLATO.

    Science.gov (United States)

    Dugdale, Sharon; Kibbey, David

    Computer-based courseware for the intermediate grades developed by the PLATO Elementary Mathematics Project was tested for a three year period in the public schools of Champaign and Urbana, Illinois. This brief report describes the project in terms of the student session, curriculum, educational effectiveness, and data feedback to teachers.…

  6. Communities in University Mathematics

    Science.gov (United States)

    Biza, Irene; Jaworski, Barbara; Hemmi, Kirsti

    2014-01-01

    This paper concerns communities of learners and teachers that are formed, develop and interact in university mathematics environments through the theoretical lens of "Communities of Practice." From this perspective, learning is described as a process of participation and reification in a community in which individuals belong and form…

  7. Mathematics and Sports

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 12. Mathematics and Sports. Vivek S Borkar. Book Review Volume 4 Issue 12 December 1999 pp 107-108. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/004/12/0107-0108. Author Affiliations.

  8. Mathematics in Action

    DEFF Research Database (Denmark)

    December 2004-November 2007 Denmark, Hungary, Lithuania, the Netherlands, Norway, Slovenia and Spain have cooperated in the project Mathematics in Action (MiA). The MiA project is supported by the Grundtvig action in the Socrates program of the European Commission. The aim of the project is to su......December 2004-November 2007 Denmark, Hungary, Lithuania, the Netherlands, Norway, Slovenia and Spain have cooperated in the project Mathematics in Action (MiA). The MiA project is supported by the Grundtvig action in the Socrates program of the European Commission. The aim of the project...... is to support quality of learning and teaching of mathematics in adult education in the EU countries and to support participation and success rates of adult learners. The target groups are teachers in adult learning institutions and teacher trainers. As a result of the MiA project this handbook presents...... examples of good practices and theoretical thoughts about doing and learning mathematics in actual real life situations. The first chapter gives an overview. The second chapter concerns important papers from the European Commission on key competences and how they set up challenges for teachers in adult...

  9. Freedom in mathematics

    CERN Document Server

    Cartier, Pierre; Heinzmann, Gerhard; Villani, Cédric

    2016-01-01

    This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cédric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cédric Villani’s popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political esta...

  10. The story of mathematics

    CERN Document Server

    Mankiewicz, Richard

    2000-01-01

    Questioning how mathematics has evolved over the centuries and for what reasons; how human endeavour and changes in the way we live have been dependent on mathematics, this book tells the story of the impact this intellectual activity has had across cultures and civilizations. It shows how, far from being just the obsession of an elite group of philosophers, priests and scientists, mathematics has in some shape or other entered every area of human activity. The mysterious tally sticks of prehistoric peoples and the terrestial maps used for trade, exploration and warfare; the perennial fascination with the motions of heavenly bodies and changing perspectives on the art and science of vision; all are testament to a mathematics at the heart of history. The path of this changing discipline is marked by a wealth of images, from medieval manuscripts to the unsettling art of Dali or Duchamp, from the austere beauty of Babylonian clay tablets to the delicate complexity of computer-generated images. The text encompass...

  11. World Mathematical Year 2000

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 1. World Mathematical Year-2000 Event. Information and Announcements Volume 6 Issue 1 January 2001 pp 99-99. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/01/0099-0099. Resonance ...

  12. Mathematics for quantum chemistry

    CERN Document Server

    Anderson, Jay Martin

    2005-01-01

    This concise volume offers undergraduates an introduction to mathematical formalism in problems of molecular structure and motion. The main topics cover the calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics and applications to molecular motion. Answers to problems. 1966 edition.

  13. Every Day Is Mathematical

    Science.gov (United States)

    Barger, Rita H.; Jarrah, Adeeb M.

    2012-01-01

    March 14 is special because it is Pi Day. Mathematics is celebrated on that day because the date, 3-14, replicates the first three digits of pi. Pi-related songs, websites, trivia facts, and more are at the fingertips of interested teachers and students. Less celebrated, but still fairly well known, is National Metric Day, which falls on October…

  14. The Teaching of Mathematics.

    Science.gov (United States)

    Henriksen, Melvin, Ed.; Wagon, Stan, Ed.

    1991-01-01

    Presented with appropriate formulas and illustrations are five lessons suitable for college mathematics undergraduate students, including Pi and the limit of (sin alpha)/alpha, the structure of orthogonal transformations, a simple proof of Zorn's Lemma, the converse of Liouville's Theorem, and visualizing the p-adic integers. (JJK)

  15. Mathematics and Sports

    Indian Academy of Sciences (India)

    planning the players' diet. In the next chapter, real games meet mathematical games. Applications? Well, there are applications to strategic planning in swim teams, ski teams, weight-lifting, etc. that are described, but the place of pride goes to a newsclip about a hockey game where game theoretic planning won the day.

  16. Mathematics and Engineering in Real Life through Mathematical Competitions

    Science.gov (United States)

    More, M.

    2018-01-01

    We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build…

  17. Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

    Science.gov (United States)

    Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

    2016-01-01

    This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

  18. Racial Differences in Mathematics Test Scores for Advanced Mathematics Students

    Science.gov (United States)

    Minor, Elizabeth Covay

    2016-01-01

    Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…

  19. "Mathematics Is Like a Lion": Elementary Students' Beliefs about Mathematics

    Science.gov (United States)

    Markovits, Zvia; Forgasz, Helen

    2017-01-01

    The aim of this study was to explore the beliefs of elementary school students about mathematics and about themselves as mathematics learners. The participants, Israeli grade 4 and grade 6 students, completed questionnaires. Using an "animal metaphor" to tap beliefs, some students perceived mathematics as difficult and complicated, while…

  20. History of Modern Applied Mathematics in Mathematics Education

    Science.gov (United States)

    Jankvist, Uffe Thomas

    2009-01-01

    This article discusses the integration of history of modern applied mathematics in mathematics education as well as the possible teaching and learning benefits of introducing a newer history of mathematics over an old(er) one--something that seems to be done most often when integrating history. Three cases of the history of modern applied…