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A Comment on "On Some Contradictory Computations in Multi-dimensional Mathematics"

de Oliveira, E. Capelas; Rodrigues Jr, W. A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/03/2006 Português
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In this paper we analyze the status of some `unbelievable results' presented in the paper `On Some Contradictory Computations in Multi-Dimensional Mathematics' [1] published in Nonlinear Analysis, a journal indexed in the Science Citation Index. Among some of the unbelievable results `proved' in the paper we can find statements like that: (i) a linear transformation which is a rotation in R^2 with rotation angle theta different from nphi/2, is inconsistent with arithmetic, (ii) complex number theory is inconsistent. Besides these 'results' of mathematical nature [1],offers also a `proof' that Special Relativity is inconsistent. Now, we are left with only two options (a) the results of [1] are correct and in this case we need a revolution in Mathematics (and also in Physics) or (b) the paper is a potpourri of nonsense. We show that option (b) is the correct one. All `proofs' appearing in [1] are trivially wrong, being based on a poor knowledge of advanced calculus notions. There are many examples (some of them discussed in [2,3,4,5,6]of complete wrong papers using nonsequitur Mathematics in the Physics literature. Taking into account also that a paper like [1] appeared in a Mathematics journal we think that it is time for editors and referees of scientific journals to become more careful in order to avoid the dissemination of nonsense.

The Maslov dequantization, idempotent and tropical mathematics: A brief introduction

Litvinov, G. L.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/07/2005 Português
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This paper is a brief introduction to idempotent and tropical mathematics. Tropical mathematics can be treated as a result of the so-called Maslov dequantization of the traditional mathematics over numerical fields as the Planck constant $\hbar$ tends to zero taking imaginary values.; Comment: English and Russian versions. This article, a result of a very considerable expansion of math.GM/0501038, is to appear in Journal of Mathematical Sciences (Notes of Scientific Seminars of the V.A. Steklov Mathematical Institute), see . Dedicated to Anatoly Vershik with admiration and gratitude. Russian version to be published in "Zapiski Nauchnykh Seminarov POMI"

The Maslov dequantization, idempotent and tropical mathematics: a very brief introduction

Litvinov, Grigori
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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This paper is a very brief introduction to idempotent mathematics and related topics.; Comment: 24 pages, 2 figures. An introductory paper to the volume "Idempotent Mathematics and Mathematical Physics" (G.L. Ltvinov, V.P. Maslov, eds.; AMS Contemporary Mathematics, 2005). More misprints corrected

Not served on a silver platter! Access to online mathematics information in Africa

Wandahl, Anders
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/05/2009 Português
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This paper argues that, contrary to the beliefs of many, the amount of mathematics information available for African researchers, including electronic scientific journals and databases, is indeed substantial. However, whereas information resources are served on a silver platter at the "northern" universities, researchers at universities in developing countries have to work hard for their treats. The scientific information available for low-income countries is scattered among a large number of providers, websites, access methods, price models, and country- or institution-specific programmes. It is therefore quite hard for individual researchers to see the whole picture and establish what actually is available and what is not. This paper presents a number of key information sources for mathematics. Some are aimed primarily at disciplines other than mathematics but nevertheless contain extremely important and high-ranking mathematics journals. Brief instructions are also given on how to register for and maintain access to various relevant and useful resources.; Comment: Presentation at the First International Conference on the Mathematical Sciences - University of Buea, Cameroon, May 2009

Universal algorithms, mathematics of semirings and parallel computations

Litvinov, G. L.; Maslov, V. P.; Rodionov, A. Ya.; Sobolevski, A. N.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/05/2010 Português
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This is a survey paper on applications of mathematics of semirings to numerical analysis and computing. Concepts of universal algorithm and generic program are discussed. Relations between these concepts and mathematics of semirings are examined. A very brief introduction to mathematics of semirings (including idempotent and tropical mathematics) is presented. Concrete applications to optimization problems, idempotent linear algebra and interval analysis are indicated. It is known that some nonlinear problems (and especially optimization problems) become linear over appropriate semirings with idempotent addition (the so-called idempotent superposition principle). This linearity over semirings is convenient for parallel computations.; Comment: 36 pages, 1 figure. To appear in Springer Lecture Notes in Computational Science and Engineering.

The Call of Mathematics

Kutateladze, S. S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 28/05/2007 Português
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A few remarks on how mathematics quests for freedom.; Comment: A draft of a talk at the conference "Mathematics in the Modern World," Novosibirisk, September 17-23, 2007

Mathematics discovered, invented, and inherited

Borovik, Alexandre
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: is new mathematics discovered or invented? Using an example from my own mathematical life, I argue that there is also a third way: new mathematics can also be inherited -- and in the process briefly discuss a remarkable paper by W. Burnside of 1900.; Comment: Version 2: A few references have been added http://www.borovik.net/selecta/

Women's Representation in Mathematics Subfields: Evidence from the arXiv

Brisbin, Abra; Whitcher, Ursula
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 25/09/2015 Português
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We use data from papers posted to the Mathematics section of the arXiv to explore the representation of women in mathematics research. We show that women are under-represented as authors of mathematics papers on the arXiv, even in comparison to the proportion of women who hold full-time positions in mathematics departments. However, some subfields have much greater participation than others.; Comment: 11 pages, 3 figures, 11 tables

Jordan structures in mathematics and physics

Iordanescu, Radu
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/06/2011 Português
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The aim of this paper is to offer an overview of the most important applications of Jordan structures inside mathematics and also to physics, up-dated references being included. For a more detailed treatment of this topic see - especially - the recent book Iordanescu [364w], where sugestions for further developments are given through many open problems, comments and remarks pointed out throughout the text. Nowadays, mathematics becomes more and more nonassociative and my prediction is that in few years nonassociativity will govern mathematics and applied sciences. Keywords: Jordan algebra, Jordan triple system, Jordan pair, JB-, JB*-, JBW-, JBW*-, JH*-algebra, Ricatti equation, Riemann space, symmetric space, R-space, octonion plane, projective plane, Barbilian space, Tzitzeica equation, quantum group, B\"acklund-Darboux transformation, Hopf algebra, Yang-Baxter equation, KP equation, Sato Grassmann manifold, genetic algebra, random quadratic form.

Two topics in financial mathematics : Forward utility and consumption functions & Hedging with variance swaps in infinite dimensions

Berrier, Francois
Fonte: University of Cambridge; Department of Pure Mathematics and Mathematical Statistics Publicador: University of Cambridge; Department of Pure Mathematics and Mathematical Statistics
Tipo: Thesis; doctoral; PhD
Português
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Financial Mathematics is often presented as being composed of two main branches: one dealing with investment and consumption, with the aim of answering the now ancient question of how people should invest and spend their money, and the other dealing with the pricing and hedging of derivative instruments. This distinction between both branches of Financial Mathematics is reflected in my thesis, which is a compilation of two very different subjects on which I have worked during the past three years. The first chapter, entitled ?Forward Utility and Consumption Functions?, contributes to the investment branch of Financial Mathematics. Forward utilities have been introduced (under different names) a few years ago by Musiela and Zariphopoulou on the one hand, and by Henderson and Hobson on the other hand. Their idea is to define families (indexed by time and randomness) of utility functions which make the investment decisions of agents consistent over time. The contribution of this chapter is to extend the definition of forward utilities by adding consumption into the story and by giving explicit ways of constructing consumption functions from utilities and vice versa. The last part of this first chapter characterizes, in a Laplace integral form...

Portuguese Language and Mathematics in Technological Courses: Studies on Logic of Language and Language of Logic; Língua portuguesa e matemática em cursos tecnológicos: estudos sobre lógica da linguagem e linguagem da lógica

Guaranha, Manoel Francisco; Bortolete, Juliano Cavalcante
Fonte: Universidade de São Paulo. Faculdade de Filosofia, Letras e Ciências Humanas Publicador: Universidade de São Paulo. Faculdade de Filosofia, Letras e Ciências Humanas
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; ; Formato: application/pdf
Publicado em 30/06/2015 Português
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: Technological education aims to fulfill social and labor world demands. Thus, its teaching-learning processes are directed to the application of new information technologies and require an approach of logic concepts as basis for reading practices, text production and understanding of mathematical concepts. This paper presents strategies approach between two areas: Linguistics and Mathematics, based on the studies of Oswald Ducrot (1981) on the argumentative conception of language, especially when describing the logic of language. Thus, the research aims at developing, from reflections on logic and language, interdisciplinary methods of approach in the Communication and Mathematics subjects that might provide students who attend technological higher education a greater mastery at logic, both in argumentative as well in Mathematics; and encourage them to apply mathematical skills toward solving practical problems and understanding Mathematics as a formal instrument of expression and communication, which seeks to achieve real aspects for multiple sciences. We present a reading method of a verbal text by decomposing it in logical propositions, and chaining them in logical expressions. More than translating one language to another, we tried to bring the two areas as a strategy to make the student aware on the logical-mathematical structure of the language.; O ensino tecnológico visa ao atendimento das demandas sociais e do mundo do trabalho. Por isso...

Um ensaio sobre as concepções de professores de Matemática: possibilidades metodológicas e um exercício de pesquisa; An essay on the conceptions of Mathematics teachers: methodological possibilities and a research exercise

Garnica, Antonio Vicente Marafioti
Fonte: Universidade de São Paulo. Faculdade de Educação Publicador: Universidade de São Paulo. Faculdade de Educação
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; ; ; ; ; ; Formato: application/pdf
Publicado em 01/12/2008 Português
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Este artigo tem como tema principal as concepções dos professores de Matemática. Considerando o termo "concepção" a partir do pragmatismo de Peirce, elabora-se um conjunto de parâmetros metodológicos - chamado de "método indireto" - a ser aplicado no estudo das concepções de professores de Matemática. Trata-se, em síntese, de investigar as concepções dos professores interpelando-os não sobre suas crenças, mas sobre suas práticas. Fundamentando essa abordagem indireta e explicitando-a em sua natureza qualitativa, o artigo segue apresentando, como exemplo, um exercício desse "método indireto": um estudo sobre os critérios que os professores utilizam quando escolhem livros-texto para sua sala de aula, abordando, conseqüentemente, quais concepções de Matemática e de seu ensino e aprendizagem tais critérios desvendam. Partindo de depoimentos de professores de Matemática, o estudo indica que os professores agem com certa independência quando escolhem os materiais utilizados em suas atividades docentes. Buscam, ao mesmo tempo, apoio em uma vasta gama de livros didáticos, desconsiderando as particularidades de cada obra e as abordagens e perspectivas defendidas por seus autores. Embora submetam-se ao livro didático - considerado uma referência legítima e segura -...

Concurrent system design: Applied mathematics & modeling in software engineering education

Lutz, Michael; Vallino, James
Fonte: American Society for Engineering Education Publicador: American Society for Engineering Education
Tipo: Proceedings
Português
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A hallmark of engineering design is the use of models to explore the consequences of design decisions. Sometimes these models are physical prototypes or informal drawings, but the sine qua non of contemporary practice is the use of formal, mathematical models of system structure and behavior. Whether circuit models in electrical engineering, heat-transfer models in mechanical engineering, or queuing theory models in industrial engineering, mathematics makes it possible to perform rigorous analysis that is the cornerstone of modern engineering. Until recently, such modeling was impractical for software systems. Informal models abounded, such as those created in UML1, but rigorous models from which one could derive significant properties were either so rudimentary or so tedious to use that it was difficult to justify the incremental benefit in other than the most critical of systems. In part this is a reflection of the relative immaturity of software engineering, but it also reflects a key distinction between software and traditional engineering: whereas the latter builds on numerical computation and continuous functions, software is more appropriately modeled using logic, set theory, and other aspects of discrete mathematics. Most of the models stress relationships between software components...

Directions in recognizing tabular structures of handwritten mathematics notation

Zanibbi, Richard; Blostein, Dorothea; Cordy, James
Fonte: Proc. Fourth Int'l IAPR Workshop on Graphics Recognition Publicador: Proc. Fourth Int'l IAPR Workshop on Graphics Recognition
Tipo: Proceedings
Português
Relevância na Pesquisa
35.44%
Mathematics notation contains a variety of tabular structures, including matrices, lists of expressions in a derivation, stacked limit expressions in a summation, and conditional expressions in a function definition. Tabular structures are particularly difficult to recognize in handwritten mathematics notation, due to irregular placement and sizing of symbols. In this paper we briefly survey prior work, describe a representation for tabular structures in mathematics notation, and present possible directions for recognizing tabular structures in handwritten notation.; "Directions in Recognizing Tabular Structures of Handwritten Mathematics Notation," Proc. Fourth Int'l IAPR Workshop on Graphics Recognition. Held in Kingston, Canada: 7-8 September 2001

Utilizing a Response to Intervention framework to support student achievement in mathematics at Cape Henlopen High School

Young, Michael Scott
Fonte: University of Delaware Publicador: University of Delaware
Tipo: Tese de Doutorado
Português
Relevância na Pesquisa
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Farley-Ripple, Elizabeth; This paper examines the critical components required to establish a Response to Intervention (RTI) program at the secondary level in mathematics. The difficulty accomplishing this is that the majority of existing RTI programs focus on reading at the elementary level. My attempt is to create a framework I can utilize in a high school setting that will allow the facilitation of RTI. The development of a secondary RTI framework is critical in order for a successful mathematics intervention program to be developed. Without a functional framework, the RTI program will not succeed. In order to maintain focus throughout the project, I utilized several guiding questions when attempting to identify various RTI framework components: 1. Is the identified RTI framework component specific to the secondary level or can a school modify it for the secondary level? 2. Is the RTI framework component specific to a mathematics program or can a school utilize it in a mathematics program? 3. Has the identified RTI component been used in an RTI program that has experienced success? 4. How can a school modify its schedule to accommodate an RTI program? I developed the framework by considering the answers to these questions.; University of Delaware...

Shifting mathematics planning and instructional practices to align with the expectations of the Common Core State Standards: a multi-faceted approach

Dingle, Catherine Green
Fonte: University of Delaware Publicador: University of Delaware
Tipo: Tese de Doutorado
Português
Relevância na Pesquisa
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Buttram, Joan; As a result of the shift to the Common Core State Standards (CCSS), the expectations for teaching and learning have changed significantly. During the time of No Child Left Behind, the state department of education provided grade level standards on which Fairview County Public Schools based their curriculum. The curriculum was circular in nature and focused on exposure to concepts and skills, rather than mastery. The same concepts and skills were introduced throughout many grade levels, which promoted surface level learning. The CCSS, however, are focused on depth of understanding and mastery; the standards build on one another from year to year, and students are expected to use that knowledge to expand and deepen their understanding as the years go on. The expectations for learning at each grade level have also become more rigorous; for example, complex texts and complex mathematical concepts are now introduced in earlier grade levels. In order for students to be successful with the CCSS, teachers must change the way that they plan for instruction as well as the way that they deliver instruction. This Education Leadership Portfolio describes strategies that were designed and implemented at one elementary school in an effort to shift mathematics planning and instructional practices to better align with the CCSS expectations. I engaged in activities to increase my knowledge of mathematics and professional learning so that I could lead the improvement efforts successfully and support teachers in a meaningful way. A variety of professional learning experiences was provided to help teachers increase their content-area knowledge and expand their repertoire of strategies to teach mathematics. The results of these professional development strategies on teacher practices are discussed and recommendations are made to inform future professional learning activities focused on shifting mathematics planning and instructional practices.; University of Delaware...

Wittgenstein’s Philosophies of Mathematics: Systemic Intentionalism and the Employment of a New Method (Regarding Wittgenstein’s Philosophy of Mathematics Development); As Filosofias da Matemática de Wittgenstein: Intensionalismo Sistêmico e a Aplicação de um Novo Método (Sobre o Desenvolvimento da Filosofia da Matemática de Wittgenstein)

Engelmann, Mauro; UFMG
Fonte: UFPR Publicador: UFPR
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; ; Formato: application/pdf
Publicado em 20/04/2010 Português
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This essay intends to identify intentionalism (infinity given by rules, notby extensions) and the idea of multiple complete mathematical systems (several“mathematics”) as the central characteristics of Wittgenstein’s philosophy ofmathematics. We intend to roughly show how these ideas come up, interact toeach other, how they develop and, in the end, how they are abandoned in the lateperiod. According to the Tractatus Logico-Philosophicus, infinities can only begiven by rules and there is a single numerical system (the number’s essence is thegeneral idea of ordering). Intentionalism is up to at least 1933, but the idea of asingle system is abandoned in 1929-30 (already in the Philosophische Bemerkungen).In its place one finds the idea of multiple, independent and completenumerical systems. This idea will engender some key moves in Wittgenstein’sphilosophy of Mathematics. The notion of “seeing an aspect” from the Big Typescript,of instance, comes up so as to explain such systems. From 1934 onwards,Wittgenstein gradually abandons intentionalism and the idea of multiple, independentand complete systems. In his late philosophy, both ideas are used onlyas instruments to dissolve philosophical prose regarding mathematics.; Este ensaio visa estabelecer o intensionalismo (infinitos são dados por regras...

Objetivos e resultados da pesquisa em Modelagem Matemática na Educação Matemática brasileira: o caso de uma categoria; Objectives and results of research in Mathematical Modeling in Brazilian Mathematics Education: the case of a category

Burak, Dionísio; Universidade Estadual do Centro-Oeste; Brandt, Celia Finck; UEPG; Silva, Vantielen da Silva; UNICENTRO
Fonte: MTM/PPGECT/CFM/UFSC Publicador: MTM/PPGECT/CFM/UFSC
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; Formato: application/pdf
Publicado em 29/07/2014 Português
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http://dx.doi.org/10.5007/1981-1322.2014v9nespp21Neste artigo apresentamos considerações em relação aos dados que envolvem a categoria: Objetivos que buscam relacionar a Modelagem Matemática com outras teorias, tendências ou tecnologias e seus respectivos resultados revelados nos trabalhos apresentados e constantes nos anais da VI Conferência Nacional de Modelagem em Educação Matemática - VICNMEM. A questão de fundo é: Como se apresentam os objetivos e os resultados dos trabalhos publicados no âmbito da VI CNMEM? A natureza da investigação é predominantemente qualitativa e a análise dos dados se pautou nas orientações de Bardin (2009) para a análise de conteúdo. Foram analisados quinze (15) trabalhos submetidos ao evento, com o auxílio do software Atlas t.i. Alguns resultados mostram o avanço na busca de associar a Modelagem com outras tendências da Educação Matemática, mas também ainda uma pequena contribuição em relação à consolidação do campo da Modelagem na Educação Matemática.; http://dx.doi.org/10.5007/1981-1322.2014v9nespp21This article presents considerations regarding the data involving the category: Objectives that seek association of Modeling Mathematics with other theories, trends or technologies and their results presented and disclosed in constant work in the annals of the Sixth National Conference on Mathematical Modeling in Education - VICNMEM . The question to be answered is: How if show the objectives and results of published works within the VI CNMEM? The nature of research is predominantly qualitative and data analysis was based under the guidelines of Bardin (2009) for content analysis. Were analised 15 papers submitted to the event...

Learning mathematics with adult learners: drawing from parents' perspective

Díez-Palomar,Javier; Menéndez,José María; Civil,Marta
Fonte: Comité Latinoamericano de Matemática Educativa Publicador: Comité Latinoamericano de Matemática Educativa
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/03/2011 Português
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This article explores issues related to the relationship between everyday mathematics and academic mathematics within adult education, through a series of workshops with parents. Participants were encouraged to reflect on their perspective on learning and teaching mathematics through different activities in the workshops. All sessions were videotaped. Our analy sis of multiple episodes revealed three topics: contextualization, transferring the mathematical knowledge, and sense making. We use three vignettes to illustrate these topics. Our study implications for adult education focus on mathematics as a situated practice produced as a consequence of interaction among learners in egalitarian spaces.

Exploring rural high school learners' experience of mathematics anxiety in academic settings

Hlalele,Dipane
Fonte: South African Journal of Education Publicador: South African Journal of Education
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2012 Português
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The purpose of the study was to explore rural high school learners' experience of mathematics anxiety in academic settings. Mathematics anxiety has been found to have an adverse effect on confidence, motivation and achievement. This quantitative study is exploratory and descriptive in nature. The participants were 403 learners doing mathematics in 18 rural schools in the Free State province of South Africa. Participants completed a 20-item questionnaire and 373 (92.5%) questionnaires were found to contain valid responses and were analysed by a professional statistician at the University of the Free State using the Statistical Package for the Social Sciences (SPSS), Version 17.0. The questionnaire was testedfor reliability using the Cronbach alpha coefficient and was found to have a reliability score of .841, indicating an acceptable reliability coefficient. Findings reveal that all learners sometimes, often, or always experience mathematics anxiety in academic settings. It is therefore important for teachers and authorities in education to observe its prevalence and to implement strategies toward the alleviation of the effects ofmathematics anxiety.