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Shibalovich, Paul. "Fundamental theorem of algebra." CSUSB ScholarWorks, 2002. https://scholarworks.lib.csusb.edu/etd-project/2203.
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The fundamental theorem of algebra (FTA) is an important theorem in algebra. This theorem asserts that the complex field is algebracially closed. This thesis will include historical research of proofs of the fundamental theorem of algebra and provide information about the first proof given by Gauss of the theorem and the time when it was proved.
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Bartolini, Gabriel. "On Poicarés Uniformization Theorem." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7968.
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A compact Riemann surface can be realized as a quotient space $\mathcal{U}/\Gamma$, where $\mathcal{U}$ is the sphere $\Sigma$, the euclidian plane $\mathbb{C}$ or the hyperbolic plane $\mathcal{H}$ and $\Gamma$ is a discrete group of automorphisms. This induces a covering $p:\mathcal{U}\rightarrow\mathcal{U}/\Gamma$.
For each $\Gamma$ acting on $\mathcal{H}$ we have a polygon $P$ such that $\mathcal{H}$ is tesselated by $P$ under the actions of the elements of $\Gamma$. On the other hand if $P$ is a hyperbolic polygon with a side pairing satisfying certain conditions, then the group $\Gamma$ generated by the side pairing is discrete and $P$ tesselates $\mathcal{H}$ under $\Gamma$.
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CUNEO, Alejandro Javier. "Math for freedom. An original proof of the fundamental theorem of algebra within the ambit of real numbers." Doctoral thesis, Università degli studi di Bergamo, 2013. http://hdl.handle.net/10446/28645.
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At the beginning of my work there’s a description of a particular philosophy of mathematics, the mathematics for freedom, which is used to ultimately justify thoughts and positions about the didactics of mathematics. The main remark is that didactics of mathematics won’t be incisive by remaining on general considerations and thus avoiding the specific features of each topic to be learned. The origin of the didactic hints relative to specific topics can only derive from a profound mathematical study of these topics. The last observation is naturally followed by an explanation and a classification of what a profound mathematical study of a topic is. For many elementary topics in mathematics there is not enough mathematical research already performed at high levels of profundity, and this causes a serious didactic difficulty. For this reason, didactical concerns can motivate mathematical research. This is the case of the fundamental theorem of algebra in the ambit of real numbers. The existing proofs of this result make use of the complex numbers. The use of complex numbers causes that the fundamental ideas on which the proofs rely become very difficult to be identified. This motivates the development of an original proof of this result that avoids the use of complex numbers. As expected the proof I developed enlightens on the fundamental ideas on which the result rests. The zero-level curves that correspond to the remainder of the division between a generic even-degree polynomial and a quadratic polynomial present an interweaved pattern in a region far away enough from the origin, and this implies the existence of an intersection of these zero-level curves and therefore also the existence of a quadratic polynomial dividing the given even-degree polynomial. The proof makes extensive use of the recursive properties of the algebraic expression of the remainder and of continuity.
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Munoz, Susana L. "A Fundamental Unit of O_K." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/133.
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In the classical case we make use of Pells equation to compute units in the ring OF. Consider the parallel to the classical case and the quadratic field extension that creates the ring OK. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units.
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Steggles, L. J. "Extensions of higher-order algebra : fundamental theory and case studies." Thesis, Swansea University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.639103.
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In this thesis we take as our starting point the existing theory of higher-order algebra developed by K. Meinke and B. Möller. We will both apply and extend this theory. To illustrate the use of higher-order algebra as a formalism for formal specification and verification we present two case studies. In the first case study we consider the formal specification of two systolic algorithms for convolution. We formally verify the correctness of these two algorithms using higher-order equational logic and investigate the metamathematics of our verification proofs. The second case study considers the correctness of a dataflow algorithm for computing the Hamming stream. We present a non-constructive higher-order Horn specification of the Hamming stream and develop a semantic proof to verify the correctness of the dataflow algorithm. This second case study illustrates the power of higher-order algebraic methods using non-constructive techniques to capture abstract properties of the Hamming stream. For specification in the large we need to be able to structure specifications in a modular fashion and allow for the reuse of specifications. To this end we present a theory of parameterised higher-order specifications. We take a standard theory of parameterised first-order specifications and extend it to the higher-order case. We demonstrate our theory by presenting a parameterised specification of convolution in which the stream space is a parameter. One of the limitations of higher-order algebra using only ? and → types is the difficulty in modelling objects which are parametric in type, such as polymorphic functions, generic data structures and infinite families of algorithms and architectures. We propose to overcome this limitation by extending the type system of higher-order algebra with limit types. We refer to the resulting theory as higher-order algebra with transfinite types. The idea is that a limit type contains all the types below it in a natural transfinite type hierarchy and thus provides a "universal" type in which all the lower types can be embedded.
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Rocha, Vitail José. "Números complexos e o teorema fundamental da álgebra." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/3683.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The objective of this work is to tell a little bit about the emergence and development of the Fundamental Theorem of Algebra, having as plot the historical context and the formalization of Complex Numbers, which mixes with this theorem. Considering the mathematical rigor in the construction of this subject, which o ered structure for the consolidation of this theorem. This work aims to achieve a more accessible demonstration, due to their necessary presence in high school, but in an axiomatic form.
O objetivo deste trabalho é contar um pouco sobre o surgimento e desenvolvimento do Teorema Fundamental da Álgebra, tendo como enredo o contexto histórico e formaliza ção dos Números Complexos, que se mistura com este teorema. Levando em consideração o rigor matemático na construção deste corpo, o qual ofereceu estrutura para a consolidação deste teorema. Este trabalho busca alcançar uma demonstração mais acessível, devido a sua presença necessária no Ensino Médio, mas de forma axiom ática .
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Mathew, Panakkal J. "Three Topics in Analysis: (I) The Fundamental Theorem of Calculus Implies that of Algebra, (II) Mini Sums for the Riesz Representing Measure, and (III) Holomorphic Domination and Complex Banach Manifolds Similar to Stein Manifolds." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_diss/2.
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We look at three distinct topics in analysis. In the first we give a direct and easy proof that the usual Newton-Leibniz rule implies the fundamental theorem of algebra that any nonconstant complex polynomial of one complex variable has a complex root. Next, we look at the Riesz representation theorem and show that the Riesz representing measure often can be given in the form of mini sums just like in the case of the usual Lebesgue measure on a cube. Lastly, we look at the idea of holomorphic domination and use it to define a class of complex Banach manifolds that is similar in nature and definition to the class of Stein manifolds.
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Costa, Allan Inocêncio de Souza. "Uma demonstração do teorema fundamental da álgebra." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/8723.
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Não recebi financiamento
In this work we explain an elegant and accessible proof of the Fundamental Theorem of Algebra using the Lagrange Multipliers method. We believe this will be a valuable resource not only to Mathematics students, but also to students in related areas, as the Lagrange Multipliers method that lies at the heart of the proof is widely taught.
Neste trabalho expomos uma demonstração acessível e elegante do Teorema Fundamental da Álgebra utilizando o método dos multiplicadores de Lagrange. Acreditamos que este trabalho seria uma fonte valiosa não são para estudantes de Matemática, mas também para estudantes de áreas relacionadas, uma vez que o método dos multiplicadores de Lagrange é amplamente ensinado em cursos de exatas.
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Costa, Antônio Geraldo Lacerda da. "Números complexos: um pouco de história, ensino e aplicações." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7509.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
We present the main properties related to complex numbers. We justify as the history of mathematics can contribute to learning that content. Then we describe briefly the history of complex numbers. We also show where the complex numbers can be applied both within mathematics itself, and beyond.
Neste trabalho apresentamos as principais propriedades referentes aos números complexos. Justificamos como a História da Matemática pode contribuir para a aprendizagem desse conteúdo. Em seguida descreveremos de forma sucinta a história dos números complexos. Mostramos também onde os números complexos podem ser aplicados, tanto dentro da própria Matemática, como fora dela.
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Toledo, André Ferraz de. "Teorema fundamental da álgebra : uma abordagem visual para o Ensino Médio." reponame:Repositório Institucional da UFABC, 2016.
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Orientadora: Profa. Dra. Ana Carolina BoeroDissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2016.
O Teorema Fundamental da Álgebra é um tópico de grande relevância para a Matemática, com o qual o aluno toma contato na 3a série do Ensino Médio. Talvez porque todas as demonstrações conhecidas desse resultado utilizem argumentos que não podem ser apresentados de modo preciso nessa etapa de ensino, sua abordagem em diversos livros didáticos resume-se, basicamente, a destacar algumas de suas consequências e aplicações. O propósito deste trabalho é fornecer um material que possa ser utilizado por professores da Educação Básica no intuito de explorar esse fascinante resultado. Para atingirmos esse objetivo, apresentamos uma breve contextualizaçãohistória do Teorema Fundamental da Álgebra, que serve tanto para apontar sua utilidade em outros ramos da Matemática como também para observar a evolução de certos conceitos matemáticos. Em seguida, apresentamos uma prova rigorosa desse resultado, com o menor nível de complexidade possível, além de duas abordagens alternativas com apelo visual que podem ser utilizadas para apresentar uma justificativa de sua validade aos alunos do Ensino Médio.
The Fundamental Theorem of Algebra is a topic of great relevance to Mathematics, with which the student makes contact in the 3rd grade of High School. Perhaps because all known demonstrations of this result use arguments that can not be accurately presented at this stage of teaching, its approach in several textbooks basically boils down to highlighting some of its consequences and applications. The purpose of this work is to provide a material that can be used by teachers of Basic Education in order to explore this fascinating result. To reach this goal, we present a brief history of the Fundamental Theorem of Algebra, which serves both to point out its usefulness in other branches of mathematics and also to observe the evolution of certain mathematical concepts. Next, we present a rigorous proof of this result, with the lowest level of complexity possible, as well as two alternative approaches with visual appeal that can be used to present a justification of its validity to high school students.
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Nicacio, Nilson Herminio. "Uma justificava da validade do teorema fundamental da ?lgebra para o ensino m?dio." Universidade Federal do Rio Grande do Norte, 2013. http://repositorio.ufrn.br:8080/jspui/handle/123456789/18666.
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Previous issue date: 2013-08-14Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior
Among several theorems which are taught in basic education some of them can be proved in the classroom and others do not, because the degree of difficulty of its formal proof. A classic example is the Fundamental Theorem of Algebra which is not proved, it is necessary higher-level knowledge in mathematics. In this paper, we justify the validity of this theorem intuitively using the software Geogebra. And, based on [2] we will present a clear formal proof of this theorem that is addressed to school teachers and undergraduate students in mathematics
Dentre os v?rios teoremas que s?o ensinados na educa??o b?sica, alguns podem ser demonstrados em sala de aula e outros n?o, devido o grau de dificuldade de sua prova formal. Um exemplo cl?ssico e o Teorema Fundamental da Alg?bra, que n?o ? demonstrado, pois ? necess?rio conhecimentos em Matem?tica de n?vel superior. Neste trabalho, justicamos intuitivamente a validade do Teorema Fundamental da Algebra usando o software Geogebra. E, baseados em [2], apresentamos uma clara demonstra??o formal desse teorema que est? endere?ada aos professores do ensino b?sico e alunos de licenciatura em Matem?tica
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Yokoo, Seiichiro. "Model for a fundamental theory with supersymmetry." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1182.
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Barros, Jéssica Laís Calado de. "O teorema da aplicação de Riemann: uma prova livre de integração." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-13122017-161946/.
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Neste trabalho, seguindo a abordagem de Weierstrass, temos o objetivo de responder a seguinte questão: conhecida a equivalência entre holomorfia e analiticidade no caso complexo, quais propriedades das funções analíticas podem ser obtidas sem assumir tal equivalência? Analisando esta situação, resultados interessantes serão obtidos sem o uso de qualquer teorema de integração complexa e, para alcançar tal objetivo, nossas principais ferramentas serão a teoria de somas não ordenadas de famílias em C e propriedades do índice de caminhos fechados. Entre os resultados apresentados estão os conhecidos Teorema Fundamental da Álgebra, Lema de Schwarz, Teorema de Montel, Teorema da Série Dupla de Weierstrass, Princípio do Argumento, Teorema de Rouché, Teorema da Fatoração de Weierstrass, Pequeno Teorema de Picard e o Teorema da Aplicação de Riemann.In this work, following the Weierstrass\'s approach, we aim to answer the following question: knowing the equivalence between holomorphy and analyticity in the complex case, which properties of analytic functions can be obtained without assuming such equivalence? Through analyzing this situation, interesting results will be obtained without employing of any complex integration theorem and in order to achieve this goal, our main tools will be the theory of unordered sums in C and properties of winding numbers of closed paths. Among the proven results are the well known Fundamental Theorem of Algebra, Schwarz\'s Lemma, Montel\'s Theorem, Weierstrass\'s Double Series Theorem, Argument Principle, Rouché\'s Theorem, Weierstrass\'s Factorization Theorem, Picard\'s Little Theorem and the Riemann\'s Mapping Theorem.
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Costa, Emerson Tomaz da. "O teorema fundamental da álgebra e o software TFA: atividades investigativas no ensino/aprendizagem pelas TICs." Universidade Federal de Juiz de Fora, 2013. https://repositorio.ufjf.br/jspui/handle/ufjf/1161.
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Esta pesquisa, de caráter qualitativo, tem como objetivo investigar, identificar e analisar o uso de Tecnologias da Informação e Comunicação (TICs) no ensino do Teorema Fundamental da Álgebra (TFA) no Ensino Médio (EM). Especificamente, o objetivo é organizar e delinear atividades investigativas em que se utilizem as TICs no estudo dos Polinômios, no que concerne à apreciação de pontos, círculos e curvas de R2 em R2 . As atividades foram desenvolvidas com alunos do 3º ano do Ensino Médio, de uma escola militar, identificando as contribuições que ocorreram no processo de ensino e aprendizagem do TFA com o uso do Software TFA. A fundamentação da Metodologia de Pesquisa quanto ao uso das TICs na Educação Matemática pautou-se nas ideias de Miskulin (1999), Borba e Penteado (2010) e outros. O resultado da pesquisa revela uma expressiva necessidade de atividades inovadoras com o uso pelas TICs no estudo dos Polinômios, em que aluno e professor possam interagir de forma que, a aprendizagem do objeto matemático e a prática pedagógica, se torne evidente nesse processo. Dessa forma, como Produto Educacional, resultado da presente Dissertação, são apresentadas atividades investigativas que podem ser desenvolvidas no Ensino Médio, no estudo dos Polinômios.
This search with qualitative character has as an aims to investigate, identify and analyze the use of information and Communication Technologies (ICTs) in teaching the Fundamental Theorem of algebra (TFA) in high school (in). Specifically, the goal is to organize and outline investigative activities in wich ICTs are used in the study of polynomials, concerning the assessment of points, circles and curve of R2 at R2. The activities were developed with students of the third of high year school, a military school, by identifying the contributions that have occurred in the process of teaching an learning software rising the TFA. The basis of the research methodology for the use of ICT in mathematics education was based on the ideas of Miskulin (1999), Borba, Penteado (2010) and others. The result of the research reveals a significant need for innovative activities using ICT in the study of polynomials, where students and teachers can interact so that, learning the objective mathematical and pedagogical practice, this process becomes evident. Thus, educational product as a result of this dissertation are presented research that can be developed in high school, in the study if polynomials.
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Moreira, Charles dos Anjos [UNESP]. "Linguagem de categorias e o Teorema de van Kampen." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/152195.
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Esse trabalho trata de elementos da Topologia Algébrica, a qual tem como fundamental aplicação abordar questões acerca de Espaços Topológicos sob o ponto de vista algébrico. Uma das questões é tentar responder se dois espaços topológicos X e Y são homeomorfos. Neste sentido, o grupo fundamental é uma ferramenta algébrica útil por se tratar de um invariante topológico. Além disso, apresentamos o Teorema de van Kampen do ponto de vista da Linguagem de Categorias e Funtores.
This work treats of elements of the Algebraic Topology, which has as fundamental application to approach subjects concerning Topological Spaces under the algebraic point of view. One of the subjects is to try to answer if two topological spaces X and Y are homeomorphics. In this sense, the fundamental group is an useful algebraic tool for treating of an topological invariant. In addition, we presented the van Kampen's Theorem of the point of view of the language of Categories and Functors.
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Aguiar, Marcia. "O percurso da didatização do pensamento algébrico no ensino fundamental: uma análise a partir da transposição didática e da teoria antropológica do didático." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/48/48134/tde-01042015-135259/.
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O ensino de álgebra nos três últimos anos do Ensino Fundamental tem se reduzido a um momento destinado ao treino e à fixação de regras e procedimentos algébricos. Ao que parece, os livros didáticos corroboram com essa visão do ensino de álgebra. Por outro lado, sabemos que no livro didático estão presentes algumas intenções didáticas legitimadas, de certa forma, por todos aqueles que participam do processo de ensino. Ao professor, que muitas vezes só possui o livro didático como material para preparar as suas aulas, cabe transformá-lo no saber que será ensinado na sala de aula. A álgebra é uma ciência ensinada predominantemente na escola e é relevante para capacitar os sujeitos a compreender o desenvolvimento científico e tecnológico atual. Por isso, parece-nos que o ensino de álgebra nos 7º, 8º e 9º anos do Ensino Fundamental deveria contribuir para a construção de um pensamento algébrico, superando as práticas rotinizadas. Assim, o objetivo do nosso trabalho é analisar de que modo os livros didáticos desse nível de ensino permitem a construção do pensamento algébrico. Ou seja, investigar o percurso de didatização da álgebra no Ensino Fundamental ou, mais propriamente, nos livros didáticos. Para essa análise utilizamos a Teoria da Transposição Didática e a Teoria Antropológica do Didático, propostas por Yves Chevallard. Essas teorias propiciaram uma análise mais aprofundada sobre os materiais e também demonstram ser uma ferramenta consistente para auxiliar o professor na sua prática pedagógica. Analisamos três materiais pedagógicos: dois livros didáticos, que vieram da lista de livros aprovados no PNLD-2011 e o Caderno elaborado pelo governo do Estado de São Paulo proveniente da proposta São Paulo Faz Escola. Com essas análises conseguimos perceber que a programabilidade do saber legitimada pela noosfera impossibilita muitas inovações na didatização referente ao ensino de álgebra, e que alguns livros ainda mantêm o ensino de álgebra voltado para o treino de procedimentos e resoluções. Por outro lado, também conseguimos encontrar outros percursos de didatização nos quais está presente um ensino voltado para o desenvolvimento do pensamento algébrico.The teaching of algebra in the last three years of elementary school has been reduced to a point aimed at training and to set rules and algebraic procedures. Apparently, textbooks corroborate this view of teaching algebra. On the other hand, we know that in the textbook are didactic intentionalities, in a way, to all who participate in the teaching process. In the teacher, who often only have the textbook and material to prepare their lessons, will lie the responsability to turn it in the knowledgment which will be taught in the classroom. Algebra is a science predominantly taught in the school and it is relevant to enable the students to understand the current technological and scientific development. Therefore, it seems that the teaching of algebra in 7th, 8th and 9th grades of elementary school should contribute to the construction of an algebraic thinking, overcoming the routinized practices. The objective of our work is to analyze how that grade level books allow the construction of algebraic thinking. In other words, to investigate the route of didactization algebra in elementary school or, more properly, in textbooks. For this analysis, we will use the theories of Didactic Transposition and Anthropological Theory of Didactic proposed by Yves Chevallard. These theories provided a deeper analysis of the materials and also prove to be a consistent tool to assist teachers in their teaching. We analyze three teaching materials: two textbooks, which came from the list of approved books in PNLD-2011 and the Booklet prepared by the state government of São Paulo from the proposed São Paulo Faz Escola. With this analysis we can see that the programmability of knowledge legitimized by the noosphere prevents many innovations in didactization concerning the teaching of algebra and some books still keeps teaching algebra facing the training procedures and resolutions. On the other hand, we did find other paths of didactization in which an education directed to the development of algebraic thinking prevails.
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Ballarin, Clemens Michael. "Computer algebra and theorem proving." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624429.
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Kikuchi, Luzia Maya. "Obstáculos à aprendizagem de conceitos algébricos no ensino fundamental: uma tentativa de aproximação entre os obstáculos epistemológicos e a teoria dos campos conceituais." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/48/48134/tde-23102012-131046/.
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Esta pesquisa tem como objetivo investigar os obstáculos à aprendizagem de Álgebra no Ensino Fundamental com o intuito de ajudar na compreensão das dificuldades envolvidas no aprendizado desse tópico. Para tal efeito, foi feito um levantamento da bibliografia relacionada à construção da ideia de obstáculo, erros e dificuldades relativos à aprendizagem de Matemática no Brasil e no exterior. Através desse levantamento, constatou-se que elevados índices de erros cometidos por alunos do Ensino Fundamental em países como a Inglaterra e os Estados Unidos, em problemas matemáticos relacionados à Álgebra, aproximam-se da realidade brasileira, como mostram os dados do último relatório fornecido pelo INEP (Instituto Nacional de Estudos e Pesquisas). Para confirmar esses fatos, foi aplicada uma pesquisa entre os alunos do 9º ano do Ensino Fundamental, da rede pública do estado de São Paulo, com questões adaptadas do SARESP (Sistema de Avaliação do Rendimento Escolar do Estado de São Paulo). Para efeitos de análise, os obstáculos encontrados foram classificados sob a perspectiva de quatro categorias (Epistemológicos, Didáticos, Psicológicos e Ontogenéticos) definidas por Guy Brousseau para o ensino de Matemática. Utilizou-se também o aspecto conceitual do domínio do funcionamento cognitivo do \"sujeito-emsituação\", cujas bases são advindas e ampliadas da teoria piagetiana de operações lógicas e das estruturas gerais do pensamento, conhecida como a Teoria dos Campos Conceituais de Gérard Vergnaud. Esta pesquisa trata do conhecimento-em-ação e sua influência no aprendizado de Álgebra, o que é um teorema-em-ação e uma invariante operatória, além de mostrar o funcionamento dos esquemas. Desta forma, foi possível oferecer alguns indicativos ao professor do que seria necessário para compreender as dificuldades e obstáculos que envolvem o aprendizado de Álgebra e conscientizá-lo de que é relevante um acompanhamento em longo prazo e aprofundado de seus alunos para realmente obter respostas concretas sobre os obstáculos epistemológicos e os aspectos psicológicos envolvidos na aprendizagem, como definidos por Vergnaud (1994).The aim of this study is to examine obstacles and understand difficulties involved in the learning of Algebra in elementary school. The work consists in a review of the academic production and theoretical studies concerning the construction of the idea of obstacles, difficulties and errors in the learning of Mathematics in Brazil and overseas. The analyses of the studies revealed that a high level of errors made by students in elementary school in some countries, such as England and the United States, on mathematical problems related to Algebra, are close to the Brazilian reality, as shown by the data of the last report provided by INEP (National Institute of Studies and Research). Also an empirical study was applied among students in the 9th grade of elementary school, all from public schools of Sao Paulo. The questions applied in this study have been adapted from SARESP (System for Evaluation of Educational Achievement of Sao Paulo). For analysis purposes, the obstacles encountered were classified from the perspective of four categories (Epistemological, Educational, Psychological and Ontogenetic) defined by Guy Brousseau for teaching mathematics in addition to the conceptual aspect in the field of cognitive functioning of \"subject in a situation\", whose bases are arisen and extended from Piaget\'s theory of logical operations and the general structures of thought, known as Theory of Conceptual Fields (Vergnaud, 1990). This study also treats with knowledge-in-action and their influence on the learning of Algebra, what are theorems-in-action and operative invariants in addition to showing the function of schemes. Thus it was possible to offer some indications for teachers and helping them to understand difficulties and obstacles involving in the learning of Algebra. In addition, it is relevant to keep in mind that a long term and careful tracking of their students must be required. In that way, it is possible to infer answers involving obstacles on the epistemological and psychological aspects, as defined by Vergnaud (1994).
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Fors, Hannes. "Group representations and Maschke’s Theorem." Thesis, Uppsala universitet, Algebra och geometri, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-388121.
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Lac, Jacquelyn Ha. "Chinese remainder theorem and its applications." CSUSB ScholarWorks, 2008. https://scholarworks.lib.csusb.edu/etd-project/3373.
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Mellquist, Ebba. "Galois Theory and the Artin-Schreier Theorem." Thesis, Uppsala universitet, Algebra och geometri, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414097.
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Singh, Jesper. "On the fundamental theorem of calculus." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-103809.
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The Riemann integral has many flaws, some that becomes visible in the fundamental theorem of calculus. The main point of this essay is to introduce the gauge integral, and prove a much more suitable version of that theorem.Riemannintegralen har många brister. Vissa utav dessa ser man i integralkalkylens huvudsats. Huvudmålet med denna uppsats är att introducera gauge integralen och visa en mer lämplig version av huvudsatsen.
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Matsson, Isak. "The Nichols-Zoeller Theorem for Quasi-Hopf Algebras." Thesis, Uppsala universitet, Algebra och geometri, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-388631.
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Gustavsson, Bim. "Representations of Finite-Dimensional Algebras and Gabriel’s Theorem." Thesis, Uppsala universitet, Algebra och geometri, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-395660.
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Précenth, Rasmus. "The (1, 2, 4, 8)-Theorem for Composition Algebras." Thesis, Uppsala universitet, Algebra och geometri, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-201501.
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Cuszynski-Kruk, Mikolaj. "On Frobenius Theorem and Classication of 2-Dimensional Real Division Algebras." Thesis, Uppsala universitet, Algebra och geometri, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414086.
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Schweighofer, Markus. "Iterated rings of bounded elements and generalizations of Schmüdgen's theorem." [S.l. : s.n.], 2002. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB9911683.
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McCallum, Rupert Gordon Mathematics & Statistics Faculty of Science UNSW. "Generalisations of the fundamental theorem of projective geometry." Publisher:University of New South Wales. Mathematics & Statistics, 2009. http://handle.unsw.edu.au/1959.4/43385.
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The fundamental theorem of projective geometry states that a mapping from a projective space to itself whose range has a sufficient number of points in general position is a projective transformation possibly combined with a self-homomorphism of the underlying field. We obtain generalisations of this in many directions, dealing with the case where the mapping is only defined on an open subset of the underlying space, or a subset of positive measure, and dealing with many different spaces over many different rings.
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Kitani, Patricia Massae. "Aplicações de metodos de topologia algebrica em teoria de grupos." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306933.
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Orientador: Dessislava Hristova KochloukovaDissertação (mestrado) - Universidade Estadual de Campinas. Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho consistiu no estudo das aplicações de topologia algébrica (recobrimentos, teorema de Van Kampen) em teoria de grupos e também, no estudo detalhado do resultado de R. Bieri, R. Strebel [Proc. London Math. Soc. (3) 41 (1980), no. 3, 439¿464], que para um grupo G do tipo FP2, ou G contém subgrupo livre não cíclico ou para qualquer subgrupo normal N C G tal que Q = G/N é abeliano, N/[N,N] é um ZQ-módulo manso via conjugação. A definição de módulo manso usa o invariante de Bieri-Strebel §A(Q), nesse caso A = N/[N,N]
Abstract: This work consisted of the study of the applications of algebraic topology (covering maps, Van Kampen theorem) in group theory and also, in the detailed study of a result of R. Bieri, R. Strebel [Proc. London Math. Soc. (3) 41 (1980), no. 3, 439¿464], that for a group G of type FP2, either G has a free non-cyclic subgroup or for any normal subgroup N C G such that Q = G/N is abelian, N/[N,N] is a tame ZQ-module where Q acts via conjugation. The definition of tame module uses the Bieri-Strebel invariant §A(Q), in this case A = N/[N,N]
Mestrado
Algebra
Mestre em Matemática
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Granberg, Olsson Mattias. "A Model-Theoretic Proof of Gödel's Theorem : Kripke's Notion of Fulfilment." Thesis, Stockholms universitet, Matematiska institutionen, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-157490.
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The notion of fulfilment of a formula by a sequence of numbers, an approximation of truth due to Kripke, is presented and subsequently formalised in the weak arithmetic theory IΣ1, in some detail. After a number of technical results connecting the formalised notion to the meta-theoretical one a version of Gödel’s Incompleteness Theorem, that no consistent, recursively axiomatisable, Σ2-sound extension T of Peano arithmetic is complete, is shown by construction of a true Π2-sentence and a model of T where it is false, yielding its independence from T. These results are then generalised to a more general notion of fulfilment, proving that IΣ1 has no complete, consistent, recursively axiomatisable, Σ2-sound extensions by a similar construction of an independent sentence. This generalisation comes at the cost of some naturality, however, and an explicit falsifying model will only be obtained under additional assumptions. The aim of the thesis is to reproduce in some detail the notions and results developed by Kripke and Quinsey and presented by Quinsey and Putnam. In particular no novel results are obtained.
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Cohen, Jeremy S. (Jeremy Stein) 1975. "Implementation and application of the fundamental theorem of probability." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/46277.
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Thesis (M.Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (leaves 64-65).
The "RIK" (Reasoning with Incomplete Knowledge) algorithm, a mathematical programming based algorithm for performing probabilistic inference on (possibly) incompletely specified systems of discrete events is reviewed and implemented. Developed by Myers, Freund, and Kaufman, it is a tractable reformulation of the computational approach implicit to the Fundamental Theorem of Probability as stated by De Finetti and extended by Lad, Dickey and Rahman. Enhancements to the original algorithm are presented and several applications of the algorithm to real-world systems including fault trees and belief networks are explored. The system is solved successfully for moderately large problems, providing practical information for system designers coping with uncertainty.
by Jeremy S. Cohen.
M.Eng.and S.B.
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Runge, Piotr. "A Comparison Theorem for the Topological and Algebraic Classification of Quaternionic Toric 8-Manifolds." DigitalCommons@USU, 2009. https://digitalcommons.usu.edu/etd/501.
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In order to discuss topological properties of quaternionic toric 8-manifolds, we introduce the notion of an algebraic morphism in the category of toric spaces. We show that the classification of quaternionic toric 8-manifolds with respect to an algebraic isomorphism is finer than the oriented topological classification. We construct infinite families of quaternionic toric 8-manifolds in the same oriented homeomorphism type but algebraically distinct. To prove that the elements within each family are of the same oriented homeomorphism type, and that we have representatives of all such types of a quaternionic toric 8-manifold, we present and use a method of evaluating the first Pontrjagin class for an arbitrary quaternionic toric 8-manifold.
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Reff, Nathan. "A generalization of the Birkhoff-von Neumann theorem /." Online version of thesis, 2007. http://hdl.handle.net/1850/5967.
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Delbaen, Freddy, and Walter Schachermayer. "The fundamental theorem of asset pricing for unbounded stochastic processes." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/850/1/document.pdf.
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The Fundamental Theorem of Asset Pricing states - roughly speaking - that the absence of arbitrage possibilities for a stochastic process S is equivalent to the existence of an equivalent martingale measure for S. It turns out that it is quite hard to give precise and sharp versions of this theorem in proper generality, if one insists on modifying the concept of "no arbitrage" as little as possible. It was shown in [DS94] that for a locally bounded R^d-valued semi-martingale S the condition of No Free Lunch with Vanishing Risk is equivalent to the existence of an equivalent local martingale measure for the process S. It was asked whether the local boundedness assumption on S may be dropped. In the present paper we show that if we drop in this theorem the local boundedness assumption on S the theorem remains true if we replace the term equivalent local martingale measure by the term equivalent sigma-martingale measure. The concept of sigma-martingales was introduced by Chou and Emery - under the name of "semimartingales de la classe (Sigma_m)". We provide an example which shows that for the validity of the theorem in the non locally bounded case it is indeed necessary to pass to the concept of sigma-martingales. On the other hand, we also observe that for the applications in Mathematical Finance the notion of sigma-martingales provides a natural framework when working with non locally bounded processes S. The duality results which we obtained earlier are also extended to the non locally bounded case. As an application we characterize the hedgeable elements. (author's abstract)Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
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Näslund, Marcus. "The Hales-Jewett theorem and its application to further generalisations of m, n, k-games." Thesis, Uppsala universitet, Algebra och geometri, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-202188.
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Thomas, Teri M. "A Generalization of Sylow’s Theorem." Youngstown State University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1256911896.
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Alves, Aline de Paula 1985. "Desmistificando o teorema fundamental da álgebra." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306555.
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Orientador: Sergio Antonio TozoniDissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica
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Resumo: Para viabilizar um contexto de desmistificação do Teorema Fundamental da Álgebra elaboramos esta dissertação por meio de pesquisas bibliográficas, que apresentam o referido teorema inserido no percurso histórico do desenvolvimento matemático, em especial, da resolução das equações polinomiais. Remetemo-nos, então, a uma investigação e comprovação minuciosa das definições, teoremas, lemas, proposições e propriedades sobre os números complexos. Neste quadro, caminhamos para uma abordagem sobre continuidade e limites infinitos, destacando formalmente os itens essenciais para a demonstração do Teorema Fundamental da Álgebra utilizando basicamente elementos da matemática elementar. Por fim, apresentamos resultados provenientes do teorema supracitado e uma breve perspectiva de como este tema é desenvolvido no ensino médio. Enfim, visamos colaborar para que o enunciado de teorema e sua demonstração sejam mais presentes e assumam seu papel de importância no ensino, sem afligir aqueles que dele necessitem de sua compreensão ou que estejam envolvidos em sua transmissão
Abstract: To enable a context of demystification of the Fundamental Theorem of Algebra, we elaborated this thesis through bibliographic researches, which introduce the cited theorem in the historical parth of the mathematical development, specially in the resolution of polynomial equations. We worked in a thorough investigation of definitions, theorems, lemmas, propositions and properties of the complex numbers. In this context, we conducted a study about continuity and infinite limits, formally presenting the most important steps in the demonstration of the Fundamental Theorem of Algebra, using only elements of elementary mathematics. Finally, we present results about the above theorem and a brief overview of how this theme is developed in high school. In this work, our objective was to contribute to make the theorem and its proof more present and take their role of importance in teaching, without afflicting those who need their understanding or who are involved in its transmission
Mestrado
Matemática em Rede Nacional
Mestra em Matemática em Rede Nacional
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La, Fleur Stephen J. "Some fundamentals for Nielsen theory on torus configuration spaces." abstract and full text PDF (free order & download UNR users only), 2008. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1453597.
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Kaufmann, Stefan-Harald. "Does the parameter represent a fundamental concept of linear algebra?" Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80339.
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In mathematics the parameter is used as a special kind of a variable. The classification of the terms \"variable\" and \"parameter\" is often done by intuition and changes due to different situations and needs. The history of mathematics shows that these two terms represent the same abstract object in mathematics. In today´s mathematics, compared to variables, the parameter is declared as an unknown
constant measure. This interpretation of parameters can be used in set theory for describing sets with an infinite number of elements. Due to this perspective the structure of vector spaces can be developed as a special structured set theory. Further, the concept of parameters can be seen as a model for developing mathematics education in linear algebra.
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Li, Wenda. "Towards justifying computer algebra algorithms in Isabelle/HOL." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/289389.
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As verification efforts using interactive theorem proving grow, we are in need of certified algorithms in computer algebra to tackle problems over the real numbers. This is important because uncertified procedures can drastically increase the size of the trust base and under- mine the overall confidence established by interactive theorem provers, which usually rely on a small kernel to ensure the soundness of derived results. This thesis describes an ongoing effort using the Isabelle theorem prover to certify the cylindrical algebraic decomposition (CAD) algorithm, which has been widely implemented to solve non-linear problems in various engineering and mathematical fields. Because of the sophistication of this algorithm, people are in doubt of the correctness of its implementation when deploying it to safety-critical verification projects, and such doubts motivate this thesis. In particular, this thesis proposes a library of real algebraic numbers, whose distinguishing features include a modular architecture and a sign determination algorithm requiring only rational arithmetic. With this library, an Isabelle tactic based on univariate CAD has been built in a certificate-based way: external, untrusted code delivers solutions in the form of certificates that are checked within Isabelle. To lay the foundation for the multivariate case, I have formalised various analytical results including Cauchy's residue theorem and the bivariate case of the projection theorem of CAD. During this process, I have also built a tactic to evaluate winding numbers through Cauchy indices and verified procedures to count complex roots in some domains. The formalisation effort in this thesis can be considered as the first step towards a certified computer algebra system inside a theorem prover, so that various engineering projections and mathematical calculations can be carried out in a high-confidence framework.
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Giampieri, Marco. "System of Imprimitivity and Mackey's Theorem." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23445/.
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The aim of this thesis is to study and classify the representations of the Poincaré group, whose elements are all the isometries of the Minkowski Spacetime. These representations are important in particle physics since
they can be considered the mathematical equivalent of the elementary particles of the Standard Model, hence it is possible to identify and classify all
such particles through the analysis of the Poincaré representations. In order to achieve this we introduce the concepts of group action, representation and semidirect product of groups and the structure of Lie group and Lie algebra. With those preliminary concepts we compute the representations of the key group SL(2,C) and introduce the fundamentals of the system of imprimitivity. Finally we obtain, through the Mackey’s Theorem, information on the representations of the semidirect product of two groups starting from the representations of the groups themselves. We apply those results to the Poincaré group, which is a semidirect product of translations and Lorentz transformations, and conclude with a brief classification of the Poincaré representations.
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Lagro, Matthew Patrick. "A Perron-Frobenius Type of Theorem for Quantum Operations." Diss., Temple University Libraries, 2015. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/339694.
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MathematicsPh.D.
Quantum random walks are a generalization of classical Markovian random walks to a quantum mechanical or quantum computing setting. Quantum walks have promising applications but are complicated by quantum decoherence. We prove that the long-time limiting behavior of the class of quantum operations which are the convex combination of norm one operators is governed by the eigenvectors with norm one eigenvalues which are shared by the operators. This class includes all operations formed by a coherent operation with positive probability of orthogonal measurement at each step. We also prove that any operation that has range contained in a low enough dimension subspace of the space of density operators has limiting behavior isomorphic to an associated Markov chain. A particular class of such operations are coherent operations followed by an orthogonal measurement. Applications of the convergence theorems to quantum walks are given.
Temple University--Theses
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Bonadiman, Adriana. "Álgebra no ensino fundamental : produzindo significados para as operações básicas com expressões algébricas." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2007. http://hdl.handle.net/10183/11228.
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Nesta dissertação destacamos nossa preocupação com o ensino e aprendizagem da álgebra elementar, sempre muito presente em nossa prática docente. Nosso principal objetivo foi a elaboração, implementação e validação de uma proposta didática para o desenvolvimento de um ensino que promovesse a compreensão das operações básicas com expressões algébricas no Ensino Fundamental. De acordo com os referenciais teóricos utilizados buscamos construir uma proposta que contemplasse a produção de significados para a atividade algébrica em um ambiente de aprendizagem cooperativa, fazendo uso de representações múltiplas e de materiais manipulativos juntamente com a resolução de situações-problema. A implementação da proposta foi desenvolvida em duas fases: a primeira, enfocando o uso das letras em álgebra e a segunda voltada para a produção de significados para as operações com expressões algébricas. Apresentamos o resultado da investigação realizada com um grupo de alunos do segundo ano do terceiro ciclo (equivalente à 7ª série) do Ensino Fundamental numa escola da Rede Municipal de Ensino de Porto Alegre. Este estudo mostrou que a proposta implementada contribuiu para o aprimoramento do pensamento algébrico dos alunos que produziram significados para as operações realizadas com expressões algébricas, adquiriram desenvoltura no uso das letras e compreenderam algumas propriedades algébricas, dentre elas a comutatividade da multiplicação e a distributividade da multiplicação em relação à adição, além de estabelecerem condições para a realização da adição e subtração entre expressões algébricas. Notamos, ainda, o progresso dos alunos quanto à autonomia presente nos processos de observação, levantamento de hipóteses, elaboração de conclusões e de justificações. Concluímos, destacando a relevância desta pesquisa no âmbito do trabalho do professor, relacionada à construção de uma atitude de busca de compreensão dos processos de aprendizagem de seus alunos.This work emphasizes the concern about teaching and learning elementary algebra. The main purpose was the elaboration, implementation and legalization of a didatic proposal having in mind a teaching development that would promote the understanding of basic expressions with algebraic operations in the Elementary School. Based on the chosen theoretical references forementioned, we intended to motivate students to learn algebra in a cooperative directed way through the use of multiple representative allusions with a wide deversity of symbolic, visual and material resources. This proposal implementation was developed in two phases: First it emphasized the algebra letter usage and second the significance production related to algebraic expressions. The accomplished investigation result was presented with a first grade group of students in a county school. This investigation showed that the implemented proposal improved the students algebraic thinking, also they started giving significance to the accomplished operation with algebraic expressions and acquired agility in using letters and understanding some of the algebraic properties including commutation in multiplication and distributions related to multiplication and additions besides establishing conditions to elaborate addition and subtraction among algebraic expressions. It was also noticed the students progress concerning the observation process, hipothesis, propositions, feeling of accomplisments and justifications autonomy. This research took into account the teacher’s work considering the construction of an inquisitive searching attitude and a comprehensive understanding.
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Altmann, Kristina. "Centralisers of fundamental subgroups." Phd thesis, kostenfrei, 2007. http://elib.tu-darmstadt.de/diss/000875.
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Keppke, Charston Lima. "Álgebra nos currículos do ensino fundamental." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11518.
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Secretaria da Educação do Estado de São Paulo
This essay, which is inserted in the research of the group Curricular Innovations in Elementary Education and High School , composed by postgraduate students of the Mathematical Education Program of Post-Graduates, is aimed at identifying how Algebra has appeared in the curricula of Elementary Education in the last 50 years. Its purpose is to comparatively analyze official documents that guided the curricular composition of Mathematics in the Elementary Education in the last decades, and the view of teachers currently working in private and state-owned schools. In order to present a theoretical framework, we introduce the propositions of some authors that discuss Algebra teaching. Consecutively, we investigate the curricular recommendations on Algebra teaching through documental research, relating and comparing the indications presented by the Curricular Guides, Curricular Proposals and the National Curricular Parameters (PCNs). Finally, through the application of questionnaires to a group of teachers who work with 6th, 7th and 8th grades in Sao Paulo municipal and state-owned schools, we try to identify the teachers view of the theme and what it reveals about the Algebra they teach their students. The results show that most teachers consider Algebra as an important element for the development of generalization, abstraction, and interpretation abilities, in which they find serious difficulties. The most frequent problem is the lack of understanding of the use of letters and barriers to generalize and abstract. Aspects such as a strong belief in the cultural value of contents being the dearest learning element to the teachers; the structuralistic view on Algebra; and the mechanization as the most common technique present in the answers, help corroborate these difficulties. The PCNs are pointed out as the reference materials most used for class planning, although some of the aspects emphasized in this document are not frequently mentioned by the teachers. This denotes a historical lack of a deeper involvement with curricular questions by the teachers, as well as the need for a better training of these educators, in order that a critical reflection on the construction of the curriculum may be achieved
O presente trabalho, que se insere no grupo de pesquisa Inovações Curriculares nos Ensinos Fundamental e Médio , composto por alunos de mestrado e de doutorado do Programa de Estudos Pós-Graduados em Educação Matemática, tem como objetivo identificar como a Álgebra aparece nos currículos do ensino fundamental nos últimos 50 anos e realizar uma análise comparativa entre os documentos oficiais que guiam a composição curricular de Matemática no Ensino Fundamental nas últimas décadas e o depoimento de professores que atuam na rede pública e particular. Inicialmente, para o embasamento teórico, apresentamos, por meio de revisão bibliográfica, as proposições de alguns autores que discutem o ensino de Álgebra. Em seguida, investigamos quais as recomendações curriculares relativas ao ensino da Álgebra, por meio de pesquisa documental, relatando e comparando as indicações dos Guias Curriculares, das Propostas Curriculares e dos Parâmetros Curriculares Nacionais. Finalmente, por meio de aplicação de questionários a um grupo de professores que atuam na rede pública municipal e estadual de São Paulo, em turmas dos três últimos anos do Ensino Fundamental, buscamos identificar a visão dos professores sobre o tema Álgebra e o que revelam em relação à Álgebra que ensinam a seus alunos. Os resultados apontam que os professores consideram, em sua maioria, a Álgebra como um elemento importante para o desenvolvimento de habilidades de generalização, abstração, interpretação, mas que encontram severas dificuldades justamente no desenvolvimento dessas habilidades. Os problemas mais freqüentes apontados são: incompreensão no uso de letras e barreiras para generalizar e abstrair. Corroboram essas dificuldades aspectos como a forte crença no valor cultural dos conteúdos como o aspecto da aprendizagem mais valorizado pelos professores; a visão estruturalista da Álgebra e a mecanização como a técnica mais presente nas respostas. Os PCN são apontados como os materiais mais utilizados na preparação das aulas, embora haja aspectos altamente enfatizados nesse documento que pouco são citados pelos professores, o que denota, historicamente, a falta de um maior envolvimento dos professores em questões curriculares, bem como a necessidade de existir um maior preparo dos docentes para que haja um envolvimento consciente e uma reflexão crítica na construção do currículo
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Bembé, Daniel. "Algebraic certificates for Budan's theorem." Diss., lmu, 2011. http://nbn-resolving.de/urn:nbn:de:bvb:19-139848.
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Uramoto, Takeo. "A Modified Completeness Theorem of KAT and Decidability of Term Reducibility." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188452.
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Sracic, Mario F. "A Self-Contained Review of Thompson's Fixed-Point-Free Automorphism Theorem." Youngstown State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1403191722.
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Brooke, Phillip James. "A timed semantics for a hierarchical design notation." Thesis, University of York, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.298382.
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Vasireddy, Jhansi Lakshmi. "Applications of Linear Algebra to Information Retrieval." Digital Archive @ GSU, 2009. http://digitalarchive.gsu.edu/math_theses/71.
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Some of the theory of nonnegative matrices is first presented. The Perron-Frobenius theorem is highlighted. Some of the important linear algebraic methods of information retrieval are surveyed. Latent Semantic Indexing (LSI), which uses the singular value de-composition is discussed. The Hyper-Text Induced Topic Search (HITS) algorithm is next considered; here the power method for finding dominant eigenvectors is employed. Through the use of a theorem by Sinkohrn and Knopp, a modified HITS method is developed. Lastly, the PageRank algorithm is discussed. Numerical examples and MATLAB programs are also provided.