Thesis (Honors)--College of William and Mary, 2008. / Includes bibliographical references (leaf 47). Also available via the World Wide Web.

Thesis (Ph.D.) - University of Glasgow, 2008. / Ph.D. thesis submitted to the Department of Mathematics, Faculty of Information and Mathematical Sciences, University of Glasgow, 2008. Includes bibliographical references. Print version also available.

Thesis (M.S.) -- Mississippi State University. Department of Computer Science. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1960. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Made available in DSpace on 2015-12-10T14:22:23Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-02-24. Added 1 bitstream(s) on 2015-12-10T14:28:28Z : No. of bitstreams: 1 000853539.pdf: 809931 bytes, checksum: 9d8238626da19307dd37676a2879339e (MD5) / Este trabalho aborda conceitos básicos de Álgebra Linear e suas aplicações no desenvolvimento da Teoria de Códigos Corretores de Erros. O uso desta ferramenta matemática simpli ca a geração e a decodi cação dos códigos lineares. Destacamos também a importância de se trabalhar com este tema na educação básica / The present work addresses basic concepts of Linear Algebra and its applications in the development of the Theory of Error Correcting Codes. The use of this mathematical tool simpli es the generation and decoding of linear codes. This dissertation also highlights the importance of working with this subject in high school

A number of significant problems require the solution of a system of linear equations Ax = b in which A is large, highly sparse, nonsymmetric, and unstructured. Several iterative methods which are applicable to nonsymmetric and indefinite problems are applied to a suite of test problems derived from simulations of actual bipolar circuits and to a viscous flow problem. Methods tested include Craig’s method, GMRES(k), BiCGSTAB, QMR, KACZ (a row-projection method) and LSQR. The convergence rates of these methods may be improved by use of a suitable preconditioner. Several such techniques are considered, including incomplete LU factorization (ILU), sparse submatrix ILU, and ILU allowing restricted fill in bands or blocks. Timings and convergence statistics are given for each iterative method and preconditioner. / Master of Science

Orientador: Carina Alves / Banca: Eliris Cristina Rizziolli / Banca: Cristiane Alexandra Lázaro / Resumo: O presente trabalho mostra a importância da Álgebra Linear e em particular da Teoria de Matrizes, Determinantes e Sistemas Lineares para resolver problemas práticos e contextualizados. Mostramos aplicações em circuitos elétricos, no balanceamento de equações químicas, nos modelos aberto e fechado de Leontief, e no funcionamento do GPS. Ainda, foi aplicado um plano de aula para os alunos do segundo ano do Ensino Médio e apresentamos sugestões de exercícios de vestibulares sobre os tópicos estudados, para serem abordados em sala de aula / Abstract: The present work shows the importance of Linear Algebra and in particular of Matrix Theory, Determinants and Linear Systems to solve practical and contextualized problems. We show applications in electrical circuits, in the balancing of chemical equations, in the open and closed models of Leontief, and in the operation of GPS. Also, a lesson plan was applied to the students of the second year of high school and we presented suggestions of exercises of vestibular about the topics studied, to be approached in the classroom / Mestre

Orientador: Marcelo de Carvalho Borba / Banca: Henrique Lazari / Banca: José Luiz Magalhães de Freitas / Banca: Marco Aurélio Kalinke / Banca: Marcus Vinicius Maltempi / Resumo: O objetivo desta pesquisa é compreender o papel das tecnologias digitais (TD) nos processos educativos associados a disciplinas de Álgebra Linear de quatro cursos de Licenciatura em Matemática a distância vinculados à Universidade Aberta do Brasil (UAB), no contexto de seus Ambientes Virtuais de Aprendizagem (AVA). Trata-se de uma pesquisa qualitativa. Perspectivas associadas aos modos de descrição em Álgebra Linear, à noção de seres-humanos-com-mídias, à distância transacional e ao papel da interação e da colaboração na modalidade a distância fornecem sustentação teórica ao estudo e ao processo analítico. A Teoria Enraizada é utilizada para conduzir a análise de dados, que foram produzidos a partir de quatro fontes: observação em ambientes virtuais de aprendizagem, entrevistas, projetos político pedagógicos e notas da pesquisadora. Os resultados permitem inferir que há dois papéis em evidência, cada um analisado em uma das categorias, intituladas "TD como promotoras de variedade comunicacional" e "TD na construção de materiais didáticos digitais". Da primeira categoria foram exploradas quatro propriedades: conteúdo, agentes, temporalidade e avaliação. Da segunda, três: conteúdo, natureza e recursos envolvidos. Posteriormente, as duas categorias foram integradas em uma categoria central que sugere que as TD, a internet e o uso do AVA podem transformar esse último em Material Didático Digital Interativo (MDDI) a partir do registro automático das interações. Esta transformação pode se dar via diferentes linguagens, como a textual, a audiovisual ou a multimodal. Do ponto de vista da disciplina de Álgebra Linear, notou-se um desequilíbrio em termos de abordagem dos modos de descrição (formal, algébrico e geométrico) e destacou-se a necessidade de estimular o movimento entre eles, que pode ser favorecido pelas possibilidades que se abrem com a presença das TD. O modelo construído foi... / Abstract: The objective of this research is to understand the role of digital technologies (DT) in educational processes associated with Linear Algebra in four distance teacher education in mathematics courses linked to the Open University of Brazil (UAB), in the context of its Virtual Learning Environments (VLE). It is a qualitative study. The study and the analysis are guided by theoretical perspectives related to modes of description in Linear Algebra, the notion of humans-with-media, transactional distance and the role of interaction and collaboration in distance learning. Grounded Theory is used to analyze the data, which was produced from four sources: observation in virtual learning environments, interviews, educational projects and researcher's notes. Results show that two roles are evident (each treated as an analytic category): "DT as promoting communication range" and "DT in building digital learning materials." Four properties of the first category were explored: content, agents, temporality and evaluation. For the second category, three properties were analyzed: content, nature and resources involved. The two categories were then integrated into one central category, which suggested that DT, the internet, and the use of VLE can turn the latter into Interactive Digital Didactic Material (IDDM) through the automatic registration of interactions. This transformation can take place via different languages, such as textual, audio-visual or multimodal. With respect to the linear algebra course, an imbalance in description mode approaches (formal, algebraic, and geometric) was noted, which stressed the need to encourage movement among them. This movement can be encouraged by the possibilities introduced by DT. The model constructed was used to identify patterns of use of technologies in the institutions as a way to validate the analysis and provoke reflections about the consistency between observed practices and institutional goals. In this... / Doutor

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In Chapter One the theoretical basis for infinitesimal transformations is presented with particular emphasis on the central theme of this thesis which is the invariance of ordinary differential equations, and their first integrals, under infinitesimal transformations. The differential operators associated with these infinitesimal transformations constitute an algebra under the operation of taking the Lie Bracket. Some of the major results of Lie's work are recalled. The way to use the generators of symmetries to reduce the order of a differential equation and/or to find its first integrals is explained. The chapter concludes with a summary of the state of the art in the mid-seventies just before the work described here was initiated. Chapter Two describes the growing awareness of the algebraic properties of the paradigms of differential equations. This essentially ad hoc period demonstrated that there was value in studying the Lie method of extended groups for finding first integrals and so solutions of equations and systems of equations. This value was emphasised by the application of the method to a class of nonautonomous anharmonic equations which did not belong to the then pantheon of paradigms. The generalised Emden-Fowler equation provided a route to major development in the area of the theory of the conditions for the linearisation of second order equations. This was in addition to its own interest. The stage was now set to establish broad theoretical results and retreat from the particularism of the seventies. Chapters Three and Four deal with the linearisation theorems for second order equations and the classification of intrinsically nonlinear equations according to their algebras. The rather meagre results for systems of second order equations are recorded. In the fifth chapter the investigation is extended to higher order equations for which there are some major departures away from the pattern established at the second order level and reinforced by the central role played by these equations in a world still dominated by Newton. The classification of third order equations by their algebras is presented, but it must be admitted that the story of higher order equations is still very much incomplete. In the sixth chapter the relationships between first integrals and their algebras is explored for both first order integrals and those of higher orders. Again the peculiar position of second order equations is revealed. In the seventh chapter the generalised Emden-Fowler equation is given a more modern and complete treatment. The final chapter looks at one of the fundamental algebras associated with ordinary differential equations, the three element 8£(2, R), which is found in all higher order equations of maximal symmetry, is a fundamental feature of the Pinney equation which has played so prominent a role in the study of nonautonomous Hamiltonian systems in Physics and is the signature of Ermakov systems and their generalisations. / Thesis (Ph.D.)-University of Natal, 1995.