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Reticulados via corpos ciclotômicos

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ISBN: 9788568334393 Year: Pages: 194 DOI: 10.7476/9788568334393 Language: Portuguese
Publisher: SciELO Books - Editora UNESP
Subject: Mathematics
Added to DOAB on : 2017-05-03 11:26:21
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O primeiro capítulo, assim, introduz osconceitos de módulo, inteiro algébrico, norma e traço de um elemento,discriminante, base integral, anel de Dedekind e outros conceitosindispensáveis ao desenvolvimento dos demais capítulos. Estuda ainda as formas quadráticas, as quais se aplicam para determinar o raio de empacotamento da realização geométricade um ideal em questão.O capítulo 2 apresenta um estudo sobre corpos de números, com ênfase nos anéis dos inteiros e discriminantes de corpos quadráticos e ciclotômicos, além de abordar a decomposição de um ideal primo em uma extensão fazendo uso do Teorema de Kummer.As definições de reticulado, empacotamento esférico, volume e densidade de centro são abordadas no terceiro capítulo, que ainda trata do método de Minkowski para obtenção de reticulados via representação geométrica de ideais dos anéis de inteiros algébricos.

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MATHEMATICS

Modelagem Matemática : perspectivas, experiências, reflexões e teorizações

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ISBN: 9788577982325 Year: DOI: 10.7476/9788577982325 Language: Portuguese
Publisher: SciELO Books - Editora UEPG
Subject: Mathematics
Added to DOAB on : 2018-05-31 11:19:52
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Essa nova edição mantém os capítulos da primeira, porém, sob outra estrutura, a partir da inclusão de cinco novos, totalizando doze que constituíram quatro núcleos: 1) Sobre a perspectiva de Modelagem, 2) Modelagem Matemática nos níveis e modalidades de ensino, 3) Modelagem Matemática e Formação de Professores, 4) Modelagem Matemática e Teorizações. A partir desses núcleos foi possível apresentar um novo subtítulo que expressa a sua unidade temática: Modelagem Matemática: perspectivas, experiências, reflexões e teorizações. Para além de um novo título, esse novo livro avança em questões pertinentes ao tema e, ao agregar os capítulos, permite efetuar reflexões mais robustas do ponto de vista de cada núcleo. Com isso, esperamos que essa obra traga as devidas contribuições a todos os interessados na prática e na pesquisa em Modelagem.

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MATHEMATICS

Proceedings of the 13th International Congress on Mathematical Education: ICME-13

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Book Series: ICME-13 Monographs ISSN: 2520-8322 / 2520-8330 ISBN: 9783319625966 9783319625973 Year: Pages: 766 DOI: https://doi.org/10.1007/978-3-319-62597-3 Language: English
Publisher: Springer Nature
Subject: Mathematics
Added to DOAB on : 2017-11-24 15:18:22
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The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME-13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 brought together about 3.500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. Directly before the congress activities were offered for 450 Early Career Researchers. The proceedings give a comprehensive overview on the current state-of-the-art of the discussions on mathematics education and display the breadth and deepness of current research on mathematical teaching-and-learning processes.The book introduces the major activities of ICME-13, namely articles from the four plenary lecturers and two plenary panels, articles from the five ICMI awardees, reports from six national presentations, three reports from the thematic afternoon devoted to specific features of ICME-13. Furthermore, the proceedings contain descriptions of the 54 Topic Study Groups, which formed the heart of the congress and reports from 29 Discussion Groups and 31 Workshops. The additional important activities of ICME-13, namely papers from the invited lecturers, will be presented in the second volume of the proceedings.

Planar Maps, Random Walks and Circle Packing

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Book Series: Lecture Notes in Mathematics ISBN: 9783030279684 Year: Pages: 120 DOI: 10.1007/978-3-030-27968-4 Language: English
Publisher: Springer Nature
Subject: Mathematics
Added to DOAB on : 2020-01-29 11:21:10
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This open access book focuses on the interplay between random walks on planar maps and Koebe’s circle packing theorem. Further topics covered include electric networks, the He–Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe’s circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.

Attitudes, Beliefs, Motivation and Identity in Mathematics Education: An Overview of the Field and Future Directions

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319328102 9783319328119 Year: Pages: 35 DOI: 10.1007/978-3-319-32811-9 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2017-01-24 17:45:37
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This book records the state of the art in research on mathematics-related affect. It discusses the concepts and theories of mathematics-related affect along the lines of three dimensions. The first dimension identifies three broad categories of affect: motivation, emotions, and beliefs. The book contains one chapter on motivation, including discussions on how emotions and beliefs relate to motivation. There are two chapters that focus on beliefs and a chapter on attitude which cross-cuts through all these categories. The second dimension covers a rapidly fluctuating state to a more stable trait. All chapters in the book focus on trait-type affect and the chapter on motivation discusses both these dimensions. The third dimension regards the three main levels of theorizing: physiological (embodied), psychological (individual) and social. All chapters reflect that mathematics-related affect has mainly been studied using psychological theories.

Teaching and Learning of Calculus

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319329741 9783319329758 Year: Pages: 37 DOI: 10.1007/978-3-319-32975-8 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2017-01-24 17:52:35
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This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.

Uses of Technology in Lower Secondary Mathematics Education: A Concise Topical Survey

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319336657 9783319336664 Year: DOI: 10.1007/978-3-319-33666-4 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Education
Added to DOAB on : 2017-01-24 17:55:15
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This topical survey provides an overview of the current state of the art in technology use in mathematics education, including both practice-oriented experiences and research-based evidence, as seen from an international perspective. Three core themes are discussed: Evidence of effectiveness; Digital assessment; and Communication and collaboration.The survey’s final section offers suggestions for future trends in technology-rich mathematics education and provides a research agenda reflecting those trends. Predicting what lower secondary mathematics education might look like in 2025 with respect to the role of digital tools in curricula, teaching and learning, it examines the question of how teachers can integrate physical and virtual experiences to promote a deeper understanding of mathematics.The issues and findings presented here provide an overview of current research and offer a glimpse into a potential future characterized by the effective integration of technology to support mathematics teaching and learning at the lower secondary level.

Empirical Research in Statistics Education

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319389677 9783319389684 Year: Pages: 37 DOI: 10.1007/978-3-319-38968-4 Language: English
Publisher: Springer Nature
Subject: Statistics --- Education --- Mathematics
Added to DOAB on : 2017-01-24 18:03:53
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This ICME-13 Topical Survey provides a review of recent research into statistics education, with a focus on empirical research published in established educational journals and on the proceedings of important conferences on statistics education. It identifies and addresses six key research topics, namely: teachers’ knowledge; teachers’ role in statistics education; teacher preparation; students’ knowledge; students’ role in statistics education; and how students learn statistics with the help of technology. For each topic, the survey builds upon existing reviews, complementing them with the latest research.

Transitions in Mathematics Education

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319316215 9783319316222 Year: Pages: 34 DOI: 10.1007/978-3-319-31622-2 Language: English
Publisher: Springer Nature
Subject: Education --- Mathematics
Added to DOAB on : 2017-01-30 17:46:53
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This book examines the kinds of transitions that have been studied in mathematics education research. It defines transition as a process of change, and describes learning in an educational context as a transition process. The book focuses on research in the area of mathematics education, and starts out with a literature review, describing the epistemological, cognitive, institutional and sociocultural perspectives on transition. It then looks at the research questions posed in the studies and their link with transition, and examines the theoretical approaches and methods used. It explores whether the research conducted has led to the identification of continuous processes, successive steps, or discontinuities. It answers the question of whether there are difficulties attached to the discontinuities identified, and if so, whether the research proposes means to reduce the gap – to create a transition. The book concludes with directions for future research on transitions in mathematics education.

Assessment in Mathematics Education: Large-Scale Assessment and Classroom Assessment

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Book Series: ICME-13 Topical Surveys ISSN: 2366-5947 ISBN: 9783319323930 9783319323947 Year: Pages: 38 DOI: 10.1007/978-3-319-32394-7 Language: English
Publisher: Springer Nature
Subject: Mathematics --- Education
Added to DOAB on : 2017-01-30 17:50:18
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This book provides an overview of current research on a variety of topics related to both large-scale and classroom assessment. First, the purposes, traditions and principles of assessment are considered, with particular attention to those common to all levels of assessment and those more connected with either classroom or large-scale assessment. Assessment design based on sound assessment principles is discussed, differentiating between large-scale and classroom assessment, but also examining how the design principles overlap. The focus then shifts to classroom assessment and provides specific examples of assessment strategies, before examining the impact of large-scale assessment on curriculum, policy, instruction, and classroom assessment. The book concludes by discussing the challenges that teachers currently face, as well as ways to support them.The book offers a common language for researchers in assessment, as well as a primer for those interested in understanding current work in the area of assessment. In summary, it provides the opportunity to discuss large-scale and classroom assessment by addressing the following main themes:·Purposes, Traditions and Principles of Assessment·Design of Assessment Tasks·Classroom Assessment in Action·Interactions of Large-Scale and Classroom Assessment·Enhancing Sound Assessment Knowledge and PracticesIt also suggests areas for future research in assessment in mathematics education.

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