Group Theory Algebra And Number Theory

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Combinatorial Number Theory And Additive Group Theory

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Author : Alfred Geroldinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-15

Combinatorial Number Theory And Additive Group Theory written by Alfred Geroldinger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-15 with Mathematics categories.

Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.

Visual Group Theory

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Author : Nathan Carter
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-08

Visual Group Theory written by Nathan Carter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-08 with Education categories.

Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.

Computational Algebra And Number Theory

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Author : Wieb Bosma
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Computational Algebra And Number Theory written by Wieb Bosma and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed. Audience: Students, experts, and those performing current research in any of the topics mentioned above.

Group Theory Algebra And Number Theory

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Author : Horst G. Zimmer
language : en
Publisher: Walter de Gruyter
Release Date : 2011-07-20

Group Theory Algebra And Number Theory written by Horst G. Zimmer and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-20 with Mathematics categories.

No detailed description available for "Group Theory, Algebra, and Number Theory".

Number Shape Symmetry

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Author : Diane L. Herrmann
language : en
Publisher: CRC Press
Release Date : 2012-10-18

Number Shape Symmetry written by Diane L. Herrmann and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-18 with Mathematics categories.

Through a careful treatment of number theory and geometry, Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory helps readers understand serious mathematical ideas and proofs. Classroom-tested, the book draws on the authors’ successful work with undergraduate students at the University of Chicago, seventh to tenth grade mathematically talented students in the University of Chicago’s Young Scholars Program, and elementary public school teachers in the Seminars for Endorsement in Science and Mathematics Education (SESAME). The first half of the book focuses on number theory, beginning with the rules of arithmetic (axioms for the integers). The authors then present all the basic ideas and applications of divisibility, primes, and modular arithmetic. They also introduce the abstract notion of a group and include numerous examples. The final topics on number theory consist of rational numbers, real numbers, and ideas about infinity. Moving on to geometry, the text covers polygons and polyhedra, including the construction of regular polygons and regular polyhedra. It studies tessellation by looking at patterns in the plane, especially those made by regular polygons or sets of regular polygons. The text also determines the symmetry groups of these figures and patterns, demonstrating how groups arise in both geometry and number theory. The book is suitable for pre-service or in-service training for elementary school teachers, general education mathematics or math for liberal arts undergraduate-level courses, and enrichment activities for high school students or math clubs.

Elementary Number Theory Group Theory And Ramanujan Graphs

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Author : Giuliana Davidoff
language : en
Publisher: Cambridge University Press
Release Date : 2003-01-27

Elementary Number Theory Group Theory And Ramanujan Graphs written by Giuliana Davidoff and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-27 with Mathematics categories.

This text is a self-contained study of expander graphs, specifically, their explicit construction. Expander graphs are highly connected but sparse, and while being of interest within combinatorics and graph theory, they can also be applied to computer science and engineering. Only a knowledge of elementary algebra, analysis and combinatorics is required because the authors provide the necessary background from graph theory, number theory, group theory and representation theory. Thus the text can be used as a brief introduction to these subjects and their synthesis in modern mathematics.

Algebraic Groups And Number Theory

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Author : Vladimir Platonov
language : en
Publisher: Academic Press
Release Date : 1993-12-07

Algebraic Groups And Number Theory written by Vladimir Platonov and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-07 with Mathematics categories.

This milestone work on the arithmetic theory of linear algebraic groups is now available in English for the first time. Algebraic Groups and Number Theory provides the first systematic exposition in mathematical literature of the junction of group theory, algebraic geometry, and number theory. The exposition of the topic is built on a synthesis of methods from algebraic geometry, number theory, analysis, and topology, and the result is a systematic overview ofalmost all of the major results of the arithmetic theory of algebraic groups obtained to date.

A Course On Group Theory

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Author : John S. Rose
language : en
Publisher: Courier Corporation
Release Date : 2013-05-27

A Course On Group Theory written by John S. Rose and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-27 with Mathematics categories.

Text for advanced courses in group theory focuses on finite groups, with emphasis on group actions. Explores normal and arithmetical structures of groups as well as applications. 679 exercises. 1978 edition.

Topics In Group Theory

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Author : Geoff Smith
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-05-15

Topics In Group Theory written by Geoff Smith and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-15 with Mathematics categories.

The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject for the first time, this book reviews all the essentials. It recaps the basic definitions and results, including Lagranges Theorem, the isomorphism theorems and group actions. Later chapters include material on chain conditions and finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of "entertainments" demonstrates an assortment of results that can be achieved with the theoretical machinery.

Elementary Number Theory

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Author : Ethan D. Bolker
language : en
Publisher: Courier Corporation
Release Date : 2012-06-14

Elementary Number Theory written by Ethan D. Bolker and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-14 with Mathematics categories.

This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and more.