An Introduction to Pure and Applied Mathematics

Author: Don Redmond

Publisher: CRC Press

ISBN: 9780824796969

Category: Mathematics

Page: 772

View: 3296

This text provides a detailed introduction to number theory, demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. It contains problem sets within each section and at the end of each chapter to reinforce essential concepts, and includes up-to-date information on divisibility problems, polynomial congruence, the sums of squares and trigonometric sums.;Five or more copies may be ordered by college or university bookstores at a special price, available on application.
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Author: Vladimir Platonov,Andrei Rapinchuk,Rachel Rowen

Publisher: Academic Press

ISBN: 9780080874593

Category: Mathematics

Page: 614

View: 8175

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.
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Author: N.A

Publisher: Academic Press

ISBN: 9780080873329

Category: Mathematics

Page: 434

View: 7747

This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of the methods that are used. We have avoided that style which gives a systematic development of the apparatus and have used instead a freer style, in which the problems and the methods of solution are closely interwoven. We start from concrete problems in number theory. General theories arise as tools for solving these problems. As a rule, these theories are developed sufficiently far so that the reader can see for himself their strength and beauty, and so that he learns to apply them. Most of the questions that are examined in this book are connected with the theory of diophantine equations - that is, with the theory of the solutions in integers of equations in several variables. However, we also consider questions of other types; for example, we derive the theorem of Dirichlet on prime numbers in arithmetic progressions and investigate the growth of the number of solutions of congruences.
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Author: Theodore J. Rivlin

Publisher: Wiley-Interscience

ISBN: N.A

Category: Chebyshev polynomials

Page: 186

View: 3170

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Author: Paulo Ribenboim

Publisher: John Wiley & Sons

ISBN: N.A

Category: Mathematics

Page: 300

View: 747

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From Approximation Theory to Algebra and Number Theory

Author: Theodore J. Rivlin

Publisher: Wiley-Interscience

ISBN: N.A

Category: Mathematics

Page: 249

View: 9859

This Secodnd Edition continues the fine tradition of its predecessor by surveying the most important properties of the Chebyshev polynomials and introducing mathematical analysis. New to this edition are approximately 80 exercises and a chapter which introduces some elementary algebraic and number theoretic properties of the Chebyshev polynomials. Additional coverage focuses on extremal and iterative properties.
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Algebraic, Combinatorial and Analytic Theory

Author: Alfred Geroldinger,Franz Halter-Koch

Publisher: CRC Press

ISBN: 9781420003208

Category: Mathematics

Page: 728

View: 4429

From its origins in algebraic number theory, the theory of non-unique factorizations has emerged as an independent branch of algebra and number theory. Focused efforts over the past few decades have wrought a great number and variety of results. However, these remain dispersed throughout the vast literature. For the first time, Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory offers a look at the present state of the theory in a single, unified resource. Taking a broad look at the algebraic, combinatorial, and analytic fundamentals, this book derives factorization results and applies them in concrete arithmetical situations using appropriate transfer principles. It begins with a basic introduction that can be understood with knowledge of standard basic algebra. The authors then move to the algebraic theory of monoids, arithmetic theory of monoids, the structure of sets of lengths, additive group theory, arithmetical invariants, and the arithmetic of Krull monoids. They also provide a self-contained introduction to abstract analytic number theory as well as a modern treatment of W. Narkiewicz's analytic theory of non-unique factorizations. Non-Unique Factorizations: Algebraic, Combinatorial, and Analytic Theory builds the discussion from first principles to applied problem solving, making it ideally suited to those not familiar with the theory as well as those who wish to deepen their understanding.
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International Conference : Groups, Rings, and Group Rings, July 28-August 2, 2008, Ubatuba, Brazil

Author: A. Giambruno,César Polcino Milies,Sudarshan K. Sehgal

Publisher: American Mathematical Soc.

ISBN: 0821847716

Category: Mathematics

Page: 270

View: 3180

This volume represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. Papers in this volume contain results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras. In particular, topics such as growth functions on varieties, groups of units in group rings, representation theory of Lie algebras, Jordan, alternative and Leibniz algebras, graded identities, automorphisms of trees, and partial actions, are discussed.
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Algebraic Numbers and Functions

Author: Helmut Koch

Publisher: American Mathematical Soc.

ISBN: 9780821820544

Category: Mathematics

Page: 368

View: 3226

Early chapters discuss topics in elementary number theory, such as Minkowski's geometry of numbers, public-key cryptography and a short proof of the Prime Number Theorem, following Newman and Zagier. Next, some of the tools of algebraic number theory are introduced, such as ideals, discriminants and valuations. These results are then applied to obtain results about function fields, including a proof of the Riemann-Roch Theorem and, as an application of cyclotomic fields, a proof of the first case of Fermat's Last Theorem.There are a detailed exposition of the theory of Hecke L-series, following Tate, and explicit applications to number theory, such as the Generalized Riemann Hypothesis. Chapter 9 brings together the earlier material through the study of quadratic number fields. Finally, Chapter 10 gives an introduction to class field theory.
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Author: M. Pohst,H. Zassenhaus

Publisher: Cambridge University Press

ISBN: 9780521596695

Category: Mathematics

Page: 499

View: 2789

Classic book, addressed to all lovers of number theory.
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Fundamentals and Selected Topics

Author: Clifford Bergman

Publisher: CRC Press

ISBN: 1439851298

Category: Computers

Page: 320

View: 6118

Starting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author’s two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts of universal algebra and by introducing a variety of recent research topics. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, a clone of operations, terms, free algebras, Birkhoff’s theorem, and standard Maltsev conditions. The second part covers topics that demonstrate the power and breadth of the subject. The author discusses the consequences of Jónsson’s lemma, finitely and nonfinitely based algebras, definable principal congruences, and the work of Foster and Pixley on primal and quasiprimal algebras. He also includes a proof of Murskiĭ’s theorem on primal algebras and presents McKenzie’s characterization of directly representable varieties, which clearly shows the power of the universal algebraic toolbox. The last chapter covers the rudiments of tame congruence theory. Throughout the text, a series of examples illustrates concepts as they are introduced and helps students understand how universal algebra sheds light on topics they have already studied, such as Abelian groups and commutative rings. Suitable for newcomers to the field, the book also includes carefully selected exercises that reinforce the concepts and push students to a deeper understanding of the theorems and techniques.
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Author: Daniel Anderson

Publisher: Routledge

ISBN: 1351448935

Category: Mathematics

Page: 448

View: 1561

The contents in this work are taken from both the University of Iowa's Conference on Factorization in Integral Domains, and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City. The text gathers current work on factorization in integral domains and monoids, and the theory of divisibility, emphasizing possible different lengths of factorization into irreducible elements.
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Author: Igor Frenkel,James Lepowsky,Arne Meurman

Publisher: Academic Press

ISBN: 9780080874548

Category: Mathematics

Page: 508

View: 8758

This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."
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Author: Harry Lass

Publisher: Courier Corporation

ISBN: 0486471861

Category: Mathematics

Page: 491

View: 4949

Completely self-contained, this survey explores the important topics in pure and applied mathematics. Each chapter can be read independently of the others, and all subjects are unified by cross-references to the complete work. Numerous worked-out examples appear throughout the text, and review questions and references conclude each section. 1957 edition.
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Author: N.A

Publisher: Academic Press

ISBN: 9780080873701

Category: Mathematics

Page: 219

View: 9554

Algebraic Number Fields
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Proceedings of the International Conference held in Graz, Austria, August 30 to September 5, 1998

Author: F. Halter-Koch,Robert F. Tichy

Publisher: Walter de Gruyter

ISBN: 3110801957

Category: Mathematics

Page: 571

View: 9325

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
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