Elementary Number Theory

This text provides a simple account of classical number theory, as well as some of the historical background in which the subject evolved. It is intended for use in a one-semester, undergraduate number theory course.

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Author: BURTON

Publisher: Tata McGraw-Hill Education

ISBN: 9781259025761

Category:

Page:

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Elementary Number Theory with Applications

This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell ...

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Author: Thomas Koshy

Publisher: Elsevier

ISBN: 9780080547091

Category: Mathematics

Page: 800

View: 667

This second edition updates the well-regarded 2001 publication with new short sections on topics like Catalan numbers and their relationship to Pascal's triangle and Mersenne numbers, Pollard rho factorization method, Hoggatt-Hensell identity. Koshy has added a new chapter on continued fractions. The unique features of the first edition like news of recent discoveries, biographical sketches of mathematicians, and applications--like the use of congruence in scheduling of a round-robin tournament--are being refreshed with current information. More challenging exercises are included both in the textbook and in the instructor's manual. Elementary Number Theory with Applications 2e is ideally suited for undergraduate students and is especially appropriate for prospective and in-service math teachers at the high school and middle school levels. * Loaded with pedagogical features including fully worked examples, graded exercises, chapter summaries, and computer exercises * Covers crucial applications of theory like computer security, ISBNs, ZIP codes, and UPC bar codes * Biographical sketches lay out the history of mathematics, emphasizing its roots in India and the Middle East

Elementary Number Theory

The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries.

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Author: James S. Kraft

Publisher: CRC Press

ISBN: 9781498702683

Category: Mathematics

Page: 411

View: 206

Elementary Number Theory takes an accessible approach to teaching students about the role of number theory in pure mathematics and its important applications to cryptography and other areas. The first chapter of the book explains how to do proofs and includes a brief discussion of lemmas, propositions, theorems, and corollaries. The core of the text covers linear Diophantine equations; unique factorization; congruences; Fermat’s, Euler’s, and Wilson’s theorems; order and primitive roots; and quadratic reciprocity. The authors also discuss numerous cryptographic topics, such as RSA and discrete logarithms, along with recent developments. The book offers many pedagogical features. The "check your understanding" problems scattered throughout the chapters assess whether students have learned essential information. At the end of every chapter, exercises reinforce an understanding of the material. Other exercises introduce new and interesting ideas while computer exercises reflect the kinds of explorations that number theorists often carry out in their research.

Elementary Number Theory

This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research.

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Author: David Burton

Publisher: McGraw-Hill Education

ISBN: 0073383147

Category: Mathematics

Page: 448

View: 330

Elementary Number Theory, Seventh Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton’s engaging style, Elementary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history.

Elementary Number Theory

Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra.

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Author: Gareth A. Jones

Publisher: Springer Science & Business Media

ISBN: 3540761977

Category: Mathematics

Page: 302

View: 797

An undergraduate-level introduction to number theory, with the emphasis on fully explained proofs and examples. Exercises, together with their solutions are integrated into the text, and the first few chapters assume only basic school algebra. Elementary ideas about groups and rings are then used to study groups of units, quadratic residues and arithmetic functions with applications to enumeration and cryptography. The final part, suitable for third-year students, uses ideas from algebra, analysis, calculus and geometry to study Dirichlet series and sums of squares. In particular, the last chapter gives a concise account of Fermat's Last Theorem, from its origin in the ancient Babylonian and Greek study of Pythagorean triples to its recent proof by Andrew Wiles.

Elementary Number Theory

Written in a lively, engaging style by the author of popular mathematics books, this volume features nearly 1,000 imaginative exercises and problems. Some solutions included. 1978 edition.

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Author: Underwood Dudley

Publisher: Courier Corporation

ISBN: 9780486134871

Category: Mathematics

Page: 272

View: 705

Written in a lively, engaging style by the author of popular mathematics books, this volume features nearly 1,000 imaginative exercises and problems. Some solutions included. 1978 edition.

Elementary Number Theory Primes Congruences and Secrets

The goal of this book is to bring the reader closer to this world. Each chapter contains exercises, and throughout the text there are examples of calculations done using the powerful free open source mathematical software system Sage.

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Author: William Stein

Publisher: Springer Science & Business Media

ISBN: 9780387855257

Category: Mathematics

Page: 168

View: 554

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.

Elementary Number Theory

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.

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Author: Ethan D. Bolker

Publisher: Courier Corporation

ISBN: 9780486153094

Category: Mathematics

Page: 208

View: 347

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.

Elementary Number Theory and Its Applications

The fourth edition of Kenneth Rosen's widely used and successful text, Elementary Number Theory and Its Applications, preserves the strengths of the previous editions, while enhancing the book's flexibility and depth of content coverage.The ...

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Author: Kenneth H. Rosen

Publisher: Addison Wesley Publishing Company

ISBN: STANFORD:36105028630296

Category: Number theory.

Page: 638

View: 296

The fourth edition of Kenneth Rosen's widely used and successful text, Elementary Number Theory and Its Applications, preserves the strengths of the previous editions, while enhancing the book's flexibility and depth of content coverage.The blending of classical theory with modern applications is a hallmark feature of the text. The Fourth Edition builds on this strength with new examples, additional applications and increased cryptology coverage. Up-to-date information on the latest discoveries is included.Elementary Number Theory and Its Applications provides a diverse group of exercises, including basic exercises designed to help students develop skills, challenging exercises and computer projects. In addition to years of use and professor feedback, the fourth edition of this text has been thoroughly accuracy checked to ensure the quality of the mathematical content and the exercises.

Elementary Number Theory in Nine Chapters

Preface Elementary Number Theory in Nine Chapters is primarily intended for a one - semester course for upper - level students of mathematics , in particular , for prospective secondary school teachers . The basic concepts illustrated ...

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Author: James J. Tattersall

Publisher: Cambridge University Press

ISBN: 0521585317

Category: Mathematics

Page: 407

View: 330

This book serves as a one-semester introductory course in number theory. Throughout the book, Tattersall adopts a historical perspective and gives emphasis to some of the subject's applied aspects, highlighting the field of cryptography. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises has been included. The reader should have "pencil in hand" and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.