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Elementary Number Theory

Author: Underwood Dudley
Publisher: Courier Corporation
ISBN: 0486134873
Size: 19.78 MB
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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

Author: Gareth A. Jones
Publisher: Springer Science & Business Media
ISBN: 144710613X
Size: 31.67 MB
Format: PDF
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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 With Applications

Author: Thomas Koshy
Publisher: Elsevier
ISBN: 9780080547091
Size: 44.66 MB
Format: PDF, Kindle
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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

A Guide To Elementary Number Theory

Author: Underwood Dudley
Publisher: MAA
ISBN: 9780883853474
Size: 45.94 MB
Format: PDF, ePub
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"A Guide to Elementary Number Theory is a 140-page exposition of the topics considered in a first course in number theory. It is intended for those who may have seen the material before but have half-forgotten it, and also for those who may have misspent their youth by not having a course in number theory and who want to see what it is about without having to wade through traditional texts, some of which approach 500 pages in length. It will be especially useful to graduate students preparing for qualifying exams. Though Plato did not quite say, "He is unworthy of the name of man who does not know which integers are the sums of two squares," he came close. This guide can make everyone more worthy."--P. [4] of cover.

Number Theory

Author: George E. Andrews
Publisher: Courier Corporation
ISBN: 0486135101
Size: 55.35 MB
Format: PDF
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Undergraduate text uses combinatorial approach to accommodate both math majors and liberal arts students. Covers the basics of number theory, offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more

Elementary Number Theory

Author: CTI Reviews
Publisher: Cram101 Textbook Reviews
ISBN: 1467203114
Size: 24.22 MB
Format: PDF, Mobi
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Facts101 is your complete guide to Elementary Number Theory. In this book, you will learn topics such as Primes and Their Distribution, The Theory of Congruences, Fermat`s Theorem, and Number-Theoretic Functions plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Elementary Number Theory In Nine Chapters

Author: James J. Tattersall
Publisher: Cambridge University Press
ISBN: 9780521850148
Size: 13.30 MB
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This textbook is intended to serve as a one-semester introductory course in number theory and in this second edition it has been revised throughout and many new exercises have been added. 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 have been included. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.

Elementary Number Theory

Author: James S. Kraft
Publisher: CRC Press
ISBN: 1498702694
Size: 70.49 MB
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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 With Programming

Author: Marty Lewinter
Publisher: John Wiley & Sons
ISBN: 1119062764
Size: 22.36 MB
Format: PDF, Kindle
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Filling a much-needed gap in the current literature, this book expertly bridges the subjects of number theory and programming and features a multitude of examples and programming exercises in each chapter. It provides an introduction to elementary number theory with fundamental coverage of computer programming and is appropriate for students of mathematics and computer science alike who need to become acquainted with the most famous theorems, problems, and concepts of number theory. In addition, the authors provide a comprehensive presentation of the methodology and applications for readers with various levels of experience, and while theorems are provided, the authors avoid the standard theorem/proof format to aid in reader comprehension. The book features sample programs and research challenges at the end of each chapter for readers to work through, as well as an appendix that provides select answers to the chapter exercises. The authors also maintain a supplementary material website that provides additional working examples of the computer programs. Topical coverage includes: special numbers; Fibonacci sequence, primes, and the Pell equation; Pascal's triangle; divisors and prime decomposition; modular arithmetic; number theoretic functions; Euler's Phi function; sums and partitions; and cryptography. Prerequisites include basic algebra and some knowledge of any computer language.

Elementary Number Theory Primes Congruences And Secrets

Author: William Stein
Publisher: Springer Science & Business Media
ISBN: 0387855254
Size: 22.76 MB
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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.