Elementary Theory Of Numbers

Author : W. Sierpinski
Publisher : Elsevier
Page : 513 pages
File Size : 45,6 Mb
Release : 1988-02-01
Category : Mathematics
ISBN : 9780080960197

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Elementary Theory of Numbers by W. Sierpinski Pdf

Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised. The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian integers.

Author : Hsiung
Publisher : Allied Publishers
Page : 264 pages
File Size : 53,9 Mb
Release : 1995
Category : Electronic
ISBN : 8170234646

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Elementary Theory of Numbers by Hsiung Pdf

Author : William J. LeVeque
Publisher : Courier Corporation
Page : 162 pages
File Size : 49,9 Mb
Release : 2014-01-15
Category : Mathematics
ISBN : 9780486150765

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Elementary Theory of Numbers by William J. LeVeque Pdf

This superb text introduces number theory to readers with limited formal mathematical training. Intended for use in freshman- and sophomore-level courses in arts and science curricula, in teacher-training programs, and in enrichment programs for high-school students, it is filled with simple problems to stimulate readers' interest, challenge their abilities and increase mathematical strength. Contents: I. Introduction II. The Euclidean Algorithm and Its Consequences III. Congruences IV. The Powers of an Integer Modulo m V. Continued Fractions VI. The Gaussian Integers VII. Diophantine Equations Requiring only a sound background in high-school mathematics, this work offers the student an excellent introduction to a branch of mathematics that has been a strong influence in the development of higher pure mathematics, both in stimulating the creation of powerful general methods in the course of solving special problems (such as Fermat conjecture and the prime number theorem) and as a source of ideas and inspiration comparable to geometry and the mathematics of physical phenomena.

Author : Gareth A. Jones,Josephine M. Jones
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447106135

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Elementary Number Theory by Gareth A. Jones,Josephine M. Jones Pdf

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.

Author : Joe Roberts
Publisher : MIT Press (MA)
Page : 986 pages
File Size : 53,6 Mb
Release : 1925
Category : Mathematics
ISBN : UCAL:B4268284

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Elementary Number Theory by Joe Roberts Pdf

Author : William Stein
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 41,5 Mb
Release : 2008-10-28
Category : Mathematics
ISBN : 9780387855257

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Elementary Number Theory: Primes, Congruences, and Secrets by William Stein Pdf

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.

Author : Thomas Koshy
Publisher : Elsevier
Page : 801 pages
File Size : 41,8 Mb
Release : 2007-05-08
Category : Mathematics
ISBN : 9780080547091

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Elementary Number Theory with Applications by Thomas Koshy Pdf

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

Author : Calvin T. Long
Publisher : D.C. Heath
Page : 264 pages
File Size : 41,5 Mb
Release : 1972
Category : Mathematics
ISBN : CORNELL:31924001582521

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Elementary Introduction to Number Theory by Calvin T. Long Pdf

Author : Underwood Dudley
Publisher : MAA
Page : 156 pages
File Size : 50,7 Mb
Release : 2009
Category : Mathematics
ISBN : 0883853477

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A Guide to Elementary Number Theory by Underwood Dudley Pdf

An introductory guide to elementary number theory for advanced undergraduates and graduates.

Author : Charles Vanden Eynden
Publisher : Random House (NY)
Page : 306 pages
File Size : 48,9 Mb
Release : 1987
Category : Juvenile Nonfiction
ISBN : UOM:39015015605382

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Elementary Number Theory by Charles Vanden Eynden Pdf

Author : Melvyn B. Nathanson
Publisher : Springer Science & Business Media
Page : 514 pages
File Size : 46,6 Mb
Release : 2008-01-11
Category : Mathematics
ISBN : 9780387227382

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Elementary Methods in Number Theory by Melvyn B. Nathanson Pdf

This basic introduction to number theory is ideal for those with no previous knowledge of the subject. The main topics of divisibility, congruences, and the distribution of prime numbers are covered. Of particular interest is the inclusion of a proof for one of the most famous results in mathematics, the prime number theorem. With many examples and exercises, and only requiring knowledge of a little calculus and algebra, this book will suit individuals with imagination and interest in following a mathematical argument to its conclusion.

Author : Underwood Dudley
Publisher : W H Freeman & Company
Page : 249 pages
File Size : 50,9 Mb
Release : 1978
Category : Mathematics
ISBN : 071670076X

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Elementary Number Theory by Underwood Dudley Pdf

"With almost a thousand imaginative exercises and problems, this book stimulates curiosity about numbers and their properties."

Author : Wissam Raji
Publisher : The Saylor Foundation
Page : 171 pages
File Size : 53,9 Mb
Release : 2013-05-09
Category : Mathematics
ISBN : 8210379456XXX

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An Introductory Course in Elementary Number Theory by Wissam Raji Pdf

These notes serve as course notes for an undergraduate course in number theory. Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. Proofs of basic theorems are presented in an interesting and comprehensive way that can be read and understood even by non-majors with the exception in the last three chapters where a background in analysis, measure theory and abstract algebra is required. The exercises are carefully chosen to broaden the understanding of the concepts. Moreover, these notes shed light on analytic number theory, a subject that is rarely seen or approached by undergraduate students. One of the unique characteristics of these notes is the careful choice of topics and its importance in the theory of numbers. The freedom is given in the last two chapters because of the advanced nature of the topics that are presented.

Author : Underwood Dudley
Publisher : Courier Corporation
Page : 274 pages
File Size : 48,7 Mb
Release : 2008-09-25
Category : Mathematics
ISBN : 9780486469317

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Elementary Number Theory by Underwood Dudley Pdf

Minimal prerequisites make this text ideal for a first course in number theory. Written in a lively, engaging style by the author of popular mathematics books, it features nearly 1,000 imaginative exercises and problems. Solutions to many of the problems are included, and a teacher's guide is available. 1978 edition.

Author : Charles Vanden Eynden
Publisher : Waveland Press
Page : 278 pages
File Size : 42,7 Mb
Release : 2006-02-15
Category : Electronic
ISBN : 9781478639152

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Elementary Number Theory by Charles Vanden Eynden Pdf

This practical and versatile text evolved from the author’s years of teaching experience and the input of his students. Vanden Eynden strives to alleviate the anxiety that many students experience when approaching any proof-oriented area of mathematics, including number theory. His informal yet straightforward writing style explains the ideas behind the process of proof construction, showing that mathematicians develop theorems and proofs from trial and error and evolutionary improvement, not spontaneous insight. Furthermore, the book includes more computational problems than most other number theory texts to build students’ familiarity and confidence with the theory behind the material. The author has devised the content, organization, and writing style so that information is accessible, students can gain self-confidence with respect to mathematics, and the book can be used in a wide range of courses—from those that emphasize history and type A problems to those that are proof oriented.