Elementary Number Theory: Primes, Congruences, and Secrets

Elementary Number Theory: Primes, Congruences, and Secrets
Author: William Stein
Publisher: Springer Science & Business Media
Total Pages: 173
Release: 2008-10-28
Genre: Mathematics
ISBN: 0387855254

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: Primes, Congruences, and Secrets

Elementary Number Theory: Primes, Congruences, and Secrets
Author: William Stein
Publisher: Springer Verlag
Total Pages: 166
Release: 2009-01-08
Genre: Mathematics
ISBN: 9780387855240

Classical number theory and elliptic curves are examined in this textbook, which moves on from elementary topics such as primes, continued fractions, and quadratic forms, to elliptic curves and their applications to algorithmic and number theory problems.

Elementary Number Theory in Nine Chapters

Elementary Number Theory in Nine Chapters
Author: James J. Tattersall
Publisher: Cambridge University Press
Total Pages: 420
Release: 1999-10-14
Genre: Mathematics
ISBN: 9780521585316

This book is intended to serve as a one-semester introductory course in number theory. Throughout the book a historical perspective has been adopted and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. 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. It is assumed that the reader will 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.

An Introductory Course in Elementary Number Theory

An Introductory Course in Elementary Number Theory
Author: Wissam Raji
Publisher: The Saylor Foundation
Total Pages: 171
Release: 2013-05-09
Genre: Mathematics
ISBN:

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.

Discrete Mathematics and Its Applications

Discrete Mathematics and Its Applications
Author: Kenneth H. Rosen
Publisher:
Total Pages: 109
Release: 2007
Genre: Computer science
ISBN: 9780071244749

The companion Web site -- To the student -- The foundations : logic, sets, and functions -- The fundamentals : algorithms, the integers, and matrices -- Mathematical reasoning -- Counting -- Advanced counting techniques -- Relations -- Graphs -- Trees -- Boolean algebra -- Modeling computation

Elementary Number Theory

Elementary Number Theory
Author: Underwood Dudley
Publisher: Courier Corporation
Total Pages: 274
Release: 2012-06-04
Genre: Mathematics
ISBN: 0486134873

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 Methods in Number Theory

Elementary Methods in Number Theory
Author: Melvyn B. Nathanson
Publisher: Springer Science & Business Media
Total Pages: 518
Release: 2000
Genre: Mathematics
ISBN: 0387989129

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.

Elementary Number Theory

Elementary Number Theory
Author: Charles Vanden Eynden
Publisher: Waveland Press
Total Pages: 292
Release: 2006-02-15
Genre:
ISBN: 1478639156

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.

A Course in Number Theory and Cryptography

A Course in Number Theory and Cryptography
Author: Neal Koblitz
Publisher: Springer Science & Business Media
Total Pages: 245
Release: 2012-09-05
Genre: Mathematics
ISBN: 1441985921

This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.