Elementary Methods In Number Theory PDF Download
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Author | : Melvyn B. Nathanson |
Publisher | : Springer Science & Business Media |
Total Pages | : 518 |
Release | : 2008-01-11 |
Genre | : Mathematics |
ISBN | : 0387227385 |
Download Elementary Methods in Number Theory Book in PDF, ePub and Kindle
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 | : GOVE. EFFINGER |
Publisher | : CRC Press |
Total Pages | : 200 |
Release | : 2021-09-09 |
Genre | : |
ISBN | : 9781032017235 |
Download Elementary Number Theory Book in PDF, ePub and Kindle
Elementary Number Theory, Gove Effinger and Gary Mullen, This text is intended to be used as an undergraduate introduction to the theory of numbers. The authors have been immersed in this area of mathematics for many years and hope that this text will inspire students (and instructors) to study, understand, and come to love this truly beautiful subject. Each chapter, after an introduction, develops a new topic clearly broken out in sections which include theoretical material together with numerous examples, each worked out in considerable detail. At the end of each chapter, after a summary of the topic, there are a number of solved problems, also worked out in detail, followed by a set of supplementary problems. These latter problems give students a chance to test their own understanding of the material; solutions to some but not all of them complete the chapter. The first eight chapters discuss some standard material in elementary number theory. The remaining chapters discuss topics which might be considered a bit more advanced. The text closes with a chapter on Open Problems in Number Theory. Students (and of course instructors) are strongly encouraged to study this chapter carefully and fully realize that not all mathematical issues and problems have been resolved! There is still much to be learned and many questions to be answered in mathematics in general and in number theory in particular. Table of Contents 1. Divisibility in the Integers Z 2. Prime Numbers and Factorization 3. Congruences and the Sets Zn 4. Solving Congruences 5. The Theorems of Fermat and Euler 6. Applications in Modern Cryptography 7. Quadratic Residues and Quadratic Reciprocity 8. Some Fundamental Number Theory Functions 9. Diophantine Equations 10. Finite Fields 11. Some Open Problems in Number Theory Appendixes Index Bibliographies Biographies Gove Effinger received his Ph.D. in Mathematics from the University of Massachusetts (Amherst) in 1981 and subsequently taught at Bates College for 5 years and then Skidmore College for 29 years. He is the author of three books: An Elementary Transition to Abstract Mathematics (with Gary L. Mullen, CRC Press), Additive Number Theory of Polynomials over a Finite Field (with David R. Hayes), and Common-Sense BASIC: Structured Programming with Microsoft Quick BASIC (with Alice M. Dean), as well as numerous research papers. His research focus has primarily been concerned with the similarities of polynomials over a finite fields and ordinary integers. Gary L. Mullen is Professor of Mathematics at the Pennsylvania State University, University Park, PA. He has taught both undergraduate and graduate courses there for over 40 years. In addition, he has written more than 150 research papers and co-authored seven books, including both graduate as well as undergraduate textbooks. He also served as department head for seven years and has served as an editor on numerous editorial boards, including having served as Editor-in-Chief of the journal Finite Fields and Their Applications since its founding in 1995.
Author | : James S. Kraft |
Publisher | : CRC Press |
Total Pages | : 407 |
Release | : 2014-11-24 |
Genre | : Mathematics |
ISBN | : 1498702694 |
Download Elementary Number Theory Book in PDF, ePub and Kindle
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 tex
Author | : Calvin T. Long |
Publisher | : |
Total Pages | : 168 |
Release | : 1965 |
Genre | : Number theory |
ISBN | : |
Download Elementary Introduction to Number Theory Book in PDF, ePub and Kindle
Author | : Underwood Dudley |
Publisher | : American Mathematical Soc. |
Total Pages | : 141 |
Release | : 2009-12-31 |
Genre | : Mathematics |
ISBN | : 0883859181 |
Download A Guide to Elementary Number Theory Book in PDF, ePub and Kindle
An introductory guide to elementary number theory for advanced undergraduates and graduates.
Author | : James J. Tattersall |
Publisher | : Cambridge University Press |
Total Pages | : 420 |
Release | : 1999-10-14 |
Genre | : Mathematics |
ISBN | : 9780521585316 |
Download Elementary Number Theory in Nine Chapters Book in PDF, ePub and Kindle
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.
Author | : Charles Vanden Eynden |
Publisher | : |
Total Pages | : 296 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : |
Download Elementary Number Theory Book in PDF, ePub and Kindle
Author | : Paul Pollack |
Publisher | : American Mathematical Soc. |
Total Pages | : 322 |
Release | : 2009-10-14 |
Genre | : Mathematics |
ISBN | : 0821848801 |
Download Not Always Buried Deep Book in PDF, ePub and Kindle
Number theory is one of the few areas of mathematics where problems of substantial interest can be fully described to someone with minimal mathematical background. Solving such problems sometimes requires difficult and deep methods. But this is not a universal phenomenon; many engaging problems can be successfully attacked with little more than one's mathematical bare hands. In this case one says that the problem can be solved in an elementary way. Such elementary methods and the problems to which they apply are the subject of this book. Not Always Buried Deep is designed to be read and enjoyed by those who wish to explore elementary methods in modern number theory. The heart of the book is a thorough introduction to elementary prime number theory, including Dirichlet's theorem on primes in arithmetic progressions, the Brun sieve, and the Erdos-Selberg proof of the prime number theorem. Rather than trying to present a comprehensive treatise, Pollack focuses on topics that are particularly attractive and accessible. Other topics covered include Gauss's theory of cyclotomy and its applications to rational reciprocity laws, Hilbert's solution to Waring's problem, and modern work on perfect numbers. The nature of the material means that little is required in terms of prerequisites: The reader is expected to have prior familiarity with number theory at the level of an undergraduate course and a first course in modern algebra (covering groups, rings, and fields). The exposition is complemented by over 200 exercises and 400 references.
Author | : Thomas Koshy |
Publisher | : Academic Press |
Total Pages | : 748 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780124211711 |
Download Elementary Number Theory with Applications Book in PDF, ePub and Kindle
Elementary Number Theory focuses on number theory's role in the rapid development of art, coding theory, cryptology, computer science, and other necessities of modern life - confirming that human ingenuity and creativity are boundless.
Author | : David Burton |
Publisher | : McGraw Hill |
Total Pages | : 453 |
Release | : 2010-06-16 |
Genre | : Mathematics |
ISBN | : 0077145089 |
Download EBOOK: Elementary Number Theory Book in PDF, ePub and Kindle
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.