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Author: Melvyn B. Nathanson Publisher: Springer Science & Business Media ISBN: 0387227385 Category : Mathematics Languages : en Pages : 514
Book Description
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: Melvyn B. Nathanson Publisher: Springer Science & Business Media ISBN: 0387227385 Category : Mathematics Languages : en Pages : 514
Book Description
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: Paul Pollack Publisher: American Mathematical Soc. ISBN: 0821848801 Category : Mathematics Languages : en Pages : 322
Book Description
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: Edward Wall Publisher: McGraw-Hill Humanities/Social Sciences/Languages ISBN: 9780073378473 Category : Education Languages : en Pages : 0
Book Description
In response to concerns about teacher retention, especially among teachers in their first to fourth year in the classroom, we offer future teachers a series of brief guides full of practical advice that they can refer to in both their student teaching and in their first years on the job. Number Theory for Elementary School Teachers is designed for preservice candidates in early and/or elementary education. The text complements traditional Math Methods courses and provides deep content knowledge for prospective and first year teachers.
Author: Kenneth S. Williams Publisher: Cambridge University Press ISBN: 1107002532 Category : Mathematics Languages : en Pages : 307
Book Description
A gentle introduction to Liouville's powerful method in elementary number theory. Suitable for advanced undergraduate and beginning graduate students.
Author: G. Tenenbaum Publisher: Cambridge University Press ISBN: 9780521412612 Category : Mathematics Languages : en Pages : 180
Book Description
This is a self-contained introduction to analytic methods in number theory, assuming on the part of the reader only what is typically learned in a standard undergraduate degree course. It offers to students and those beginning research a systematic and consistent account of the subject but will also be a convenient resource and reference for more experienced mathematicians. These aspects are aided by the inclusion at the end of each chapter a section of bibliographic notes and detailed exercises.
Author: C. Y. Hsiung Publisher: World Scientific ISBN: 9789810205911 Category : Mathematics Languages : en Pages : 264
Book Description
This book explains clearly and in detail the basic concepts and methods of calculations of the elementary theory of numbers. It consists of 7 chapters illustrated by numerous examples and exercises. Answers together with some hints to the exercises are given at the end of the book. It may be used as a textbook for undergraduate students.
Author: James J. Tattersall Publisher: Cambridge University Press ISBN: 9780521585316 Category : Mathematics Languages : en Pages : 420
Book Description
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: Gove Effinger Publisher: CRC Press ISBN: 1000427110 Category : Mathematics Languages : en Pages : 254
Book Description
Elementary Number Theory, Gove Effinger, Gary L. 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.
Author: William Stein Publisher: Springer Science & Business Media ISBN: 0387855254 Category : Mathematics Languages : en Pages : 173
Book Description
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: Melvyn B. Nathanson
Author: Melvyn B. Nathanson
Author: Paul Pollack
Author: Edward Wall
Author: Kenneth S. Williams
Author: G. Tenenbaum
Author: C. Y. Hsiung
Author: Calvin T. Long
Author: James J. Tattersall
Author: Gove Effinger
Author: William Stein