Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 591 pages
File Size : 41,66 MB
Release : 2012-10-29
Category : Mathematics
ISBN : 1441984895
Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.
Author : Richard A. Mollin
Publisher : CRC Press
Page : 440 pages
File Size : 22,70 MB
Release : 2009-08-26
Category : Computers
ISBN : 1420083295
Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and mo
Author : Hugh L. Montgomery
Publisher : Cambridge University Press
Page : 574 pages
File Size : 38,76 MB
Release : 2007
Category : Mathematics
ISBN : 9780521849036
A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.
Author : A. Fröhlich
Publisher : Cambridge University Press
Page : 376 pages
File Size : 13,74 MB
Release : 1991
Category : Mathematics
ISBN : 9780521438346
This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as rings of integers, class groups, and units. Moreover they combine, at each stage of development, theory with explicit computations and applications, and provide motivation in terms of classical number-theoretic problems. A number of special topics are included that can be treated at this level but can usually only be found in research monographs or original papers, for instance: module theory of Dedekind domains; tame and wild ramifications; Gauss series and Gauss periods; binary quadratic forms; and Brauer relations. This is the only textbook at this level which combines clean, modern algebraic techniques together with a substantial arithmetic content. It will be indispensable for all practising and would-be algebraic number theorists.
Author : H. E. Rose
Publisher : Oxford University Press
Page : 420 pages
File Size : 14,34 MB
Release : 1995
Category : Mathematics
ISBN : 9780198523765
This textbook covers the main topics in number theory as taught in universities throughout the world. Number theory deals mainly with properties of integers and rational numbers; it is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent sub-theories and a long list of unsolved problems. This book excludes topics relying heavily on complex analysis and advanced algebraic number theory. The increased use of computers in number theory is reflected in many sections (with much greater emphasis in this edition). Some results of a more advanced nature are also given, including the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. The latest work on Fermat's last theorem is also briefly discussed. Each chapter ends with a collection of problems; hints or sketch solutions are given at the end of the book, together with various useful tables.
Author : George E. Andrews
Publisher : Courier Corporation
Page : 292 pages
File Size : 35,10 MB
Release : 2012-04-30
Category : Mathematics
ISBN : 0486135101
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.
Author : Róbert Freud
Publisher : American Mathematical Soc.
Page : 549 pages
File Size : 40,28 MB
Release : 2020-10-08
Category : Education
ISBN : 1470452758
Number Theory is a newly translated and revised edition of the most popular introductory textbook on the subject in Hungary. The book covers the usual topics of introductory number theory: divisibility, primes, Diophantine equations, arithmetic functions, and so on. It also introduces several more advanced topics including congruences of higher degree, algebraic number theory, combinatorial number theory, primality testing, and cryptography. The development is carefully laid out with ample illustrative examples and a treasure trove of beautiful and challenging problems. The exposition is both clear and precise. The book is suitable for both graduate and undergraduate courses with enough material to fill two or more semesters and could be used as a source for independent study and capstone projects. Freud and Gyarmati are well-known mathematicians and mathematical educators in Hungary, and the Hungarian version of this book is legendary there. The authors' personal pedagogical style as a facet of the rich Hungarian tradition shines clearly through. It will inspire and exhilarate readers.
Author : W.A. Coppel
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 29,69 MB
Release : 2006-02-02
Category : Mathematics
ISBN : 9780387298511
This two-volume book is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A is accessible to first-year undergraduates and deals with elementary number theory. Part B is more advanced and gives the reader an idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches a broad picture is obtained. The book contains a treasury of proofs, several of which are gems seldom seen in number theory books.
Author : G. Tenenbaum
Publisher : Cambridge University Press
Page : 180 pages
File Size : 40,1 MB
Release : 1995-06-30
Category : Mathematics
ISBN : 9780521412612
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 : Emmanuel Kowalski
Publisher : Cambridge University Press
Page : 271 pages
File Size : 28,55 MB
Release : 2021-05-06
Category : Mathematics
ISBN : 1108899560
Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful area of mathematics.
