Author: Publisher:
ISBN: 9787115156112
Category : Number theory
Languages : zh-CN
Pages : 435
Book Description
本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。
An Introduction to the Theory of Numbers
Author: Leo MoserPublisher: The Trillia Group
ISBN: 1931705011
Category : Mathematics
Languages : en
Pages : 95
Book Description
"This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text."--Publisher's description
Author: Ivan Niven
Author: Ivan NivenAn Illustrated Theory of Numbers
Author: Martin H. WeissmanPublisher: American Mathematical Soc.
ISBN: 1470463717
Category : Education
Languages : en
Pages : 341
Book Description
News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.
Introduction to Number Theory
Author: Anthony VazzanaPublisher: CRC Press
ISBN: 1584889381
Category : Computers
Languages : en
Pages : 530
Book Description
One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topi
Number Theory and Its History
Author: Oystein OrePublisher: Courier Corporation
ISBN: 0486136434
Category : Mathematics
Languages : en
Pages : 404
Book Description
Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.
An Introduction to the Theory of Numbers
Author: G. H. HardyPublisher: Oxford University Press
ISBN: 0199219869
Category : Mathematics
Languages : en
Pages : 645
Book Description
The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat's Last Theorem, a foreword by Andrew Wiles and extensively revised and updated end-of-chapter notes.
Introduction To Number Theory
Author: Richard Michael HillPublisher: World Scientific Publishing Company
ISBN: 1786344734
Category : Mathematics
Languages : en
Pages : 262
Book Description
'Probably its most significant distinguishing feature is that this book is more algebraically oriented than most undergraduate number theory texts.'MAA ReviewsIntroduction to Number Theory is dedicated to concrete questions about integers, to place an emphasis on problem solving by students. When undertaking a first course in number theory, students enjoy actively engaging with the properties and relationships of numbers.The book begins with introductory material, including uniqueness of factorization of integers and polynomials. Subsequent topics explore quadratic reciprocity, Hensel's Lemma, p-adic powers series such as exp(px) and log(1+px), the Euclidean property of some quadratic rings, representation of integers as norms from quadratic rings, and Pell's equation via continued fractions.Throughout the five chapters and more than 100 exercises and solutions, readers gain the advantage of a number theory book that focuses on doing calculations. This textbook is a valuable resource for undergraduates or those with a background in university level mathematics.
A Classical Introduction to Modern Number Theory
Author: Kenneth IrelandPublisher: Springer Science & Business Media
ISBN: 147572103X
Category : Mathematics
Languages : en
Pages : 406
Book Description
This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, some of them new. This second edition contains two new chapters that provide a complete proof of the Mordel-Weil theorem for elliptic curves over the rational numbers and an overview of recent progress on the arithmetic of elliptic curves.
