数论中的基本方法第1版 Elementary Methods in Number Theory 英文原版 Melvyn B Nathanson

基本信息

Format Paperback | 514 pages

Dimensions 155 x 235 x 27.69mm | 819g

Publication date 02 May 2013

Publisher Springer-Verlag New York Inc.

Language English

Edition Statement Softcover reprint of the original 1st ed. 2000

Illustrations note XVIII, 514 p.

ISBN10 1475773927

ISBN13 9781475773927

书籍简介

对数论的基本介绍非常适合那些以前不了解该主题的人。 涵盖了可分性、同余性和素数分布的主要主题。 特别有趣的是包含了对数学中著名的结果之一的证明，即素数定理。 本书有很多例子和练习，只需要一点微积分和代数的知识，这本书适合那些有想象力和兴趣的人，他们会根据数学论证得出结论。

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.

目录

A First Course in Number Theory.- Divisibility and Primes.- Congruences.- Primitive Roots and Quadratic Reciprocity.- Fourier Analysis on Finite Abelian Groups.- The abc Conjecture.- Divisors and Primes in Multiplicative Number Theory.- Arithmetic Functions.- Divisor Functions.- Prime Numbers.- The Prime Number Theorem.- Primes in Arithmetic Progressions.- Three Problems in Additive Number Theory.- Waring's Problem.- Sums of Sequences of Polynomials.- Liouville's Identity.- Sums of an Even Number of Squares.- Partition Asymptotics.- An Inverse Theorem for Partitions.

作者简介

梅尔文·伯纳德·内森森（Melvyn Bernard Nathanson，1944 年 10 月 10 日出生于宾夕法尼亚州费城）是美国数学家，专攻数论，也是雷曼学院和研究生中心（纽约城市大学）的数学教授。 他的主要工作是加法和组合数论。 他是 150 多篇数学研究论文的作者，和 20 本书的作者或编辑。

Melvyn Bernard Nathanson (born October 10, 1944, in Philadelphia, Pennsylvania) is an American mathematician, specializing in number theory, and a Professor of Mathematics at Lehman College and The Graduate Center (City University of New York).His principal work is in additive and combinatorial number theory. He is the author of over 150 research papers in mathematics,and author or editor of 20 books.