包邮数论概论(英文版.第4版)|3661721 下载 mobi epub pdf 电子书 2024

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出版社：机械工业出版社

ISBN：9787111385813

商品编码：27159077396

丛书名：华章数学原版精品系列

出版时间：2012-06-01

页数：409

图书描述

书[0名0]：	数论概论(英文版.[0第0]4版)\|3661721
图书定价：	69元
图书作者：	(美)Joseph H. Silverman
出版社：	[1机1] 械工业出版社
出版日期：	2012/6/1 0:00:00
ISBN号：	9787111385813
开本：	16开
页数：	409
版次：	4-1

作者简介

Joseph H．Silverman 拥有哈佛[0大0][0学0]博士[0学0]位。他目前为布朗[0大0][0学0]数[0学0]教授，之前曾任教于麻省理工[0学0]院和波士顿[0大0][0学0]。1998年，他获得了美[0国0]数[0学0][0会0]Steele奖的著述奖，获奖著作为《The Arithmetic of Elliptic Curves》和《Advanced Topics in the Arithmetic of Elliptic Curves》。他的研究兴趣是数论、椭圆曲线和密码[0学0]等。

内容简介

《数论概论(英文版.[0第0]4版)》面向非数[0学0]专业[0学0]生，讲述了有关数论的[0知0]识，教给他们如何用数[0学0]方[0法0]思考问题，同时介绍了目前数论研究的某些前沿课题。本书采用轻松的写作风格，读者进入美妙的数论世界，不断激发读者的好奇心，并通过一些精心设计的练习来培养读者的探索精神与创[亲斤]能力。对于定理的证明，则强调证明方[0法0]而不仅仅是得到特定的结果。与[0第0]3版相比，本版的具体更[亲斤]如下： [亲斤]增一章，详细介绍数[0学0]归纳[0法0]（[0第0]26章）。前言部分给出了各章之间依赖关系的流程图，便于读者选择阅读。调整了内容的组织结构，将反证[0法0]的相关材料前移至[0第0]8章，原根的相关章节移至二次互反律与平方和之后，上一版[0第0]47~50章的内容移至网上。给出了二次互反律的完整证明，以及雅可比符号二次互反律的部分证明。更[亲斤]了书中的实例及章后练习题。

《数论概论(英文版.[0第0]4版)》
Preface
Flowchart of Chapter Dependencies
Introduction
1 What Is Number Theory?
2 Pythagorean Triples
3 Pythagorean Triples and the Unit Circle
4 Sums of Higher Powers and Fermat's Last Theorem
5 Divisibility and the Greatest Common Divisor
6 Linear Equations and the Greatest Common Divisor
7 Factorization and the Fundamental Theorem of Arithmetic
8 Congruences
9 Congruences, Powers, and Fermat's Little Theorem
10 Congruences, Powers, and Euler's Formula
11 Euler's Phi Function and the Chinese Remainder Theorem
12 Prime Numbers
13 Counting Primes
14 Mersenne Primes
15 Mersenne Primes and Perfect Numbers
16 Powers Modulo tn and Successive Squaring
17 Computing k th Roots Modulo tn
18 Powers, Roots, and "Unbreakable" Codes
19 Primality Testing and Carmichael Numbers
20 Squares Mdulo p
21 Is -1 a Square Modulop? Is 2?
22 Quadratic Reciprocity
23 Proof of Quadratic Reciprocity
24 Which Primes Are Sums of Two Squares?
25 Which Numbers Are Sums of Two Squares?
26 As Easy as One, Two, Three
27 Euler's Phi Function and Sums of Divisors
28 Powers Modulo p and Primitive Roots
29 Primitive Roots and Indices
30 The Equation X4+y4=Z4
31 Square-Triangular Numbers Revisited
32 Pell's Equation
33 Diophantine Approximation
34 Diophantine Approximation and Pell's Equation
35 Number Theory and Imaginary Numbers
36 The Gaussian Integers and Unique Factorization
37 Irrational Numbers and Transcendental Numbers
38 Bi[0no0]mial Coefficients ~md Pascal's Triangle
39 Fibonacci's Rabbits and Linear Recurrence Sequences
40 Oh, What a Beautiful Function
41 Cubic Curves and Elliptic Curves
42 Elliptic Curves with Few Rational Points
43 Points on Elliptic Curves Modulo p
44 Torsion Collections Modulo p and Bad Primes
45 Defect Bounds and Modularity Patterns
46 Elliptic Curves and Fermat's Last Theorem
Further Reading
Index
47 The Topsy-Turvy World of Continued Fractions [online]
48 Continued Fractions and Pell's Equation [online]
49 Generating Functions [online]
50 Sums of Powers [online]
A Factorization of Sm[0all0] Com [p1o1s] ite Integers [online]
B A List of Primes [online]

包邮数论概论(英文版.第4版)|3661721 下载 mobi epub pdf txt 电子书格式