包郵數論概論(英文版.第4版)|3661721 下載 mobi epub pdf 電子書 2024

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圖書介紹

店鋪：互動創新圖書專營店

齣版社：機械工業齣版社

ISBN：9787111385813

商品編碼：27159077396

叢書名：華章數學原版精品係列

齣版時間：2012-06-01

頁數：409

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圖書描述

書[0名0]：	數論概論(英文版.[0第0]4版)\|3661721
圖書定價：	69元
圖書作者：	(美)Joseph H. Silverman
齣版社：	[1機1] 械工業齣版社
齣版日期：	2012/6/1 0:00:00
ISBN號：	9787111385813
開本：	16開
頁數：	409
版次：	4-1

作者簡介

Joseph H．Silverman 擁有哈佛[0大0][0學0]博士[0學0]位。他目前為布朗[0大0][0學0]數[0學0]教授，之前曾任教於麻省理工[0學0]院和波士頓[0大0][0學0]。1998年，他獲得瞭美[0國0]數[0學0][0會0]Steele奬的著述奬，獲奬著作為《The Arithmetic of Elliptic Curves》和《Advanced Topics in the Arithmetic of Elliptic Curves》。他的研究興趣是數論、橢圓麯綫和密碼[0學0]等。

內容簡介

《數論概論(英文版.[0第0]4版)》麵嚮非數[0學0]專業[0學0]生，講述瞭有關數論的[0知0]識，教給他們如何用數[0學0]方[0法0]思考問題，同時介紹瞭目前數論研究的某些前沿課題。本書采用輕鬆的寫作風格，讀者進入美妙的數論世界，不斷激發讀者的好奇心，並通過一些精心設計的練習來培養讀者的探索精神與創[親斤]能力。對於定理的證明，則強調證明方[0法0]而不僅僅是得到特定的結果。與[0第0]3版相比，本版的具體更[親斤]如下： [親斤]增一章，詳細介紹數[0學0]歸納[0法0]（[0第0]26章）。前言部分給齣瞭各章之間依賴關係的流程圖，便於讀者選擇閱讀。調整瞭內容的組織結構，將反證[0法0]的相關材料前移至[0第0]8章，原根的相關章節移至二次互反律與平方和之後，上一版[0第0]47~50章的內容移至網上。給齣瞭二次互反律的完整證明，以及雅可比符號二次互反律的部分證明。更[親斤]瞭書中的實例及章後練習題。

《數論概論(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]

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