數論概論（英文版·第4版） pdf epub mobi txt 电子书 下载 2025

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[美] Joseph H. Silverman 著

齣版社： 機械工業齣版社

ISBN：9787111385813

版次：4

商品編碼：11025285

品牌：機工齣版

包裝：平裝

叢書名： 華章數學原版精品係列

開本：其他

齣版時間：2012-06-01

用紙：膠版紙

頁數：409

正文語種：英文

內容簡介

　　《數論概論（英文版·第4版）》英文影印版由PearsonEducationAsiaLtd.授權機械工業齣版社獨門齣版。未經齣版者書麵許可，不得以任何方式復製或抄襲本書內容。

內頁插圖

目錄

Preface
Flowchart ofChapter Dependencies
Introduction
1 What Is Number Theory·
2 Pythagorean Triples
3 Pythagorean Triples and the Unit Circle
4 Sums ofHigher Powe and Fermat’S Last Theorem
5 Divisibility and the Greatest Common Divisor
6 Linear Equatio and the Greatest Common Divisor
7 Factorization and the Fundamental Theorem ofArithmetic
8 Congruences
9 Congruences，Powe ，andFermat’S LittleTheorem
10 Congruences，Powe ，and Euler’S Formula
11 Euler’S Phi Function and the Chinese Remainder Theorem
12 Prime Numbe
13 Counting Primes
14 Me enne Primes
15 Me enne Primes and Perfect Numbe
16 Powe Modulo m and Successive Squaring
17 Computing kth Roots Modulo m
18 Powe ，Roots，and“Unbreakable Codes
l9 Primality Testing and Carmichael Numbe
20 Squares Modulo р
21 Is-l a Square Modulo р·Is 2·
22 Quadratic Reciprocity
23 Proofof Quadratic Reciprocity
24 Which Primes Are Sums ofTwo Squares
25 Which Numbe Are Sums ofTwo Squares
26 As Easy as One，TwO，Three
27 Euler’S Phi Function and Sums of Diviso
28 Powe Modulo р and Primitive Roots
29 Primitive Roots and Indices
30 The Equation X4+Y4=Z
3l Square-Triangular Numbe Revisited
32 Pell’S Equation
33 Diophantine Approximation
34 Diophantine Approximation and Pell’S Equation
35 Number Theory and Imaginary Numbe
36 The Gaussian Intege and Unique Factorization
37 Irrational Numbe and Tra cendental Numbe
38 Binomial Coefficients and 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 р
44 To ion Collectio Modulo р and Bad Primes
45 Defect Bounds and Modularity Patter
46 Elliptic Curves and Fermat’S Last Theorem
Further Reading
Index
47 The Topsy-Turvy World of Continued Fractio [online]
48 Continued Fractio and Pell’s Equation[online]
49 Generating Functio [9nline]
50 Sums of Powe [online]
A Factorization of Small Composite Intege [online]
B A List of Primes [online]

前言/序言

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數論概論（英文版·第4版）

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　　安德烈?德昂 (André Dahan)於1935年齣生於阿爾及利亞，後來到巴黎留學，從國立巴黎工藝大學畢業後，在巴黎裝飾美術學校教書，目前與妻子和女兒居住於巴黎。德昂雖然很晚纔開始他的繪本創作生涯，於五十二歲纔推齣第一部繪本作品《月亮，你好嗎》（My Friend the Moon），可是他作品中獨樹一幟、既溫暖又純真的夢幻世界，以及每一幅圖畫裏色彩與情境的美妙共振，都強烈吸引讀者的目光。德昂創造的繪本故事世界彷佛是用一塊一塊精巧的魔法磚頭搭蓋的，除卻繽紛斑斕的畫?麵本身，故事意欲傳達的信息與其間流泄的詩意都會敲開觀者的心門，所以他已發錶的二十多種作品在全世界廣受歡迎?，已於十幾國推齣譯本。