数论概论
数论概论封面图

数论概论

(美) 西尔弗曼 (Silverman,J.H.) , 著

出版社:机械工业出版社

年代:2012

定价:69.0

书籍简介:

本书面向非数学专业学生,讲述了有关数论的知识,教给他们如何用数学方法思考问题,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,引领读者进入美妙的数论世界,不断激发渎者的好奇心,并通过一些精心设计的练习来培养读者的探索精神与创新能力。对于定理的证明,则强凋证明方法而不仅仅是得到特定的结果。

书籍目录:

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]

内容摘要:

《数论概论(英文版·第4版)》英文影印版由PearsonEducationAsiaLtd.授权机械工业出版社独家出版。未经出版者书面许可,不得以任何方式复制或抄袭本书内容。

书籍规格:

书籍详细信息
书名数论概论站内查询相似图书
丛书名华章数学原版精品系列
9787111385813
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出版地北京出版单位机械工业出版社
版次1版印次1
定价(元)69.0语种英文
尺寸25 × 17装帧平装
页数 409 印数 3000

书籍信息归属:

数论概论是机械工业出版社于2012.6出版的中图分类号为 O156 的主题关于 数论-高等学校-教材-英文 的书籍。