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书名 数论概论(英文版第4版)/华章统计学原版精品系列
分类 科学技术-自然科学-数学
作者 (美)西尔弗曼
出版社 机械工业出版社
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美国西尔弗曼编著的《数论概论》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新能力。对于定理的证明,则强调证明方法而不仅仅是得到特定的结果。

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 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 ofArithmetic

8 Congruences

9 Congruences,Powers,andFermat’S LittleTheorem

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 m and Successive Squaring

17 Computing kth Roots Modulo m

18 Powers,Roots,and“Unbreakable Codes

l9 Primality Testing and Carmichael Numbers

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 Squares7

25 Which Numbers Are Sums ofTwo Squares7

26 As Easy as One,TwO,Three

27 Euler’S Phi Function and Sums of Divisors

28 Powers Modulo р and Primitive Roots

29 Primitive Roots and Indices

30 The Equation X4+Y4=Z4

3l 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 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 Torsion Collections Modulo р 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[9nline]

50 Sums of Powers [online]

A Factorization of Small Composite Integers[online]

B A List of Primes [online]

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