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,同时介绍了目前数学研究的前沿课题。本书采用轻松的写作风格,并包括大量数值示例。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。
本书协作风格独特,书中提供了极佳的示例,以引出定理的叙述和证明。
本书为全英文版。
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书名 | 数论概论(英文版第3版)/经典原版书库 |
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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简介 | 编辑推荐 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,同时介绍了目前数学研究的前沿课题。本书采用轻松的写作风格,并包括大量数值示例。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。 本书协作风格独特,书中提供了极佳的示例,以引出定理的叙述和证明。 本书为全英文版。 目录 Preface 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 m and Successive Squaring 17 Computingk‘h Roots Modulo m 1 8 Powers,Roots。and“Unbreakable”Codes 19 Primality Testing and Carmichael Numbers 20 Euler’s Phi Function and Sums ofDivisors 21 Powers Modulo口and Primitive Roots 22 Primitive Roots and Indices 23 Squares Modulo P 24 Is一1 a Square Modulop?Is 2? 25 Quadratic Reciprocity 26 Which Primes Are Sums ofTwO Squares? 27 Which Numbers Are Sums ofTwo Squares? 28 The Equation X4+y4=Z4 29 Square-Triangular Numbers Revisited 30 Pell’S Equation 31 Diophantine Approximation 32 Diophantine Approximation and Pell’S Equation 33 Number Theory and Imaginary Numbers 34 The Gaussian Integers and Unique Factorization 35 Irrational Numbers and Transcendental Numbers 36 Binomial Coefficients and Pascal’S Triangle 37 Fibonacci’S Rabbits and Linear Recurrence Sequences 38 Oh,What a Beautiful Function 39 The Topsy—Turvy Wlorld of Continued Fractions 40 Continued Fractions,Square Roots,and Pell’S Equation 41 Generating Functions 42 Sums of Powers 43 Cubic Curves and Elliptic Curves 44 Elliptic Curves with FeW Rational Points 45 Points on Elliptic Curves Modulo P 46 Torsion Collections Modulo P and Bad Primes 47 Defect Bounds and Modularity PaRerns 48 Elliptic Curves and Fermat’S Last Theorem Further Reading A Factorization of Small Composite Integers B A List ofPrimes Index |
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