纯数学教程(纪念版)(英文版)

《纯数学教程（纪念版）》是“剑桥数学图书馆 ”系列丛书之一。这部部世纪经典著作，以简洁易懂 的数学语言，全面系统地介绍了基础数学的各个方面 ，并对许多经典的数学论证给出了严谨的证明。本书 共分10章，在介绍了实数、复数的概念后，从第4章和 第5章引入了极限的概念，较之一般书的处理方法更为 轻松自然、易于接受。另外，书中每章后面配有大量 有代表性的杂例，供读者参考练习以巩固所学知识。 本书适合高校数学系及对相关专业学生和教师学习和 参考。

CHAPTER Ⅰ REAL VARIABLES 1-2.Rational numbers 3-7.Irrational numbers 8.Real numbers 9.Relations of magnitude between real numbers 10-11.Algebraical operations with real numbers 12.The number√2 13-14.Quadratic surds 15.The continuum 16.The continuous real variable 17.Sections of the real numbers. Dedekind's theorem 18.Points of accumulation 19.Weierstrass's theorem Miscellaneous examples CHAPTER Ⅱ FUNCTIONS OF REAL VARIABLES 20.The idea of a function 21.The graphical representation of functions. Coordinates 22.Polar coordinates 23.Polynomia s 24-25.Rational functions 26-27.Algebraical functions 28-29.Transcendental functions 30.Graphical solution of equations 31.Functions of two variables and their graphical representation 32.Curves in a plane 33.Loci in space Miscellaneous examples CHAPTER Ⅲ COMPLEX NUMBER 34-38.Displacements 39-42.Complex numbers 43.The quadratic equation with real coefficients 44.Argand's diagram 45.De Moivre's theorem 46.Rational functions of a complex variable 47-49.Roots of complex numbers Miscellaneous examples CHAPTER Ⅳ LIMITS OF FUNCTIONS OF A POSITIVE INTEGRAL VARIABLE 50.Functions of a positive integral variable 51.Interpolation 52.Finite and infinite classes 53-57.Properties possessed by a function of n for large values of n 58-61.Definition of a limit and other definitions 62.Oscillating functions 63-68.General theorems concerning limits 69-70.Steadily increasing or decreasing functions 71.Alternative proof of Weierstrass's theorem 72.The limit of xn 73.The limit of (1+1/n) n 74.Some algebraical lemmas 75.The limit of n □