《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 □
76-77.Infinite series
78.The infinite geometrical series
79.The representation of functions of a continuous real variable by means of limits
80.The bounds of a bounded aggregate
81.The bounds of a bounded function
82.The limits of indetermination of a bounded function
83-84.The general principle of convergence
85-86.Limits of complex functions and series of complex terms
87-88.Applications to zn and the geometrical series
89.The symbols 0, o, ～
Miscellaneous examples
CHAPTER Ⅴ LIMITSOFFUNCTIONSOFACONTINUOUSVARIABLE.CONTINUOUS AND DISCONTINUOUS FUNCTIONS
90-92.Limits as x→ ∞ or x → ∞
93-97.Limits as x → a
98.The symbols O, o, ～: orders of smallness and greatness
99-100.Continuous functions of a real variable
101-105.Properties of continuous functions. Bounded functions The oscillation of a function in an interval
106-107.Sets of intervals on a line. The Heine-Borel theorem
108.Continuous functions of several variables
109-110.Implicit and inverse functions
Miscellaneous examples
CHAPTER Ⅵ DERIVATIVES AND INTEGRALS
111-113.Derivatives
114.General rules for diferentiation
115.Derivatives of complex functions
116.The notation of the differential calculus
117.Differentiation of polynomials
118.Differentiation of rational functions
119.Differentiation of algebraical functions
120.Differentiation of transcendental functions
121.Repeated differentiation
122.General theorems concerning derivatives Rolle's theorem
123-125.Maxima and minima
126-127.The mean value theorem
128.Cauchy's mean value theorem
129.A theorem of Darboux
130-131.Integration. The logarithmic function
132.Integration of polynomials
133-134.Integration of rational functions
135-142.Integration of algebraical functions. Integration by rationalisation. Integration by parts
143-147. Integration of transcendental functions
148.Areas of plane curves
149.Lengths of plane curves
Miscellaneous examples
CHAPTER Ⅶ ADDTTTONAL THEOREMS IN THE DIFFERENTIAL AND INTEGRAL CALCULUS
150-151.Taylor's theorem
152.Taylor's series
153.Applications of Taylor's theorem to maxima and minima
154.The calculation of certain limits
155.The contact