Degree students of mathematics are often daunted by the mass of definitions and theorems with which they must familiarize themselves. In the fields algebra and analysis this burden will now be reduced because in A Handbook of Terms they will find sufficient explanations of the terms and the symbolism that they are likely to come across in their university courses. Rather than being like an alphabetical dictionary, the order and division of the sections correspond to the way in which mathematics can be developed. This arrangement, together with the numerous notes and examples that are interspersed with the text, will give students some feeling for the underlying mathematics. Many of the terms are explained in several sections of the book, and alternative definitions are given. Theorems, too, are frequently stated at alternative levels of generality. Where possible, attention is drawn to those occasions where various authors ascribe different meanings to the same term. The handbook will be extremely useful to students for revision purposes. It is also an excellent source of reference for professional mathematicians, lecturers and teachers.
Author(s): A. G. Howson
Publisher: CUP
Year: 1972
Language: English
Pages: 249
Cover......Page 1
Title......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 8
1 Some mathematical language......Page 12
2 Sets and functions......Page 19
3 Equivalence relations and quotient sets......Page 29
4 Number systems I......Page 31
5 Groups I......Page 36
6 Rings and fields......Page 41
7 Homomorphisms and quotient algebras......Page 45
8 Vector spaces and matrices......Page 49
9 Linear equations and rank......Page 57
10 Determinants and multilinear mappings......Page 62
11 Polynomials......Page 66
12 Groups II......Page 69
13 Number systems II......Page 76
14 Fields and polynomials......Page 83
15 Lattices and Boolean algebra......Page 86
16 Ordinal numbers......Page 91
17 Eigenvectors and eigenvalues......Page 94
18 Quadratic forms and inner products......Page 98
19 Categories and functors......Page 105
20 Metric spaces and continuity......Page 110
21 Topological spaces and continuity......Page 116
22 Metric spaces II......Page 119
23 The real numbers......Page 124
24 Real-valued functions of a real variable......Page 126
25 Differentiable functions of one variable......Page 133
26 Functions of several real variables......Page 137
27 Integration......Page 145
28 Infinite series and products......Page 151
29 Improper integrals......Page 157
30 Curves and arc length page......Page 161
31 Functions of a complex variable......Page 164
32 Multiple integrals......Page 170
33 Logarithmic, exponential and trigonometric functions......Page 173
34 Vector algebra......Page 179
35 Vector calculus......Page 184
36 Line and surface integrals......Page 188
37 Measure and Lebesgue integration......Page 195
38 Fourier series......Page 203
Appendix i Some `named' theorems and properties......Page 209
Appendix 2 Alphabets used in mathematics......Page 226
Index of symbols......Page 228
Subject index......Page 236
