A Handbook of Terms used in Algebra and Analysis

In A Handbook of Terms they will find sufficient explanations of the terms and the symbolism that they are likely to come across.

A. G. Howson (Author)

9780521096959, Cambridge University Press

Paperback / softback, published 7 September 1972

252 pages
23 x 15.5 x 1.4 cm, 0.372 kg

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.

1. Some mathematical language
2. Sets and functions
3. Equivalence relations and quotient sets
4. Number systems I
5. Groups I
6. Rings and fields
7. Homomorphisms and quotient algebra's
8. Vector spaces and matrices
9. Linear Equations and rank
10. Determinants and multi linear mappings
11. Polynomials
12. Groups II
13. Number systems II
14. Fields and polynomials
15. Lattices and Boolean algebra
16. Ordinal numbers
17. Eigenvectors and eigenvalues
18. Quadratic forms and inner products
19. Categories and functors
20. Metric spaces and continuity
21. Topological spaces and continuity
22. Metric Spaces II
23. The real numbers
24. Real-valued function of real variable
25. Differentiable functions of one variable
26. Functions of several real variables
27. Integration
28. Infinite series and products
29. Improper integrals
30. Curves and arc length
31. Functions of a complex variable
32. Multiple integrals
33. Logarithmic, exponential and trigonometric functions
34. Vector algebra
35. Vector calculus
36. Line and surface integrals
37. Measure and lebesgue integration
38. Fourier series
Appendix 1 some 'named' theorems and properties
Appendix 2 Alphabets used in mathematics
Index of symbols
Subject index.

Subject Areas: Mathematics [PB]