A Handbook of Terms used in Algebra and Analysis

Author: A. G. Howson  

Publisher: Cambridge University Press‎

Publication year: 1972

E-ISBN: 9780511864339

P-ISBN(Paperback): 9780521096959

Subject: O1-0 mathematical theory

Keyword: 数学理论

Language: ENG

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A Handbook of Terms used in Algebra and Analysis

Description

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.

Chapter

Some special types of function

Composition of functions

Inverse images and inverse functions

Functions of several variables

Operations

3 Equivalence relations and quotient sets

Binary relations

Quotient sets

4 Number systems I

Peano's Axioms

A set-theoretic approach

The rational integers

The rational numbers

5 Groups I

Subgroups

6 Rings and fields

7 Homomorphisms and quotient algebras

8 Vector spaces and matrices

9 Linear equations and rank

Linear equations

Elementary operations and special types of matrices

10 Determinants and multilinear mappings

Permutations and determinants

Multilinear mappings

11 Polynomials

12 Groups II

Free groups, generators and relations

13 Number systems II

Real numbers

Complex numbers

The quaternion algebra

14 Fields and polynomials

15 Lattices and Boolean algebra

Algebras of sets

16 Ordinal numbers

17 Eigenvectors and eigenvalues

18 Quadratic forms and inner products

19 Categories and functors

20 Metric spaces and continuity

Open and closed sets

Continuous functions

21 Topological spaces and continuity

22 Metric spaces II

Limits and sequences

Compactness and connectedness

Normed spaces

23 The real numbers

Decimals

24 Real-valued functions of a real variable

Sequences of functions

Limit superior and limit inferior

25 Differentiable functions of one variable

26 Functions of several real variables

Coordinate systems

27 Integration

The Cauchy integral

The Riemann integral

The Riemann-Stieltjes integral

28 Infinite series and products

Power series

Series of functions

Double series

Infinite products

29 Improper integrals

Unbounded integrands

30 Curves and arc length

Connectedness and regions

31 Functions of a complex variable

Contour integrals

32 Multiple integrals

33 Logarithmic, exponential and trigonometric functions

General logarithms

Hyperbolic functions

Circular functions

Complex variable

Complex circular functions

34 Vector algebra

Triple products

35 Vector calculus

36 Line and surface integrals

Line integrals

Surface integrals

37 Measure and Lebesgue integration

Lebesgue measure

Measurable functions

Integration

38 Fourier series

Functions with periods other than 2Л

Appendix 1 Some 'named' theorems and properties

Appendix 2 Alphabets used in mathematics

Index of symbols

Subject index

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