Introductory mathematics : algebra and analysis介绍数学:代数和分析

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作者： Geoffrey C. Smith著

出版社：漓江出版社

出版时间： 2000-2-1字数：版次： 1页数： 215印刷时间： 2000/02/01开本： 16开印次： 1纸张：胶版纸I S B N ： 9783540761785包装：平装内容简介

Provides a self-contained introduction to Pure Mathematics, & bridges the gap between school & university work, styled less formally than most textbooks & appropriate for either first semester students or as introductory self-instruction. Paper. DLC: Mathematics.

Preface

1Sets, Functions and Relations

1.1 Sets

1.2 Subsets

1.3 Well-known Sets

1.4 Rationals, Reals and Pictures

1.5 Set Operations

1.6 Sets of Sets

1.7 Paradox

1.8 Set-theoretic Constructions

1.9 Notation

1.10 Venn Diagrams

1.11 Quantifiers and Negation

1.12 Informal Description of Maps

1.13 Injective, Surjective and Bijective Maps

1.14 Composition of Maps

1.15 Graphs and Respectability Reclaimed

1.16 Characterizing Bijections

1.17 Sets of Maps

1.18 Relations

1.19 Intervals

2Proof

2.1 Induction

2.2 Complete Induction

2.3 Counter-examples and Contradictions

2.4 Method of Descent

2.5 Style

2.6 Implication

2.7 Double Implication

2.8 The Master Plan

3 Complex Numbers and Related Functions

3.1 Motivation

3.2 Creating the Complex Numbers

3.3 A Geometric Interpretation

3.4 Sine, Cosine and Polar Form

3.5 e

3.6 Hyperbolic Sine and Hyperbolic Cosine

3.7 Integration Tricks

3.8 Extracting Roots and Raising to Powers

3.9 Logarithm

3.10 Power Series

4 Vectors and Matrices

4.1 Row Vectors

4.2 Higher Dimensions

4.3 Vector Laws

4.4 Lengths and Angles

4.5 Position Vectors

4.6 Matrix Operations

4.7 Laws of Matrix Algebra

4.8 Identity Matrices and Inverses

4.9 Determinants

4.10 Geometry of Determinants

4.11 Linear Independence

4.12 Vector Spaces

4.13 Transposition

5Group Theory

5.1 Permutations

5.2 Inverse Permutations

5.3 The Algebra of Permutations

5.4 The Order of a Permutation

5.5 Permutation Groups

5.6 Abstract Groups

5.7 Subgroups

……

6Sequences and Series

7 Mathematical Analysis

8 Creating the Real Numbers