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Introduction to Abstract Mathematics

1st Edition

Author:
eBook ISBN: 9781483276595
Published Date: 1st January 1971
Page Count: 232
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Description

Introduction to Abstract Mathematics focuses on the principles, approaches, and operations involved in abstract mathematics, including metric spaces, sets, axiom systems, and open sentences. The book first offers information on logic and set theory, natural numbers, and integers and rational numbers. Discussions focus on rational numbers and ordered fields, ordering, arithmetic, axiom systems and methods of proof, functions of kindred matters, ordered pairs and relations, sets, and statements and open sentences. The text then examines real and complex numbers, metric spaces, and limits. Topics include generalized limits, continuous functions, openness, closedness, and neighborhood systems, definition and basic properties, and construction of R. The publication is a vital reference for mathematicians and students interested in abstract mathematics.

﻿Preface

Acknowledgments

I. Logic and Set Theory

1.1 Introduction

1.2 Statements and Open Sentences

Exercises 1.2

1.3 Sets

Exercises 1.3

1.4 Ordered Pairs and Relations

Exercises 1.4

1.5 Functions and Kindred Matters

Exercises 1.5

1.6 Axiom Systems and Methods of Proof

II. The Natural Numbers

2.1 Introduction

2.2 Arithmetic

Exercises 2.2

2.3 Ordering

Exercises 2.3

III. The Integers and the Rational Numbers

3.1 Introduction

3.2 Preliminaries

Exercises 3.2

Exercises 3.3

3.4 The Rational Numbers and Ordered Fields

Exercises 3.4

IV. The Real and Complex Numbers

4.1 Introduction

4.2 Construction of R

Exercises 4.2

V. Metric Spaces

5.1 Introduction

5.2 Definition and Basic Properties

Exercises 5.2

5.3 Openness, Closedness, and Neighborhood Systems

Exercises 5.3

5.4 Continuous Functions

Exercises 5.4

VI. Limits

6.1 Introduction

Exercise 6.1

6.2 Generalized Limits

Exercises 6.2

6.3 Some Examples

Exercises 6.3

References

Subject Index

No. of pages:
232
Language:
English