Introduction to Abstract Mathematics

Introduction to Abstract Mathematics

1st Edition - January 1, 1971

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  • Author: T. A. Bick
  • eBook ISBN: 9781483276595

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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.

Table of Contents


  • 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

    3.3 Additional Topics

    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

    Answers to Selected Exercises

    Subject Index

Product details

  • No. of pages: 232
  • Language: English
  • Copyright: © Academic Press 1971
  • Published: January 1, 1971
  • Imprint: Academic Press
  • eBook ISBN: 9781483276595

About the Author

T. A. Bick

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