Introduction to Abstract Mathematics
- 1st Edition - January 1, 1971
- Imprint: Academic Press
- Author: T. A. Bick
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 6 2 0 - 9
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 6 5 9 - 5
Introduction to Abstract Mathematics focuses on the principles, approaches, and operations involved in abstract mathematics, including metric spaces, sets, axiom systems, and open… Read more
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Request a sales quoteIntroduction 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
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
- Edition: 1
- Published: January 1, 1971
- Imprint: Academic Press
- No. of pages: 232
- Language: English
- Paperback ISBN: 9781483236209
- eBook ISBN: 9781483276595
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