**Pure and Applied Undergraduate Texts**

Volume: 23;
2015;
144 pp;
Hardcover

MSC: Primary 97;

Print ISBN: 978-1-4704-2018-5

Product Code: AMSTEXT/23

List Price: $61.00

Individual Member Price: $48.80

**Electronic ISBN: 978-1-4704-2218-9
Product Code: AMSTEXT/23.E**

List Price: $61.00

Individual Member Price: $48.80

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#### Supplemental Materials

# Number Systems: An Introduction to Algebra and Analysis

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*Sergei Ovchinnikov*

This book offers a rigorous and coherent
introduction to the five basic number systems of mathematics, namely
natural numbers, integers, rational numbers, real numbers, and complex
numbers. It is a subject that many mathematicians believe should be
learned by any student of mathematics including future teachers.

The book starts with the development of Peano arithmetic in the
first chapter which includes mathematical induction and elements of
recursion theory. It proceeds to an examination of integers that also
covers rings and ordered integral domains. The presentation of
rational numbers includes material on ordered fields and convergence
of sequences in these fields. Cauchy and Dedekind completeness
properties of the field of real numbers are established, together with
some properties of real continuous functions. An elementary proof of
the Fundamental Theorem of Algebra is the highest point of the chapter
on complex numbers. The great merit of the book lies in its extensive
list of exercises following each chapter. These exercises are designed
to assist the instructor and to enhance the learning experience of the
students.

#### Readership

Undergraduate students interested in foundations of algebra and analysis.

#### Table of Contents

# Table of Contents

## Number Systems: An Introduction to Algebra and Analysis

- Cover Cover11 free
- Title page i2 free
- Contents v6 free
- Preface vii8 free
- Chapter 1. Natural numbers 110 free
- Chapter 2. Integers 3746
- Chapter 3. Rational numbers 5968
- Chapter 4. Real numbers 8594
- Chapter 5. Complex numbers 107116
- Appendix A. Sets, relations, functions 127136
- Bibliography 139148
- Index 141150 free
- Back Cover Back Cover1154