**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: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

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

List Price: $61.00

AMS Member Price: $48.80

MAA Member Price: $54.90

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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.

An instructor's manual for this title is available
electronically to those instructors who have adopted the textbook for
classroom use. Please send email to textbooks@ams.org for more
information.

#### 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