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Hardcover ISBN:  9781470420185 
Product Code:  AMSTEXT/23 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 
Sale Price:  $51.35 
eBook ISBN:  9781470422189 
Product Code:  AMSTEXT/23.E 
List Price:  $75.00 
MAA Member Price:  $67.50 
AMS Member Price:  $60.00 
Sale Price:  $48.75 
Hardcover ISBN:  9781470420185 
eBook ISBN:  9781470422189 
Product Code:  AMSTEXT/23.B 
List Price:  $154.00 $116.50 
MAA Member Price:  $138.60 $104.85 
AMS Member Price:  $123.20 $93.20 
Sale Price:  $100.10 $75.73 

Book DetailsPure and Applied Undergraduate TextsVolume: 23; 2015; 144 ppMSC: Primary 97
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.
Ancillaries:
ReadershipUndergraduate students interested in foundations of algebra and analysis.

Table of Contents

Cover

Title page

Contents

Preface

Chapter 1. Natural numbers

Chapter 2. Integers

Chapter 3. Rational numbers

Chapter 4. Real numbers

Chapter 5. Complex numbers

Appendix A. Sets, relations, functions

Bibliography

Index

Back Cover


Additional Material

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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.
Ancillaries:
Undergraduate students interested in foundations of algebra and analysis.

Cover

Title page

Contents

Preface

Chapter 1. Natural numbers

Chapter 2. Integers

Chapter 3. Rational numbers

Chapter 4. Real numbers

Chapter 5. Complex numbers

Appendix A. Sets, relations, functions

Bibliography

Index

Back Cover