eBook ISBN:  9780883859193 
Product Code:  NML/1.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 
eBook ISBN:  9780883859193 
Product Code:  NML/1.E 
List Price:  $50.00 
MAA Member Price:  $37.50 
AMS Member Price:  $37.50 

Book DetailsAnneli Lax New Mathematical LibraryVolume: 1; 2002; 140 pp
A superb development that starts with the natural numbers and carries the reader through the rationals and their decimal representations to algebraic numbers and then to the real numbers. Along the way, readers will see characterizations of the rationals and of certain special (Liouville) transcendental numbers. This material is basic to all of algebra and analysis. This book may be read with profit by interested high school students as well as by college students and others who want to know more about the basic aspects of pure mathematics.

Table of Contents

Chapters

Preface

Introduction

Chapter 1. Natural Numbers and Integers

Chapter 2. Rational Numbers

Chapter 3. Real Numbers

Chapter 4. Irrational Numbers

Chapter 5. Trigonometric and Logarithmic Numbers

Chapter 6. The Approximation of Irrationals by Rationals

Chapter 7. The Existence of Transcendental Numbers

Appendix A. Proof That There Are Infinitely Many Prime Numbers

Appendix B. Proof of the Fundamental Theorem of Arithmetic

Appendix C. Cantor’s Proof of the Existence of Transcendental Numbers

Appendix D. Trigonometric Numbers


Reviews

A fine job of presenting the materials at a level which is attainable for the intended reading public.
The Mathematics Teacher


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A superb development that starts with the natural numbers and carries the reader through the rationals and their decimal representations to algebraic numbers and then to the real numbers. Along the way, readers will see characterizations of the rationals and of certain special (Liouville) transcendental numbers. This material is basic to all of algebra and analysis. This book may be read with profit by interested high school students as well as by college students and others who want to know more about the basic aspects of pure mathematics.

Chapters

Preface

Introduction

Chapter 1. Natural Numbers and Integers

Chapter 2. Rational Numbers

Chapter 3. Real Numbers

Chapter 4. Irrational Numbers

Chapter 5. Trigonometric and Logarithmic Numbers

Chapter 6. The Approximation of Irrationals by Rationals

Chapter 7. The Existence of Transcendental Numbers

Appendix A. Proof That There Are Infinitely Many Prime Numbers

Appendix B. Proof of the Fundamental Theorem of Arithmetic

Appendix C. Cantor’s Proof of the Existence of Transcendental Numbers

Appendix D. Trigonometric Numbers

A fine job of presenting the materials at a level which is attainable for the intended reading public.
The Mathematics Teacher