eBook ISBN: | 978-0-88385-919-3 |
Product Code: | NML/1.E |
List Price: | $50.00 |
MAA Member Price: | $37.50 |
AMS Member Price: | $37.50 |
eBook ISBN: | 978-0-88385-919-3 |
Product Code: | NML/1.E |
List Price: | $50.00 |
MAA Member Price: | $37.50 |
AMS Member Price: | $37.50 |
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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.
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Table of Contents
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Chapters
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Preface
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Introduction
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Chapter 1. Natural Numbers and Integers
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Chapter 2. Rational Numbers
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Chapter 3. Real Numbers
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Chapter 4. Irrational Numbers
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Chapter 5. Trigonometric and Logarithmic Numbers
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Chapter 6. The Approximation of Irrationals by Rationals
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Chapter 7. The Existence of Transcendental Numbers
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Appendix A. Proof That There Are Infinitely Many Prime Numbers
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Appendix B. Proof of the Fundamental Theorem of Arithmetic
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Appendix C. Cantor’s Proof of the Existence of Transcendental Numbers
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Appendix D. Trigonometric Numbers
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Reviews
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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.
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Chapters
-
Preface
-
Introduction
-
Chapter 1. Natural Numbers and Integers
-
Chapter 2. Rational Numbers
-
Chapter 3. Real Numbers
-
Chapter 4. Irrational Numbers
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Chapter 5. Trigonometric and Logarithmic Numbers
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Chapter 6. The Approximation of Irrationals by Rationals
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Chapter 7. The Existence of Transcendental Numbers
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Appendix A. Proof That There Are Infinitely Many Prime Numbers
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Appendix B. Proof of the Fundamental Theorem of Arithmetic
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Appendix C. Cantor’s Proof of the Existence of Transcendental Numbers
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Appendix D. Trigonometric Numbers
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A fine job of presenting the materials at a level which is attainable for the intended reading public.
The Mathematics Teacher