J. Bell9780792359722, 0792359720
A compact survey, at the elementary level, of some of the most important concepts of mathematics. Attention is paid to their technical features, historical development and broader philosophical significance. Each of the various branches of mathematics is discussed separately, but their interdependence is emphasised throughout. Certain topics — such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics — are discussed in detail. Appendices outline from scratch the proofs of two of the most celebrated limitative results of mathematics: the insolubility of the problem of doubling the cube and trisecting an arbitrary angle, and the Godel incompleteness theorems. Additional appendices contain brief accounts of smooth infinitesimal analysis — a new approach to the use of infinitesimals in the calculus — and of the philosophical thought of the great 20th century mathematician Hermann Weyl. Readership: Students and teachers of mathematics, science and philosophy. The greater part of the book can be read and enjoyed by anyone possessing a good high school mathematics background. |
Table of contents :
1. Numerals and notation……Page 6
2. The Mathematics of Anient Greece……Page 14
3. The Development of the Number Concept……Page 33
4. The Evolution of Algebra, I……Page 58
5. The Evolution of Algebra, II……Page 77
6. The Evolution of Algebra, III……Page 94
7. The Development of Geometry, I……Page 116
8. The Development of Geometry, II……Page 134
9.The Calculus and Mathematical Analysis……Page 157
10. The Continuous and the Discrete……Page 179
11. The Mathematics of the Infinite……Page 187
12. The Philosophy of Mathematics……Page 198
Appendix 1 – The Insolubility of some Geometric Construction Problems……Page 215
Appendix 2 – The Goedel Incompleteness Theorems……Page 221
Appendix 3 – The Calculus in SMooth Infinitesimal Analysis……Page 229
Appendix 4 – The Philosophical Thought of a GreatMathematician: Hermann Weyl……Page 236
Biblography……Page 241 |
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