Mathematics

A Concise History and Philosophy

W.S. Anglin

262 pages, parution le 01/07/1994

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Résumé

This is a concise introductory textbook for a one semester course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. It is shorter than the standard textbooks in that area and thus more accessible to students who have trouble coping with vast amounts of reading. Furthermore, there are many detailed explanations of the important mathematical procedures actually used by famous mathematicians, giving more mathematically talented students a greater opportunity to learn the history and philosophy by way of problem solving. Several important philosophical topics are pursued throughout the text, giving the student an opportunity to come to a full and consistent knowledge of their development. These topics include infinity, the nature of motion, and Platonism.

This book offers, in fewer pages, a deep penetration into the key mathematical and philosophical aspects of the history of mathematics.

Contents

Preface

1 Mathematics for Civil Servants 1
2 The Earliest Number Theory 7
3 The Dawn of Deductive Mathematics 13
4 The Pythagoreans 17
5 The Pythagoreans and Perfection 23
6 The Pythagoreans and Polyhedra 29
7 The Pythagoreans and Irrationality 35
8 The Need for the Infinite 43
9 Mathematics in Athens Before Plato 49
10 Plato 57
11 Aristotle 61
12 In the Time of Eudoxus 69
13 Ruler and Compass Constructions 75
14 The Oldest Surviving Math Book 81
15 Euclid's Geometry Continued 87
16 Alexandria and Archimedes 95
17 The End of Greek Mathematics 105
18 Early Medieval Number Theory 113
19 Algebra in the Early Middle Ages 119
20 Geometry in the Early Middle Ages 123
21 Khayyam and the Cubic 127
22 The Later Middle Ages 131
23 Modern Mathematical Notation 137
24 The Secret of the Cubic 141
25 The Secret Revealed 147
26 A New Calculating Device 153
27 Mathematics and Astronomy 157
28 The Seventeenth Century 161
29 Pascal 167
30 The Seventeenth Century II 175
31 Leibniz 181
32 The Eighteenth Century 185
33 Lagrange 191
34 Nineteenth-Century Algebra 195
35 Nineteenth-Century Analysis 199
36 Nineteenth-Century Geometry 203
37 Nineteenth-Century Number Theory 209
38 Cantor 213
39 Foundations 217
40 Twentieth-Century Number Theory 221

References 227
Appendix A Sample Assignments and Tests 229
Appendix B Answers to Selected Exercises 245
Index 257

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	W.S. Anglin
Parution	01/07/1994
Nb. de pages	262
Format	16 x 24
Couverture	Relié
Poids	549g
Intérieur	Noir et Blanc
EAN13	9780387942803
ISBN13	978-3-540-94280-1