Mathematics: A Concise History and Philosophy: A Concise History and Philosophy

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Springer Science & Business Media, 1994 - Mathematics - 261 pages
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This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors ac quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. The way I myself teach the material, stu dents are given a choice between mathematical assignments, and more his torical or philosophical assignments. (Some sample assignments and tests are found in an appendix to this book. ) This book differs from standard textbooks in several ways. First, it is shorter, and thus more accessible to students who have trouble coping with vast amounts of reading. Second, there are many detailed explanations of the important mathematical procedures actually used by famous mathe maticians, giving more mathematically talented students a greater oppor tunity to learn the history and philosophy by way of problem solving.
  

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User Review  - rashtastic - LibraryThing

Well. It's a pleasant book, something useful: a very accessible run through the history of mathematics with a paragraph per major contributor, small sections, really an interesting development of what ... Read full review

Contents

Mathematics for Civil Servants
1
The Earliest Number Theory
7
The Dawn of Deductive Mathematics
13
The Pythagoreans
17
The Pythagoreans and Perfection
23
The Pythagoreans and Polyhedra
29
The Pythagoreans and Irrationality
35
The Need for the Infinite
43
The Later Middle Ages
131
Modern Mathematical Notation
137
The Secret of the Cubic
141
The Secret Revealed
147
A New Calculating Device
153
Mathematics and Astronomy
157
The Seventeenth Century
161
Pascal
167

Mathematics in Athens Before Plato
49
Plato
57
Aristotle
61
In the Time of Eudoxus
69
Ruler and Compass Constructions
75
The Oldest Surviving Math Book
81
Euclids Geometry Continued
87
Alexandria and Archimedes
95
The End of Greek Mathematics
105
Early Medieval Number Theory
113
Algebra in the Early Middle Ages
119
Geometry in the Early Middle Ages
123
Khayyam and the Cubic
127
The Seventeenth Century II
175
Leibniz
181
The Eighteenth Century
185
Lagrange
191
NineteenthCentury Algebra
195
NineteenthCentury Analysis
199
NineteenthCentury Geometry
203
NineteenthCentury Number Theory
209
Cantor
213
Foundations
217
TwentiethCentury Number Theory
221
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References to this book

The Heritage of Thales
W.S. Anglin
Limited preview - 1995
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