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Mathematics : A Concise History and Philosophy - W. S. Anglin


A Concise History and Philosophy

Hardcover Published: 4th April 1996
ISBN: 9780387942803
Number Of Pages: 265

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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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"...The book is well written and will help those who look for a deeper understanding of mathematical culture." -- MATHEMATICAL REVIEWS

Mathematics for Civil Servantsp. 1
The Earliest Number Theoryp. 7
The Dawn of Deductive Mathematicsp. 13
The Pythagoreansp. 17
The Pythagoreans and Perfectionp. 23
The Pythagoreans and Polyhedrap. 29
The Pythagoreans and Irrationalityp. 35
The Need for the Infinitep. 43
Mathematics in Athens Before Platop. 49
Platop. 57
Aristotlep. 61
In the Time of Eudoxusp. 69
Ruler and Compass Constructionsp. 75
The Oldest Surviving Math Bookp. 81
Euclid's Geometry Continuedp. 87
Alexandria and Archimedesp. 95
The End of Greek Mathematicsp. 105
Early Medieval Number Theoryp. 113
Algebra in the Early Middle Agesp. 119
Geometry in the Early Middle Agesp. 123
Khayyam and the Cubicp. 127
The Later Middle Agesp. 131
Modern Mathematical Notationp. 137
The Secret of the Cubicp. 141
The Secret Revealedp. 147
A New Calculating Devicep. 153
Mathematics and Astronomyp. 157
The Seventeenth Centuryp. 161
Pascalp. 167
The Seventeenth Century IIp. 175
Leibnizp. 181
The Eighteenth Centuryp. 185
Lagrangep. 191
Nineteenth-Century Algebrap. 195
Nineteenth-Century Analysisp. 199
Nineteenth-Century Geometryp. 203
Nineteenth-Century Number Theoryp. 209
Cantorp. 213
Foundationsp. 217
Twentieth-Century Number Theoryp. 221
Referencesp. 227
Appendix A Sample Assignments and Testsp. 229
Appendix B Answers to Selected Exercisesp. 245
Indexp. 257
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387942803
ISBN-10: 0387942807
Series: Readings in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 265
Published: 4th April 1996
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 2.54
Weight (kg): 0.54
Edition Number: 2