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

Mathematics

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 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.

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

Preface
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