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Mathematics: A Concise History and Philosophy

  • Textbook
  • © 1994

Overview

Authors:
  1. W. S. Anglin

    1. Keane Inc., Darien, USA

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Part of the book series: Undergraduate Texts in Mathematics (UTM)

Part of the book sub series: Readings in Mathematics (READINMATH)

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Table of contents (40 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Mathematics for Civil Servants

    • W. S. Anglin
    Pages 1-6

  3. The Earliest Number Theory

    • W. S. Anglin
    Pages 7-11

  4. The Dawn of Deductive Mathematics

    • W. S. Anglin
    Pages 13-16

  5. The Pythagoreans

    • W. S. Anglin
    Pages 17-21

  6. The Pythagoreans and Perfection

    • W. S. Anglin
    Pages 23-27

  7. The Pythagoreans and Polyhedra

    • W. S. Anglin
    Pages 29-34

  8. The Pythagoreans and Irrationality

    • W. S. Anglin
    Pages 35-41

  9. The Need for the Infinite

    • W. S. Anglin
    Pages 43-47

  10. Mathematics in Athens Before Plato

    • W. S. Anglin
    Pages 49-55

  11. Plato

    • W. S. Anglin
    Pages 57-60

  12. Aristotle

    • W. S. Anglin
    Pages 61-67

  13. In the Time of Eudoxus

    • W. S. Anglin
    Pages 69-73

  14. Ruler and Compass Constructions

    • W. S. Anglin
    Pages 75-80

  15. The Oldest Surviving Math Book

    • W. S. Anglin
    Pages 81-86

  16. Euclid’s Geometry Continued

    • W. S. Anglin
    Pages 87-94

  17. Alexandria and Archimedes

    • W. S. Anglin
    Pages 95-104

  18. The End of Greek Mathematics

    • W. S. Anglin
    Pages 105-111

  19. Early Medieval Number Theory

    • W. S. Anglin
    Pages 113-117

  20. Algebra in the Early Middle Ages

    • W. S. Anglin
    Pages 119-121
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Keywords

About this book

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.

Reviews

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

Authors and Affiliations

  • Keane Inc., Darien, USA

    W. S. Anglin

Bibliographic Information

  • Book Title: Mathematics: A Concise History and Philosophy

  • Authors: W. S. Anglin

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0875-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • Hardcover ISBN: 978-0-387-94280-3Published: 29 September 1994

  • Softcover ISBN: 978-1-4612-6930-4Published: 20 November 2012

  • eBook ISBN: 978-1-4612-0875-4Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XI, 265

  • Topics: Philosophy of Science, Mathematics, general, Physics, general

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