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Mathematics and Its History

  • John Stillwell

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

Table of contents

  1. Front Matter
    Pages i-x
  2. John Stillwell
    Pages 1-12
  3. John Stillwell
    Pages 13-26
  4. John Stillwell
    Pages 27-36
  5. John Stillwell
    Pages 37-47
  6. John Stillwell
    Pages 48-64
  7. John Stillwell
    Pages 65-77
  8. John Stillwell
    Pages 78-99
  9. John Stillwell
    Pages 100-117
  10. John Stillwell
    Pages 118-134
  11. John Stillwell
    Pages 135-151
  12. John Stillwell
    Pages 152-166
  13. John Stillwell
    Pages 167-187
  14. John Stillwell
    Pages 188-203
  15. John Stillwell
    Pages 204-219
  16. John Stillwell
    Pages 220-236
  17. John Stillwell
    Pages 237-254
  18. John Stillwell
    Pages 255-274
  19. John Stillwell
    Pages 275-291
  20. John Stillwell
    Pages 292-312
  21. John Stillwell
    Pages 313-331
  22. Back Matter
    Pages 333-373

About this book

Introduction

One of the disappointments experienced by most mathematics students is that they never get a course in mathematics. They get courses in calculus, algebra, topology, and so on, but the division of labor in teaching seems to prevent these different topics from being combined into a whole. In fact, some of the most important and natural questions are stifled because they fall on the wrong side of topic boundary lines. Algebraists do not discuss the fundamental theorem of algebra because "that's analysis" and analysts do not discuss Riemann surfaces because "that's topology," for example. Thus if students are to feel they really know mathematics by the time they graduate, there is a need to unify the subject. This book aims to give a unified view of undergraduate mathematics by approaching the subject through its history. Since readers should have had some mathematical experience, certain basics are assumed and the mathe­ matics is not developed as formally as in a standard text. On the other hand, the mathematics is pursued more thoroughly than in most general histories of mathematics, as mathematics is our main goal and history only the means of approaching it. Readers are assumed to know basic calculus, algebra, and geometry, to understand the language of set theory, and to have met some more advanced topics such as group theory, topology, and differential equations.

Keywords

Calc Finite Mathematica analytic geometry computation development function geometry group theory history of mathematics logic mathematics projective geometry themes theorem

Authors and affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsMonash UniversityClaytonAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4899-0007-4
  • Copyright Information Springer-Verlag New York 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4899-0009-8
  • Online ISBN 978-1-4899-0007-4
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site