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Mathematics and Its History

A Concise Edition

  • Textbook
  • © 2020

Overview

Authors:
  1. John Stillwell

    1. Department of Mathematics, University of San Francisco, San Francisco, USA

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  • Presents a concise, unified account of undergraduate mathematics by illustrating the rich historical context behind various topics
  • Balances breadth and rigor in a manageable volume that’s suitable for a one-semester course
  • Explores various moments in history through a mathematical perspective

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

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xv
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  2. The Theorem of Pythagoras

    • John Stillwell
    Pages 1-15

  3. Greek Geometry

    • John Stillwell
    Pages 17-33

  4. Greek Number Theory

    • John Stillwell
    Pages 35-49

  5. Infinity in Greek Mathematics

    • John Stillwell
    Pages 51-62

  6. Polynomial Equations

    • John Stillwell
    Pages 63-84

  7. Algebraic Geometry

    • John Stillwell
    Pages 85-97

  8. Projective Geometry

    • John Stillwell
    Pages 99-121

  9. Calculus

    • John Stillwell
    Pages 123-138

  10. Infinite Series

    • John Stillwell
    Pages 139-155

  11. Elliptic Curves and Functions

    • John Stillwell
    Pages 157-179

  12. Complex Numbers and Curves

    • John Stillwell
    Pages 181-204

  13. Complex Numbers and Functions

    • John Stillwell
    Pages 205-223

  14. Non-Euclidean Geometries

    • John Stillwell
    Pages 225-256

  15. Group Theory

    • John Stillwell
    Pages 257-282

  16. Topology

    • John Stillwell
    Pages 283-296

  17. Commutative Algebra

    • John Stillwell
    Pages 297-322

  18. Sets, Logic, and Computation

    • John Stillwell
    Pages 323-346

  19. Back Matter

    Pages 347-400
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Keywords

About this book

This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course.

The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted.

Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed.

From reviews of previous editions:

“Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel…. The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition

"The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and tothe development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition

Reviews

“This is a beautiful book. … it would be fun to teach a course from it and I hope to get that chance. … This book flows so well that I did not feel anything was lacking from it. … I am confident that the many readers of Stillwell’s work will find it satisfying and worthwhile to update their libraries with this edition. Those currently unfamiliar with his work will find this a delightful place to begin.” (Michele Intermont, MAA Reviews, October 18, 2021)

Authors and Affiliations

  • Department of Mathematics, University of San Francisco, San Francisco, USA

    John Stillwell

About the author

John Stillwell is Professor Emeritus at the University of San Francisco and formerly Associate Professor at Monash University in Melbourne, Australia. He is an accomplished author, whose Springer books include: The Four Pillars of Geometry, Elements of Algebra, Naive Lie Theory, and many more.

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