**AMS/MAA Textbooks**

Volume: 32;
2015;
331 pp;
Hardcover

MSC: Primary 01;
Secondary 97

**Print ISBN: 978-1-93951-212-3
Product Code: TEXT/32**

List Price: $60.50

AMS Member Price: $45.38

MAA Member Price: $45.38

**Electronic ISBN: 978-1-4704-5826-3
Product Code: TEXT/32.E**

List Price: $60.50

AMS Member Price: $45.38

MAA Member Price: $45.38

#### Supplemental Materials

# Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition

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*William P. Berlinghoff; Fernando Q. Gouvêa*

MAA Press: An Imprint of the American Mathematical Society

Recipient of the Mathematical Association of America's
Beckenbach Book Prize in 2007!

Where did math come from? Who thought up all those algebra symbols,
and why? What is the story behind \(\pi\)? … negative
numbers? … the metric system? … quadratic equations?
… sine and cosine? … logs? The 30 independent historical
sketches in Math through the Ages answer these questions and
many others in an informal, easygoing style that is accessible to
teachers, students, and anyone who is curious about the history of
mathematical ideas. Each sketch includes Questions and Projects to
help you learn more about its topic and to see how the main ideas fit
into the bigger picture of history.

The 30 short stories are preceded by a 58-page bird's-eye overview
of the entire panorama of mathematical history, a whirlwind tour of
the most important people, events, and trends that shaped the
mathematics we know today. “What to Read Next” and
reading suggestions after each sketch provide starting points for
readers who want to learn more.

This book is ideal for a broad spectrum of audiences, including
students in history of mathematics courses at the late high school or
early college level, pre-service and in-service teachers, and anyone
who just wants to know a little more about the origins of
mathematics.

An instructor's manual for this title is available to those
instructors who have adopted the textbook for classroom use. Please
send email to textbooks@ams.org
for more information.

#### Reviews & Endorsements

This is a beautiful and important book, a pleasure to read, in which the history recounted fully illuminates the mathematical ideas, and the ideas themselves are superbly explained: a wonderful accomplishment.

-- Barry Mazur, Harvard University

“Math through the Ages” is a treasure, one of the best history of math books at its level ever written. Somehow, it manages to stay true to a surprisingly sophisticated story, while respecting the needs of its audience. Its overview of the subject captures most of what one needs to know, and the 30 sketches are small gems of exposition that stimulate further exploration.

-- Glen van Brummelen, Quest University, President (2012–14) of the Canadian Society for History and Philosophy of Mathematics

# Table of Contents

## Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition

- Cover Cover11
- Copyright ii3
- Title iii4
- Contents xiii14
- Preface to the Second Edition vii8
- Preface to the First Edition ix10
- History in the Mathematics Classroom 116
- The History of Mathematics in a Large Nutshell 520
- Beginnings 621
- Greek Mathematics 1530
- Meanwhile, in India 2540
- Arabic Mathematics 2944
- Medieval Europe 3348
- The 15th and 16th Centuries 3550
- Algebra Comes of Age 3752
- Calculus and Applied Mathematics 4358
- Rigor and Professionalism 4863
- Abstraction, Computers, and New Applications 5469
- Mathematics Today 5974

- Sketches 6782
- 1. Keeping Count: Writing Whole Numbers 6782
- 2. Reading and Writing Arithmetic: The Basic Symbols 7590
- 3. Nothing Becomes a Number: The Story of Zero 8196
- 4. Broken Numbers: Writing Fraction 87102
- 5. Less Than Nothing?: Negative Numbers 95110
- 6. By Tens and Tenths: Metric Measurement 103118
- 7. Measuring the Circle: The Story of π 109124
- 8. The Cossic Art: Writing Algebra with Symbols 115130
- 9. Linear Thinking: Solving First Degree Equations 123138
- 10. A Square and Things: Quadratic Equations 129144
- 11. Intrigue in Renaissance Italy: Solving Cubic Equations 135150
- 12. A Cheerful Fact: The Pythagorean Theorem 141156
- 13. A Marvelous Proof: Fermat's Last Theorem 149164
- 14. On Beauty Bare: Euciid's Plane Geometry 157172
- 15. In Perfect Shape: The Platonic Solids 165180
- 16. Shapes by the Numbers: Coordinate Geometry 171186
- 17. Impossible, Imaginary, Useful: Complex Numbers 179194
- 18. Half Is Better: Sine and Cosine 187202
- 19. Strange New Worlds: The Non-Euclidean Geometries 195210
- 20. In the Eye of the Beholder: Projective Geometry 203218
- 21. What's in a Game?: The Start of Probability Theory 209224
- 22. Making Sense of Data: Statistics Becomes a Science 217232
- 23. Machines that Think?: Electronic Computers 225240
- 24. The Arithmetic of Reasoning: Boolean Algebra 233248
- 25. Beyond Counting: Infinity and the Theory of Sets 239254
- 26. Out of the Shadows: The Tangent Function 247262
- 27. Counting Ratios: Logarithms 255270
- 28. Any Way You Slice It: Conic Sections 263278
- 29. Beyond the Pale: Irrational Numbers 271286
- 30. Barely Touching: From Tangents to Derivatives 279294

- 'What to Read Next 287302
- When They Lived 295310
- Bibliography 301316
- Index 319334
- About the Authors 333348
- Back cover Back Cover1349