Math Through the Ages

by Berlinghoff, William P.; Gouvea, Fernando Q.

• ISBN13: 9780883857366
• ISBN10: 0883857367
• Edition: Revised
• Format: Hardcover
• Copyright: 2003-12-01
• Publisher: Mathematical Assn of Amer

Summary

Where did maths come from? Who thought up all those algebra symbols, and why? What's the story behind ... negative numbers? ... the metric system? ... quadratic equations? ... sine and cosine? The 25 independent sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that's accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch contains Questions and Projects to help you learn more about its topic and to see how its main ideas fit into the bigger picture of history. The 25 short stories are preceded by a 56-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. Reading suggestions after each sketch provide starting points for readers who want to pursue a topic further.

Table of Contents

Preface	vii
History in the Mathematics Classroom	1	(4)
The History of Mathematics in a Large Nutshell	5	(60)
Beginnings	6	(8)
Greek Mathematics	14	(10)
Meanwhile, in India	24	(4)
Arabic Mathematics	28	(4)
Medieval Europe	32	(3)
The 15th and 16th Centuries	35	(2)
Algebra Comes of Age	37	(5)
Calculus and Applied Mathematics	42	(5)
Rigor and Professionalism	47	(6)
Abstraction, Computers, and New Applications	53	(6)
Mathematics Today	59	(6)
Sketches
1. Keeping Count Writing Whole Numbers	65	(8)
2. Reading and Writing Arithmetic Where the Symbols Came From	73	(6)
3. Nothing Becomes a Number The Story of Zero	79	(6)
4. Broken Numbers Writing Fractions	85	(8)
5. Something Less Than Nothing? Negative Numbers	93	(8)
6. By Tens and Tenths Metric Measurement	101	(6)
7. Measuring the Circle The Story of π	107	(6)
8. The Cossic Art Writing Algebra with Symbols	113	(8)
9. Linear Thinking Solving First Degree Equations	121	(6)
10. A Square and Things Quadratic Equations	127	(6)
11. Intrigue in Renaissance Italy Solving Cubic Equations	133	(6)
12. A Cheerful Fact The Pythagorean Theorem	139	(8)
13. A Marvelous Proof Fermat's Last Theorem	147	(8)
14. On Beauty Bare Euclid's Plane Geometry	155	(8)
15. In Perfect Shape The Platonic Solids	163	(6)
16. Shapes by the Numbers Coordinate Geometry	169	(8)
17. Impossible, Imaginary, Useful Complex Numbers	177	(8)
18. Half Is Better Sine and Cosine	185	(8)
19. Strange New Worlds The Non-Euclidean Geometries	193	(8)
20. In the Eye of the Beholder Projective Geometry	201	(6)
21. What's in a Game? The Start of Probability Theory	207	(8)
22. Making Sense of Data Statistics Becomes a Science	215	(8)
23. Machines that Think? Electronic Computers	223	(8)
24. The Arithmetic of Reasoning Logic and Boolean Algebra	231	(6)
25. Beyond Counting Infinity and the Theory of Sets	237	(8)
What to Read Next	245	(8)
The Reference Shelf	245	(3)
Fifteen Historical Books You Ought to Read	248	(2)
The Internet and Other Media	250	(3)
Bibliography	253	(10)
Index	263