Math Through the Ages : A Gentle History for Teachers and Others

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

• ISBN13: 9781881929215
• ISBN10: 1881929213
• Format: Paperback
• Copyright: 2002-08-01
• Publisher: Oxton House Pub

Table of Contents

Preface	iii
History in the Mathematics Classroom	1	(4)
The History of Mathematics in a Large Nutshell	5	(186)
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	(2)
Sketches
Keeping Count
Writing Whole Numbers	61	(6)
Reading and Writing Arithmetic
Where the Symbols Came From	67	(4)
Nothing Becomes a Number
The Story of Zero	71	(4)
Broken Numbers
Writing Fractions	75	(6)
Something Less Than Nothing?
Negative Numbers	81	(6)
By Tens and Tenths
Metric Measurement	87	(4)
Measuring the Circle
The Story of π	91	(4)
The Cossic Art
Writing Algebra with Symbols	95	(6)
Linear Thinking
Solving First Degree Equations	101	(4)
A Square and Things
Quadratic Equations	105	(4)
Intrigue in Renaissance Italy
Solving Cubic Equations	109	(4)
A Cheerful Fact
The Pythagorean Theorem	113	(6)
A Marvelous Proof
Fermat's Last Theorem	119	(6)
On Beauty Bare
Euclid's Plane Geometry	125	(6)
In Perfect Shape
The Platonic Solids	131	(4)
Shapes by the Numbers
Coordinate Geometry	135	(6)
Impossible, Imaginary, Useful
Complex Numbers	141	(6)
Half Is Better
Sine and Cosine	147	(6)
Strange New Worlds
The Non-Euclidean Geometries	153	(6)
In the Eye of the Beholder
Projective Geometry	159	(4)
What's in a Game?
The Start of Probability Theory	163	(6)
Making Sense of Data
Statistics Becomes a Science	169	(6)
Machines that Think?
Electronic Computers	175	(6)
The Arithmetic of Reasoning
Logic and Boolean Algebra	181	(4)
Beyond Counting
Infinity and the Theory of Sets	185	(6)
What to Read Next	191	(8)
The Reference Shelf	191	(3)
Fifteen Historical Books You Ought to Read	194	(2)
The Internet and Other Media	196	(3)
Bibliography	199	(8)
Index	207