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Math through the Ages: A Gentle History for Teachers and Others, Expanded Edition
William P. Berlinghoff and Fernando Q. Gouvêa
Table of Contents
Preface
History in the Mathematics Classroom
The History of Mathematics in a Large Nutshell
- Beginnings
- Greek Mathematics
- Meanwhile, in India
- Arabic Mathematics
- Medieval Europe
- The 15th and 16th Centuries
- Algebra Comes of Age
- Calculus and Applied Mathematics
- Rigor and Professionalism
- Abstraction, Computers, and New Applications
- Mathematics Today
Sketches
- Keeping Count
Writing Whole Numbers - Reading and Writing Arithmetic
Where the Symbols Came From - Nothing Becomes a Number
The Story of Zero - Broken Numbers
Writing Fractions - Something Less Than Nothing?
Negative Numbers - By Tens and Tenths
Metric Measurement - Measuring the Circle
The Story of - The Cossic Art
Writing Algebra with Symbols - Linear Thinking
Solving First Degree Equations - A Square and Things
Quadratic Equations - Intrigue in Renaissance Italy
Solving Cubic Equations - A Cheerful Fact
The Pythagorean Theorem - A Marvelous Proof
Fermat's Last Theorem - On Beauty Bare
Euclid's Plane Geometry - In Perfect Shape
The Platonic Solids - Shapes by the Numbers
Coordinate Geometry - Impossible, Imaginary, Useful
Complex Numbers - Half Is Better
Sine and Cosine - Strange New Worlds
The Non-Euclidean Geometries - In the Eye of the Beholder
Projective Geometry - What's in a Game?
The Start of Probability Theory - Making Sense of Data
Statistics Becomes a Science - Machines that Think?
Electronic Computers - The Arithmetic of Reasoning
Logic and Boolean Algebra - Beyond Counting
Infinity and the Theory of Sets
What to Read Next
- The Reference Shelf
- Fifteen Historical Books You Ought to Read
- The Internet and Other Media
Bibliography
Index