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The Contents of Math through the Ages

Table of Contents

Preface to the Second Edition

Preface to the First Edition

History in the Mathematics Classroom

The History of Mathematics in a Large Nutshell


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


  1.  Keeping Count:  Writing Whole Numbers

  2.  Reading and Writing Arithmetic:  The Basic Symbols

  3.  Nothing Becomes a Number:  The Story of Zero

  4.  Broken Numbers:  Writing Fractions

  5.  Something Less Than Nothing?:  Negative Numbers

  6.  By Tens and Tenths:  Metric Measurement

  7.  Measuring the Circle:  The Story of π

  8.  The Cossic Art:  Writing Algebra with Symbols

  9.  Linear Thinking:  Solving First Degree Equations

10.  A Square and Things:  Quadratic Equations

11.  Intrigue in Renaissance Italy:  Solving Cubic Equations

12.  A Cheerful Fact:  The Pythagorean Theorem

13.  A Marvelous Proof:  Fermat's Last Theorem

14.  On Beauty Bare:  Euclid's Plane Geometry

15.  In Perfect Shape:  The Platonic Solids

16.  Shapes by the Numbers:  Coordinate Geometry

17.  Impossible, Imaginary, Useful:  Complex Numbers

18.  Half Is Better:  Sine and Cosine

19.  Strange New Worlds:  The Non-Euclidean Geometries

20.  In the Eye of the Beholder:  Projective Geometry

21.  What's in a Game?:  The Start of Probability Theory

22.  Making Sense of Data:  Statistics Becomes a Science

23.  Machines that Think?:  Electronic Computers

24.  The Arithmetic of Reasoning:  Logic and Boolean Algebra

25.  Beyond Counting:  Infinity and the Theory of Sets

26.  Out of the Shadows: The Tangent Function

27.  Counting Ratios: Logarithms

28.  Any Way You Slice It: Conic Sections

29.  Beyond the Pale: Irrational Numbers

30.  Barely Touching: From Tangents to Derivatives

What to Read Next

The Reference Shelf

Fifteen Twelve Historical Books You Ought to Read

Internet and Other Media History Online

When They Lived



To see any of the following sample pages, just click on its name.

Preface to the 1st Edition, complete

The first page of:

The History ... in a Large Nutshell

Keeping Count

The Cossic Art

Impossible, Imaginary, Useful

“This is a beautiful, important book, a pleasure to read...”

Barry Mazur, Harvard Univ.

“A marvelous book...very well organized and thus very user friendly...a wonderful resource for teachers.”

Victor Katz, U. of the District of Columbia

“I highly recommend this book for every math teacher’s personal library.”

Karen Dee Michalowicz
The Langley School, McLean, VA

Some reviewer comments:

First Edition, 2002

Expanded First Edition, 2004

Second Edition, 2014

Items in red are new in the Second Edition.

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