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Mathematics for the Million: How to Master the Magic of Numbers

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This history of mathematics spares no equation in the presentation of the order in which mathematical ideas arose. It begins before the beginning, when there was no such thing as formal mathematics. The title of the first chapter is "Mathematics in Remote Antiquity" and is a description of the mathematics used in the ancient civilizations of Egypt, Iraq, Pakistan, China and the Americas. Some of this is of course informed speculation, as in many cases the record is incomplete.
Formal mathematics in the western world began with what we call the Greek civilization, although it should more accurately be called the Eastern Mediterranean civilization. Euclid well forever go down is history as one of the greatest organizers in history, we are fortunate that his interests were in mathematics. The rules and proofs that he set down have been improved, but that has been an expansion of his ideas and not a refutation. Chapter 3 is an extensive coverage of the role of Euclid in the development of formal mathematics.
The remaining chapters are:

*) Number lore in antiquity
*) The rise and decline of Alexandrian civilization
*) The dawn of nothing
*) Mathematics for the mariner
*) The geometry of motion
*) Logarithms and the search for series
*) The calculus of Newton and Liebnitz
*) The algebra of the chessboard
*) The algebra of choice and chance

This book is an excellent choice for a text in a history of math course for junior or senior level math majors. The coverage is extensive; exercises appear at the end of each chapter and solutions to some are included in the appendix.