This Third Edition examines the elementary arithmetic, geometry, and algebra of a number of cultures for which a considerable amount of literature exists, such as Mesopotamia, Egypt, Greece, India, China, and Japan.  These ideas are then incorporated into Europe during the Medieval and Renaissance periods, culminating in the development of calculus.  Specialized topics, such as the Golden Ratio, the Mayan calendar, the number p, and the like are also included as supplemental material as is a survey on the post-calculus development of geometry, analysis, algebra, probability and statistics, logic, and set theory.   In order to master the history of mathematics, the following three main ideas are presented: the facts--the who/what/when/where of the major advances in each area; the mathematics involved on its own terms (not in a modernized version that adds to or subtracts from the significance of the result in its own time); and the integration of these two areas into a coherent picture of the development of the subject, including speculation on the motives for studying various topics and their possible applications.  Only the first of these goals can be achieved by reading the book.  The other two require carefully designed problems to guide readers to a fuller understanding of the mathematics involved and its social and historical context, all of which are included in the book as well as in supplemental material for instructors.  Exercises are provided at the end of each chapter, and a listing of related websites is included to serve as a springboard for readers who wish to pursue a specialized topic in more depth.  In addition, a generous number of photographs are included in the book and in the PowerPoint lectures.