Mathematical World 1991; 187 pp; softcover Volume: 1 Reprint/Revision History: third printing 1999 ISBN10: 0821801651 ISBN13: 9780821801659 List Price: US$26 Member Price: US$20.80 Order Code: MAWRLD/1
 Throughout the history of mathematics, maximum and minimum problems have played an important role in the evolution of the field. Many beautiful and important problems have appeared in a variety of branches of mathematics and physics, as well as in other fields of sciences. The greatest scientists of the pastEuclid, Archimedes, Heron, the Bernoullis, Newton, and many otherstook part in seeking solutions to these concrete problems. The solutions stimulated the development of the theory, and, as a result, techniques were elaborated that made possible the solution of a tremendous variety of problems by a single method. This book presents fifteen "stories" designed to acquaint readers with the central concepts of the theory of maxima and minima, as well as with its illustrious history. This book is accessible to high school students and would likely be of interest to a wide variety of readers. In Part One, the author familiarizes readers with many concrete problems that lead to discussion of the work of some of the greatest mathematicians of all time. Part Two introduces a method for solving maximum and minimum problems that originated with Lagrange. While the content of this method has varied constantly, its basic conception has endured for over two centuries. The final story is addressed primarily to those who teach mathematics, for it impinges on the question of how and why to teach. Throughout the book, the author strives to show how the analysis of diverse facts gives rise to a general idea, how this idea is transformed, how it is enriched by new content, and how it remains the same in spite of these changes. Table of Contents Part One  Ancient maximum and minimum problems
 Why do we solve maximum and minimum problems?
 The oldest problemDido's problem
 Maxima and minima in nature ( optics\()\)
 Maxima and minima in geometry
 Maxima and minima in algebra and in analysis
 Kepler's problem
 The brachistochrone
 Newton's aerodynamical problem
Part Two  Methods of solution of extremal problems
 What is a function?
 What is an extremal problem?
 Extrema of functions of one variable
 Extrema of functions of many variables. Lagrange's principle
 More problem solving
 What happened later in the theory of extremal problems?
 More accurately, a discussion
