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In this article, we take a rapid journey through the history of algebra, noting the important developments and reflecting on the importance of this history in the teaching of algebra in secondary school or university. Frequently, algebra is considered to have three stages in its historical development: the rhetorical stage, the syncopated stage, and the symbolic stage. But besides these three stages of expressing algebraic ideas, there are four more conceptual stages which have happened along side of these changes in expressions. These stages are the geometric stage, where most of the concepts of algebra are geometric ones; the static equation-solving stage, where the goal is to find numbers satisfying certain relationships; the dynamic function stage, where motion seems to be an underlying idea, and finally, the abstract stage, where mathematical structure plays the central role. The stages of algebra are, of course not entirely disjoint from one another; there is always some overlap. We discuss here high points of the development of these stages and reflect on the use of these historical stages in the teaching of algebra.

Who Gave You the Epsilon? is a sequel to the MAA bestselling book, Sherlock Holmes in Babylon. Like its predecessor, this book is a collection of articles on the history of mathematics from the MAA journals, in many cases written by distinguished mathematicians (such as G H Hardy and B.van der Waerden), with commentary by the editors. Whereas the former book covered the history of mathematics from earliest times up to the eighteenth century and was organized chronologically, the 40 articles in this book are organized thematically and continue the story into the nineteenth and twentieth centuries. The topics covered in the book are analysis and applied mathematics, Geometry, topology and foundations, Algebra and number theory, and Surveys. Each chapter is preceded by a Foreword, giving the historical background and setting and the scene, and is followed by an Afterword, reporting on advances in our historical knowledge and understanding since the articles first appeared.

Speculates on whether our knowledge of a mathematical topic is really the same as the knowledge of the topic held by our mathematical ancestors centuries ago. Provides specific examples of using the cultural context of mathematics as an instructional strategy. (DDR)

Discusses important mathematical ideas taken from combinatorics, arithmetic, and geometry which are considered in the context of their development in various societies around the globe, including Hebrew, Islamic, Italian, Mayan, German, and Anasazi work. (11 references) (MKR)

Most current American textbooks in advanced calculus devote several sections to the theorems of Green, Gauss, and Stokes. Unfortunately, the theorems referred to were not original to these men. It is the purpose of this paper to present a detailed history of these results from their origins to their generalization and unification into what is today called the generalized Stokes’ theorem. The three theorems in question each relate ak-dimensional integral to a (k− 1)-dimensional integral; since the proof of each depends on the fundamental theorem of calculus, it is clear that their origins can be traced back to

Katz reviews Mathematical Masterpieces: Further Chronicles by the Explorers by Arthur Knoebel, Reinhard Laubenbacher, Jerry Lodder, and David Pengelley.

An Imaginary Tale The Story of ÷-1. Paul J. Nahin. Princeton University Press, Princeton, NJ, 1998. 277 pp. $24.95, £18.95. ISBN 0-691-02795-1. Nahin provides an outstanding integration of the history of imaginary numbers and a lot of interesting mathematics, much of which will be new to college mathematics majors or to professional scientists and engineers.