Numbers, Revised Edition deals with numbers from the point of view of computation, beginning with the earliest number concepts from ancient Mesopotamian, Chinese, and Mayan mathematicians. It describes the origin and diffusion of Arabic numerals, and it concludes with a discussion of the way that the number system is represented within computers. A new section describes some of the IEEE standards for floating point arithmetic, and a more detailed discussion of the work of G del and Turing has been added to this edition. Irrational numbers and the idea of infinity are also examined in this...

Probability and Statistics, Revised Edition deals with the history of probability, describing the modern concept of randomness and examining "pre-probabilistic" ideas of what most people today would characterize as randomness. This revised book documents some historically important early uses of probability to illustrate some very important probabilistic questions. It goes on to explore statistics and the generations of mathematicians and non-mathematicians who began to address problems in statistical analysis, including the statistical structure of data sets as well as the theory of sampling...

Geometry, Revised Edition describes geometry in antiquity. Beginning with a brief description of some of the geometry that preceded the geometry of the Greeks, it takes up the story of geometry during the European Renaissance as well as the significant mathematical progress in other areas of the world. It also discusses the analytic geometry of Ren Descartes and Pierre Fermat, the alternative coordinate systems invented by Isaac Newton, and the solid geometry of Leonhard Euler. Also included is an overview of the geometry of one of the most successful mathematicians of the 19th century,...

This volume of the History of Mathematics series delves into the topic of how mathematical concepts are very much ingrained in the laws of nature.

Algebra, Revised Edition describes the history of both strands of algebraic thought. This updated resource describes some of the earliest progress in algebra as well as some of the mathematicians in Mesopotamia, Egypt, China, and Greece who contributed to this early period. It goes on to explore the many breakthroughs in algebraic techniques as well as how letters were used to represent numbers. New material has been added to the chapter on "modern" algebra, a type of mathematical research that continues to occupy the attention of many mathematicians today.

Beyond Geometry describes how set-theoretic topology developed and why it now occupies a central place in mathematics. Describing axiomatic method as well as providing a definition of what a geometric property is, this new resource examines how early analysts incorporated geometric thinking into their development of the calculus. It also looks at the various mathematicians who struggled to develop a new conceptual framework for mathematics and examines one of the sub-disciplines of set-theoretic topology called dimension theory.

This set features five revised editions and one brand-new volume that cover a significant portion of recent mathematical history as well as its origins. From the in-depth interviews with prominent mathematicians, readers will develop an appreciation for current work in mathematics as well as an interest in the future of this remarkable subject.