Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general...

Contains articles on the history of Soviet mathematics. This book focuses on the personal lives of Russian mathematicians, and political events that shaped the course of scientific work in the Soviet Union. It is suitable for mathematicians, historians, an

This volume contains 11 lectures delivered by the author ranging over a variety of topics in the history of mathematics. The lectures, presented between 1970 and 1987, were delivered in a variety of venues and appeared only in less accessible publications. The early differential and integral calculus, Christiaan Huygens, and the concept of construction in 17th- and 18th-century mathematics are the three themes around which much of his research has concentrated. Those who teach mathematics, as well as mathematics historians, should appreciate this insightful, wide ranging book.

For over two centuries, the work of the St. Petersburg mathematicians in number theory has constituted a glorious contribution to mathematics. The Russian book, The St. Petersburg School of Number Theory, is about the life and work of prominent members of this school, such as Chebyshev, Korkin, Zolotarev, Markov, Voronoi, and Vinogradov. These mathematicians are indeed a very distinguished group, and their work in number theory is of the highest quality and continues to have lasting significance. This English translation acquaints the reader with the most important works of these six eminent...

This volume contains original essays on Ramanujan and his work. It also includes survey articles in areas influenced by Ramanujan's mathematics. Most of the articles in the book are non-technical, but even those that are contain substantial sections that should engage the general reader. The opening section includes an account of a cryptic family history written by his younger brother, S. Lakshmi Narasimhan. Following are articles on Ramanujan's illness by R.A. Rankin, the British physician D.A.B. Young, and Nobel Laureate S. Chandrasekhar. They present a study of his symptoms, a convincing...

The idea of chaos figures prominently in mathematics today. It arose in the work of one of the greatest mathematicians of the late 19th century, Henri Poincare, on a problem in celestial mechanics: the three body problem. This ancient problem - to describe the paths of three bodies in mutual gravitational interaction - is one of those which is simple to pose but impossible to solve precisely. Poincare's famous memoir on the three body problem arose from his entry in King Oscar of Sweden's 60th birthday competition. His essay won the prize and was set up in print as a paper in Acta Mathematica...

Includes articles written by A N Kolmogorov's students and colleagues and his personal accounts of shared experiences and lifelong mathematical friendships. This volume includes the following articles: "On A N Kolmogorov" by V I Arnol'd, "In Memory of A N

Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands programme for number theory. In this title, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passage from local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He...

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...