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...
Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equ...
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...
Numbers, Revised Edition deals with numbers from the point of view of computation, beginning with the earliest number concepts from ancient Mesopotami...
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...
Probability and Statistics, Revised Edition deals with the history of probability, describing the modern concept of randomness and examining "pre-prob...
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.
Algebra, Revised Edition describes the history of both strands of algebraic thought. This updated resource describes some of the earliest progress in ...
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.
Beyond Geometry describes how set-theoretic topology developed and why it now occupies a central place in mathematics. Describing axiomatic method as ...