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Nassim Nicolás Taleb (Flaneur)There is something admirable about the school of the Russians: they are thinkers doing math, with remarkable clarity, minimal formalism, and total absence of unnecessary pedantry one finds in more modern texts (in the post Bourbaki era). This is of course surprising as one would have expected the exact opposite from the products of the communist era. Mathematicians should be using this book as a model for their own composition. You can read it and reread it. Professors should assign this in addition to modern texts, as readers can get intutions, something alas absent from modern texts.
This major survey of mathematics, featuring the work of 18 outstanding Russian mathematicians and including material on both elementary and advanced levels, encompasses 20 prime subject areas in mathematics in terms of their simple origins and their subsequent sophisticated developement. As Professor Morris Kline of New York University noted, "This unique work presents the amazing panorama of mathematics proper. It is the best answer in print to what mathematics contains both on the elementary and advanced levels."
Beginning with an overview and analysis of mathematics, the first of three major divisions of the book progresses to an exploration of analytic geometry, algebra, and ordinary differential equations. The second part introduces partial differential equations, along with theories of curves and surfaces, the calculus of variations, and functions of a complex variable. It furthur examines prime numbers, the theory of probability, approximations, and the role of computers in mathematics. The theory of functions of a real variable opens the final section, followed by discussions of linear algebra and nonEuclidian geometry, topology, functional analysis, and groups and other algebraic systems.
Thorough, coherent explanations of each topic are further augumented by numerous illustrative figures, and every chapter concludes with a suggested reading list. Formerly issued as a three-volume set, this mathematical masterpiece is now available in a convenient and modestly priced one-volume edition, perfect for study or reference.