Mathematics: Its Content, Methods and Meaning

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Aleksandr Danilovich Aleksandrov, Andreĭ Nikolaevich Kolmogorov
Dover Publications, 1999 - Mathematics - 1120 pages
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Hailed by The New York Times Book Review as "nothing less than a major contribution to the scientific culture of this world," this major survey features the work of 18 outstanding mathematicians. Primary subjects include analytic geometry, algebra, ordinary and partial differential equations, the calculus of variations, functions of a complex variable, prime numbers, and theories of probability and functions. Other topics include linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

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About the author (1999)

The Russian Equation
Representative of the tremendous impact which Russian mathematicians have had on the Dover list since the Sputnik era is this outstanding book edited by A. D. Aleksandrov and others.

Critical Acclaim for Mathematics: Its Content, Methods and Meaning:
"In effect, these volumes present a do-it-yourself course for the person who would like to know what the chief fields of modern mathematics are all about but who does not aspire to be a professional mathematician or a professional user of mathematics. The coverage is extremely wide, including such important areas as linear algebra, group theory, functional analysis, ordinary and partial differential equations, the theory of functions of real and complex variables, and related subjects. . . . What makes these volumes so readable as compared with usual mathematics textbooks is the emphasis here upon basic concepts and results rather than upon the intricate and wearying proofs that make such demands in conventional textbooks and courses. There are proofs in these volumes, but usually they are presented only for the most important results, and even then to emphasize key areas and to illustrate the kind of methodology employed. . . . It is hard to imagine that any intelligent American with a curious mind and some good recollection of his high school and college mathematics would not find many entrancing discoveries in the intellectual gold mine that is this work." — The New York Times Book Review

"An excellent reference set for bright high school students and beginning college students . . . also of value to their teachers for lucid discussions and many good elementary examples in both familiar and unfamiliar branches. The intelligentsia of laymen who care to tackle more than today's popular magazine articles on mathematics will find many rewarding introductions to subjects of current interest." — The Mathematics Teacher

"Whether a physicist wishes to know what a Lie algebra is or how it is related to a Lie group, or an undergraduate would like to begin the study of homology, or a crystallographer is interested in Fedorov groups, or an engineer in probability, or any scientist in computing machines, he will find here a connected, lucid account." — Science

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