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Book Summary of The Princeton Companion To Mathematics This is a wonderful book. The content is overwhelming. Every practicing mathematician, everyone who uses mathematics, and everyone who is interested in mathematics must have a copy of their own.--Simon A. Levin, Princeton University The Princeton Companion to Mathematics fills a vital need. It is the only book of its kind.--Victor J. Katz, professor emeritus, University of the District of Columbia I think that this is a wonderful book, completely different from anything that has been written before about mathematics and mathematicians.--Endre Suli, University of Oxford The Princeton Companion to Mathematics is a much needed--and will become a much used--reference work. In fact, it will stand alone as the reference work in mathematics.--John J. Watkins, Colorado College What is a modular form? What is the point of symplectic geometry? This one-of-a-kind reference illuminates modern pure mathematics in all its diversity. More than 200 articles, organized thematically and written by many of the worlds leading mathematicians, explain the major ideas and branches of mathematics in a clear, accessible style. Presenting not only definitions but also motivation and context for concepts, methods, theorems, and other topics of mathematical study, this is an indispensable resource for everyone with a serious interest in the field. 1. What is Mathematics?Introduces the language and grammar of mathematicsfundamental definitionsgeneral goals of mathematical researchthe subject matter of mathematics 2. The Fundamental Ideas of MathematicsExplores algebraalgorithmsgeometryhow analysis became rigorousnumbersthe crisis in the foundations of mathematics the development of the idea of proof 3. Mathematical ObjectsDefines and explains more than 75 mathematical objects, concepts, and buz

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