Mathematics
Its Content, Methods and Meaning
About the book
The work of 18 Russian mathematicians, credited to A. D. Aleksandrov, A. N. Kolmogorov and M. A. Lavrent'ev, makes up a survey of 20 major areas of mathematics at elementary and advanced levels, tracing each from simple origins to later sophisticated forms. Its first part moves from an overview of the field to algebra, analytic geometry and ordinary differential equations. The second covers the calculus of variations, curves and surfaces, complex functions, partial differential equations, prime numbers, probability, approximation and computers. The third turns to real-variable functions, topology, non-Euclidean geometry, linear algebra, functional analysis and groups. Each chapter ends with suggested reading, and the former three-volume set now appears in one volume.
Nassim Nicholas Taleb praised it as an example of the Russian school, clear, with minimal formalism and no needless pedantry, and suggested mathematicians use it as a model.
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Nassim Nicholas 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.
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A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent'ev