(Translated) Russian mathematics books

Question

Generally speaking, most Russian mathematicians are known to do and teach mathematics in a very original manner. They do it in a very intuitive yet rigorous way, with/through wonderful connections to physics.

Could anyone point out (and comment on) some of their books, especially the less known, on subjects such as calculus/classical analysis, linear/abstract algebra and geometry? Also, any online lectures notes in English?

I'm very familiar with books by mathematicians such as Vladimir Arnold, Sergei Novikov, Yakov Sinai).

Answer 1

Here's a reference of references: http://pauli.uni-muenster.de/~munsteg/arnold.html. I'd also recommend A Primer of Infinitesimal Analysis (J L Bell); it's intuitive but not Russian.

Answer 2

Well, as an applied math student, I also love Russian books so much. I found most Russian mathematicians are also interested in writing books, so it may be convenient to search by the authors.

Here are some that I know: Geometry: S.P.Novikov (as you mentioned), Fomenko (he has many books, including a book on "geometric intuition" and a nice textbook, with Mischenko).

Mechanics: V.I.Arnold (many books, including the wonderful GTM64), Sedov (expert on fluid mechanics, book on continuum mechanics and dimensional analysis), Zorich (has a famous book on mathematical analysis) wrote a book named "Mathematical Analysis of Problems in the Natural Sciences". Landau (10 vol. on physics)

Analysis: for example, Kolmogolov and Fomin's book on functional analysis

Answer 3

There's also an interesting three-volume book called "Mathematics - Its Content, Methods, and Meaning" written by Aleksandrov, Kolmogorov, and others. Originally written in the 50s and translated into English (MIT Press) in the 60s.