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Most russian mathematician(generally) are known to do and teach mathematics in a very original manner,they do in a very intuitive yet rigorous way, with/through wonderful connection to physics.

Could anyone point out(and comment on) some of their book especially the less known, on subjects such as calculus/classical analysis , linear/abstract algebra and geometry?(I'm very familiar with books by mathematicians such as Vladimir Arnold,Sergei Novikov,Yakov Sinai).

Also any online lectures notes in english ?

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    $\begingroup$ I wonder what American mathematicians are generally known for ...??? $\endgroup$ – William Aug 10 '14 at 2:46
  • $\begingroup$ Get Kolmogorov's Analysis books for classical and modern analysis. $\endgroup$ – Darrin Aug 10 '14 at 3:41
  • $\begingroup$ If you're interested in complex analysis, Markushevich has a massive and famous treatment. I don't know if the full work's ever been translated, but Silverman has a Dover edition condensing the work. $\endgroup$ – Kevin Carlson Aug 29 '14 at 16:57
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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

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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.

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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.

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