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Lately I've been interested in Lev Landau's Theoretical Minimum exams and I would like to study a bit at this level (or at least try to do so). For the Physics exams, it is easy to find appropriate literature (Landau's Course of Theoretical Physics). However, I would like to know which would be good places to study for the Mathematics exams. According to this post, the subjects of the mathematical exams are:

  1. Mathematics I: Integration, ordinary differential equations, vector algebra and tensor analysis.
  2. Mathematics II: The theory of functions of a complex variable, residues, solving equations by means of contour integrals (Laplace's method), the computation of the asymptotics of integrals, special functions (Legendre, Bessel, elliptic, hypergeometric, gamma function).

I've looked around at the websites of the Landau Institute for Theoretical Physics (which applies the exams nowadays) and at the Moscow Institute of Physics And Technology (whose students have to pass some of the exams), but couldn't find any information on literature, only the contents of the exams...

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One of the resources recommended to enter the Landau Institute as a graduate student is the "A Course of Higher Mathematics" series, by Vladimir I. Smirnov. I've been reading it and, so far, it seems to be quite complete, besides some of its exercises appear on Demidovitch's book of exercises on Analysis.

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