1. The current trends in machine science and machine operating processes.
Supervisors: K.S. Kolesnikov, P.M. Shkapov.

2. Advanced research and technology of irreversible processes in physics and astrophysics.
Supervisor: A.N. Morozov.

3. High-precision physical experiment.
Supervisors: V.O. Gladyshev, V.S. Gorelik.

4. Mathematical simulation in the control science.
Supervisors: A.P. Krishchenko, S.B. Tkachev.

5. Mathematical research techniques of non-stationary processes.
Supervisor: N.I. Sidnyaev.

6. Mathematical models of continuum mechanics.
Supervisors: V.S. Zarubin, G.N. Kuvyrkin.

7. Challenges of computational mechanics and computer simulation techniques.
Supervisor: U.I. Dimitriyenko.

8. Fundamental problems of advanced technology development.
Supervisors: A.M. Golubev, A.B. Krasovskii.

9. Scientific and methodological approaches to science teaching.
Supervisors: O.S. Erkovich, S.K. Sobolev, N.N. Dvulichanskaya.