It is well-known that Monte Carlo methods are used for solving various urgent problems in mathematical physics. A lot of new numerical stochastic algorithms and models were elaborated in Institute of Computational Mathematics and Mathematical Geophysics (ICM and MG) SD RAS during last years. The Monte Carlo schemes can be effectively illustrated on computer and presented for students. On the other hand, the special instrumental environment based on hypertext technology is developed in ICM and MG. These computer tools can be used for elaboration of training mathematical courses.
Now the electronic manual "Foundations of Monte Carlo methods" is developed in ICM and MG for students of Novosibirsk State University. This manual is based on lectures of Prof. G.A. Mikhailov and Dr. A.V. Voytishek. The central themes of this course are:
- methods of realization of generators of standard random and pseudo-random numbers,
- methods of numerical modeling of discrete and continuous stochastic values (including standard and special algorithms for discrete values; the reverse distribution function method, randomization and rejection technique for continuous values),
- numerical realization of stochastic vectors,
- methods of modeling of stochastic processes and fields,
- methods of calculation of multiple integrals,
- numerical methods of solution of the integral equations of the second kind,
- numerical solution of equations of mathematical physics,
- applications of Monte Carlo methods (including problems of the radiation transform theory).
The manual is divided in lessons containing many illustrations, diagrams, model tasks, exercises, questions, and comments.