SCL's Antun Balaz was invited to contribute to a series of Seminars on Applied Mathematics, organized by the Mathematical Institute of the Serbian Academy of Sciences and Arts. In a two-part seminar held on 9 March 2010, he first introduced basic concepts of Grid computing and available Grid resources in Serbia, and then presented an effective-action based SPEEDUP Monte Carlo algorithm for calculation of quantum mechanical transition amplitudes. Parallelization and implementation strategies for Monte Carlo codes were also discussed in the framework of MPI, OpenMP and Grid environments.