Computational power available to scientific researchers is increasing at such a rate in recent years that totally new numerical approaches to forefront problems are playing an increasingly important role in modern physics research. At the Summer School, current topics in atomic and nuclear physics where such computational approaches may be most fruitful were discussed by an internationally distinguished faculty. Major topics discussed included Ultra-relativistic Heavy Ion Collisions, the importance of sub-nucleon degrees of freedom to nuclear physics, the importance of electromagnetic processes in collisions of high-energy highly charged ions, relativistic effects in atomic and nuclear structure, current topics in quantum chemistry, modern Monte Carlo techniques, path integral methods, and applications of static and time-dependent Hartree-Fock methods in atomic and nuclear physics.