Professor Michael Mascagni
Department of Computer Science
Florida State University
Tallahassee, FL 32306-4530
Professor Michael Mascagni received his Ph.D. in Mathematics from NYU's Courant Institute of Mathematical Sciences where he worked in mathematical biology and the numerical solution of partial differential equations. He then moved to the Washington, DC area as a National Research Council Post-Doctoral Fellow at NIDDK's Mathematical Research Branch at the National Institutes of Health in Bethesda. Following, he accepted a staff position at the Institute for Defense Analyses's new Supercomputing Research Center (now the IDA Center for Computing Sciences) in Bowie, Maryland. At the beginning of 1997, he moved back to academia to coordinate the Doctoral Program in Scientific Computing at the University of Southern Mississippi. Recently, he accepted a new position in the Department of Computer Science at Florida State University. His research interests are Monte Carlo methods, numerical analysis, numerical solution of partial differential equations, parallel computing, random number generation, cryptography, distributed computing, and scalable numerical libraries.
Quasi-Monte Carlo Methods: Where Randomness and Determinism Collide
We will give a brief overview of Monte Carlo methods, methods for solving problems that involve the use of random numbers. Pseudorandom numbers are used in these simulations because they mimic the behavior of "real" random numbers. However, there are many Monte Carlo applications that do not really require randomness, but instead need numbers that uniformly cover the sample space. To meet these different requirements, quasirandom numbers have been developed. These are numbers that are very evenly distributed, but do not behave like truly random numbers. In fact, for certain problems one obtains deterministic, not probabilistic, bounds for Quasi-Monte Carlo methods. We present some of the fundamental results about this deterministic method to solve random number driven problems. We also describe some simple methods for quasirandom number generation and discuss open problems in the field.