### University of Massachusetts Dartmouth Mathematics Seminar Fall 2008

**Computational Science for Undergraduate Mathematics Students (CSUMS) Seminars**

- Wednesday, September 10, 2008, Liberal Arts 111, 2-3 pm. Gary Davis will talk on Catalan pseudoprimes.

The PowerPoint presentation for the talk is available here (davis_september_10_2008).

Catalan pseudoprimes are odd numbers that are not prime, but behave like prime numbers in that they satisfy a condition satisfied by prime numbers. To this point in time only 3 Catalan pseudoprimes are known. The talk will focus on how these Catalan pseudoprimes were found, the computational difficulty in finding others, if any, and also deal with an interesting number theory function related to the Catalan pseudoprimes, about which very little is known.

The talk is aimed at undergraduates, Freshmen on, and is part of the Research in Scientific Computing in Undergraduate Education initiative.

#### Department of Mathematics Colloquia

- Wednesday September 24 2008. Scott MacLachlan, Tufts University, will talk on algebraic multigrid in theory and practice

In recent years, computational simulation has become an important tool in many fields of science and engineering, replacing expensive or impractical experimentation in the answering of scientific questions and in the design of new technology. At the core of many of these simulations lies the solution of large-scale linear systems of equations. While these systems can, in principle, be solved using simple techniques, such as Gaussian elimination, the computational expense of these approaches makes accurate simulations intractable. In this talk, I will introduce one family of techniques, known as algebraic multigrid methods, that are used to efficiently solve the large-scale linear systems that arise in many applications. These algorithms are based on a principle of complementarity, through which different components of an error are reduced by different processes. Traditionally, this partitioning of errors has been done heuristically; new theoretical analysis, however, provides a rigorous framework for motivating the choice of components in a multigrid algorithm. I will demonstrate how this theory leads to practical algorithms for solving many real-life problems and discuss the challenges in extending these techniques.