Spring 2002

[ Wed. 3/6 1:00 | Tues. 2/26 12:30 | Thurs. 1/31 6:30 | Wed. 1/30 1:30 ]

3/6/02 1:00 - The Dynamics of Quadratic Polynomials and Newton's Method
Dr. Melkana Brakalova-Trevithick

In this talk the speaker will present some aspects of the dynamic of the quadratic function $f_c(x)=x^2+c$. She will also introduce the Mandelbrot and Julia sets for quadratic polynomials of complex variables and some of their properties. The dynamic of Newton's method on the real line and possibly in the complex plane will also be considered.

2/26/02 12:30 - Some Mathematical Thoughts on Gossip
Dr. David Weinrich
Department of Mathematics
Gettysburg College

Why do rumors percolate so quickly through a community? How is it that things once known by only a few are suddenly known by all? We will discuss the classical "gossiping dons problem" and its solution, which answers the question of how to get information that is dispersed across a community to everyone. In the process, the issue of how mathematicians think and approach problems, as well as related problems that no one knows the answer to, will be addressed.

1/31/02 6:30pm - Operations Research: Applications and Solution Strategies
Richard Forrester
Department of Applied Mathematics
Clemson University

Operations research (OR) is a scientific approach to analyzing problems and making decisions. OR can be applied in virtually every area of business and government, from capital budgeting to airline scheduling. In this talk we discuss successful applications of OR, review solution methodologies, and consider research challenges. Specifically, we examine solution techniques for linear programs, integer programs, and 0-1 quadratic programs.

1/30/02 1:30pm - Generalized Inverses of Matrices
Lisa Oberbroeckling
Department of Mathematics
University of Oregon

Matrices are used to solve systems of linear equations. If the matrix associated with a system of linear equations is invertible the system has a unique solution. If not, the system may have none or many solutions. Generalized inverses are used to get a solution if one exists or get an approximate solution if one doesn't exist. Thus they have many applications including game theory, statistics and linear programming. The talk will discuss some of the types of generalized inverses and their properties. Various applications will also be discussed.