ABSTRACT: Undergraduate numerical methods courses (like
Math 248, 448, 449) focus on learning how to use a computer to solve
mathematical problems that tend to be very practical, like solving
nonlinear equations, solving systems of linear equations and solving
differential equations, to name a few. And yet, there are any other
areas where we can use computers to help us solve more "fun"
mathematical problems. In this talk, I will show how we can solve a set
of problems related to continued fractions using a computer, starting
from something as simple as the Euclidean algorithm, and almost
accidentally building up to some questions worthy of undergraduate
research.
Note that some knowledge of basic computing (Math 248 or any first
programming course) will be helpful.
|
|
BIOGRAPHICAL SKETCH: Steve
Lucas received a 1st
Class honours degree with University Medal in Mathematics from
Wollongong
University in 1989, and a PhD in Mechanical Engineering from Sydney
University in 1994. He did a Postdoctoral Research Fellowship in the
Division of Applied Sciences, Harvard University during the period
1993-1995. From 1996-2006 he was employed by the School of Mathematics
in the University of South Australia, including a visiting position
2005-2006 at the Department of Mathematics, University of Tennessee. He
is currently a visiting associate professor within the Department
of Mathematics and Statistics, James Madison University. Steve's
research interests include analysis, fluid and solid mechanics, signal
processing, control theory, number theory, graph theory and
industrial mathematics, but the majority of his research has a
numerical
flavor. In February 2002, Steve received the Michell Medal for the
outstanding new researcher in Applied Mathematics in Australia and New
Zealand, awarded by the Australia New Zealand Industrial and Applied
Mathematics division of the Australian Mathematical Society.
|