Turning Your Computing Lab into
a Supercomputer
Andrew Leahy
Knox College
Galesburg, IL
61401
aleahy@knox.edu
Some of the most powerful and important applications of mathematics
to real world problems are carried out by computational scientists
working on large parallel computers. Until recently, the cost alone
of a computer capable of carrying out parallel computations meant
that these systems were effectively out of reach for most
undergraduates. Consequently, it wasn't realistic to describe the
techniques and algorithms needed for working on these computing
systems in undergraduate courses. But with advances in compute
networks which allow off-the-shelf desktop computers to be clustered
together to perform distributed computations, parallel computing
power is now accessible even to undergraduates.
This presentation will describe two courses-developed as a part of
an NSF-DUE CCLI project-which are designed to take advantage of
these new computing tools. The first course is designed to appeal
to students with an interest in the sciences and to introduce
students to numerical mathematics as early in the undergraduate
mathematics curriculum as possible. It is a replacement for a
second semester calculus course and emphasizes programming in
Mathematica and numerical techniques for solving calculus level
problems. These include numerical integration and ODE solving,
interpolation and Taylor series approximations, and elementary
linear algebra. The second course is a replacement for a traditional
numerical analysis course which emphasizes parallel algorithms,
their application to numerical linear algebra, and numerical
solutions to partial differential equations.
Links to course material developed as a part of this project
will be presented. We will also describe the distributed computing
cluster we have developed and the other ways it has been used in our
mathematics curriculum.