Research Experiences for Undergraduates (REU)

Summer Mathematics Research Institute

The Summer Mathematics Institute at Mount Holyoke College has been engaging selected undergraduates in useful mathematical research since 1988. Topics have been drawn from number theory, algebra, algebraic geometry, analysis, mathematical physics and statistics. Frequently the topic involves the application of computational techniques to gain further insight into the problem. The Institute is supported by the National Science Foundation's Research Experiences for Undergraduates (REU) program.

The topics chosen for the institute are serious ones connected with the main research interests of the faculty adviser, and not just artificial problems created for students. A project must meet the following criteria:

  1. It deals with mainstream mathematics;
  2. It can be attacked by computer experimentation;
  3. It has a reasonable chance of producing results which will be of interest to the larger mathematical community;
  4. It is accessible to the extent that students with a background of courses a little beyond calculus and linear algebra can be rapidly trained to understand the problem and some techniques for working on it;
  5. It involves some questions which can almost certainly be answered in the allotted time and others which have a promising, but indefinite and open-ended aspect.

Projects

Here's some of the mathematics we've been working on:

Graph of the polynomial y^5 + x^2y^3 - y

A real polynomial f(x,y) with two local extrema and no other critical points. There is also a polynomial with an arbitrary number of local maxima and no other critical points.

 

Three equilibrium shapes for red blood cells.

 

Three equilibrium shapes for red blood cells.

 

 

An unexpected property of primes in arithemetic progressions.

An unexpected property of primes in arithemetic progressions (Davidoff REU 1993; see list of past REU projects).