San Diego State University Mathematics Research Experience for Undergraduates

2012 Project: Factorization of ACMs

The general area of study will be Number Theory, specifically Nonunique Factorization Theory. An Arithmetic Congruence Monoid, or ACM, is a multiplicatively closed subset of the naturals, such as {6, 36, 66, 96, 126, 156, 186, ...} with {1} included for convenience. We are concerned with the multiplicative structure. For example, 66*66=6*726, a factorization into "primes" in two different ways.

Program Director: Vadim Ponomarenko
Dr. Ponomarenko has been directing undergraduate and REU research for over a decade. To date, almost every REU participant he has worked with has been coauthor on at least one paper as a result of this collaboration (19 so far, over 7 projects).

Technical Consultant: Scott Chapman Technical Consultant: Paul Baginski
Dr. Chapman has been involved with REU research for even longer than Dr. Ponomarenko. As of January 2012, he is the Editor-in-Chief of the American Mathematical Monthly. Dr. Baginski has been involved with REU research for over a decade, both as a participant and as a research director.

Projects from previous years: 2007, 2008, 2009