Summer 2024 Project Description:
| Project: Nonunique Factorization |
| This subject within number theory is concerned with rings and monoids where the Fundamental Theorem of Arithmetic fails. For example, consider the set of even integers, under multiplication. Here we have two different factorizations into irreducibles of 60, namely 2*30 and 6*10. In this project we will investigate properties of some of these strange beasts. Useful, but not mandatory, coursework includes number theory, combinatorics, geometry, abstract algebra, and programming. Student teams will each pick one sub-project to focus their attention on. Project details have yet to be finalized, but some projects will have a geometric flavor, while others will have an algebraic flavor. |
 | Project Director: Chris O'Neill |  | Project Director: Vadim Ponomarenko |
| Chris is an Associate Professor at San Diego State University. His research lies mostly in semigroup theory, but with varying blends of geometry, algebra, combinatorics, nd computation. Roughly half of his research publications include student coauthors. | Vadim is a Professor at San Diego State University, whose research interests are broad and centered around nonunique factorization. He has been directing undergraduate and REU research for over 20 years. Most REU participants he has worked with have been coauthors on at least one paper as a result of this collaboration. He is also the long-serving Notes Editor of the American Mathematical Monthly. |
Projects from previous years: 2007, 2008, 2009, 2012, 2013, 2014, 2016, 2017, 2018, 2019, 2022, 2023
