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, abstract algebra, and programming. 


Project: Vorticity in Hydrodynamics 
A poorly understood aspect of surface and interfacial flows in the ocean is the role that underwater eddies, or rotating fluid elements, play. Prof. Curtis, in conjuction with Prof. Henrik Kalisch at the University of Bergen, has recently developed a novel model which should allow one to explore this issue via numerical simulation. The proposed project then is to develop said simulations. A critical question that will have to be addressed is how to choose the necessary discretizations of the vorticity effectively. This will involve answering not only basic questions in numerical analysis, but also studying the graph theoretic properties of collections of moving mesh points in the simulation. 

 Project Director: Vadim Ponomarenko 
Dr. Ponomarenko has been directing undergraduate and REU research for 18 years. Most REU participants he has worked with have been coauthors on at least one paper as a result of this collaboration. He serves on the editorial board of the American Mathematical Monthly, and is Notes Editorelect of that journal. 


Project Director: Chris Curtis   
Chris Curtis is an applied mathematician specializing in asymptotic and numerical techniques for solving nonlinear free boundary value problems with the goal of modelling oceanic waves. His work has appeared in both mathematical and fluids journals, reflecting the interdisciplinary nature of his research. Prof. Curtis received his PhD in 2009 from the Department of Applied Mathematics at the University of Washington. He was then an Instructor and Research Assistant at the University of Colorado before beginning at SDSU in 2013. 

Projects from previous years: 2007, 2008, 2009, 2012, 2013, 2014, 2016