San Diego State University Mathematics Research Experience for Undergraduates

Summer 2022 Project Descriptions:

Number Theory: Numerical Semigroups Applied Mathematics: Practical Identifiability

The general area of study will be number theory, specifically numerical semigroups. A "numerical semigroup" is an additively closed subset of the nonnegative integers, such as {0,3,5,6,8,9,10,11,...}. We are concerned with arithmetic properties, such as which elements (called "generators") cannot be written as a sum of other positive elements (3 and 5 in this example), or what is the largest integer that is not an element (7 in this example). See also Link 1 and Link 2. To understand models of biological phenomena such as disease transmission and ecological recovery, one important question is to evaluate how successful the mathematics agrees with the experimental data. In general, it is very difficult to have models that fit the experimental data perfectly well. Practical identifiability is a tool used to quantify whether a model is well designed for a given purpose. In this project, we will compute practical identifiability, and use this measurement to investigate factors such as data noise type, reporting errors, and optimization. Applicants must have completed at least one course in differential equations by June 2022.

Project Director: Chris O'Neill Project Director: Tingting Tang

Chris is an Associate Professor at San Diego State University. His research lies mostly in semigroup theory, but with varying blends of algebra, combinatorics, geometry, and computation. Roughly half of his research publications include student coauthors. Dr. Tingting Tang is an assistant professor with a joint appointment at both the Department of Mathematics and Statistics in San Diego State University and SDSU Imperial Valley. She received her PhD in Mathematics in 2017 from the University of Louisiana at Lafayette and spent two years at the University of Notre Dame as a Postdoc Researcher before joining SDSU. Her research interests are numerical methods for systems of partial differential equations arising from biology and discrete population models. She is also interested in understanding how the core of machine learning-deep neural nets-work and when they work.

REU Program Director: Vadim Ponomarenko
Vadim has been directing undergraduate and REU research for 20+ years. Most REU participants he has worked with have been coauthors on at least one paper as a result of this collaboration. He has been at SDSU since 2006.

Projects from previous years: 2007, 2008, 2009, 2012, 2013, 2014, 2016, 2017, 2018, 2019

Number Theory: Numerical Semigroups		Applied Mathematics: Practical Identifiability
The general area of study will be number theory, specifically numerical semigroups. A "numerical semigroup" is an additively closed subset of the nonnegative integers, such as {0,3,5,6,8,9,10,11,...}. We are concerned with arithmetic properties, such as which elements (called "generators") cannot be written as a sum of other positive elements (3 and 5 in this example), or what is the largest integer that is not an element (7 in this example). See also Link 1 and Link 2.		To understand models of biological phenomena such as disease transmission and ecological recovery, one important question is to evaluate how successful the mathematics agrees with the experimental data. In general, it is very difficult to have models that fit the experimental data perfectly well. Practical identifiability is a tool used to quantify whether a model is well designed for a given purpose. In this project, we will compute practical identifiability, and use this measurement to investigate factors such as data noise type, reporting errors, and optimization. Applicants must have completed at least one course in differential equations by June 2022.
	Project Director: Chris O'Neill		Project Director: Tingting Tang
	Chris is an Associate Professor at San Diego State University. His research lies mostly in semigroup theory, but with varying blends of algebra, combinatorics, geometry, and computation. Roughly half of his research publications include student coauthors.		Dr. Tingting Tang is an assistant professor with a joint appointment at both the Department of Mathematics and Statistics in San Diego State University and SDSU Imperial Valley. She received her PhD in Mathematics in 2017 from the University of Louisiana at Lafayette and spent two years at the University of Notre Dame as a Postdoc Researcher before joining SDSU. Her research interests are numerical methods for systems of partial differential equations arising from biology and discrete population models. She is also interested in understanding how the core of machine learning-deep neural nets-work and when they work.

		REU Program Director: Vadim Ponomarenko
		Vadim has been directing undergraduate and REU research for 20+ years. Most REU participants he has worked with have been coauthors on at least one paper as a result of this collaboration. He has been at SDSU since 2006.