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Invited Paper Session Abstracts - Open & Accessible Problems for Undergraduate Research

Saturday, August 1, 8:00 a.m. - 10:50 a.m., Philadelphia Marriott Downtown, Grand Ballroom D

More and more mathematics faculty members around the country are conducting math research with undergraduates. As the benefits to students and faculty of engaging in undergraduate research become apparent, the number of professors with an interest in doing undergraduate research grows. Indeed, many of us would like to begin a research project with students, but we may be unsure of how to choose problems that are accessible for students. The aim of this session is to have experienced undergraduate research mentors share open and accessible problems from a variety of mathematical fields that can be used to generate ideas for new undergraduate research projects.

Organizer:
Allison Henrich, Seattle University
Debra Hydorn, University of Mary Washington
Laramie Paxton, Marian University

Sponsor: SIGMAA on Undergraduate Research (UR SIGMAA)

Accessible, and Interesting Research Problems in Combinatorics for Undergraduates

8:00 a.m. - 8:20 a.m.
Oscar Vega, California State University, Fresno

Abstract

This presentation consists of several research problems in combinatorics, mixed with some abstract algebra, that are appropriate for undergraduate students (and fun). Most of these projects do not require students to have a lot of previous coursework and will put students to work without them spending long months reading several papers just to understand what their research problem is.

 

Patterns in Trees

8:30 a.m. - 8:50 a.m.
Lara Pudwell, Valparaiso University

Abstract

One interesting enumeration problem in combinatorics asks how many trees T contain a prescribed smaller tree t. During the summers of 2010, 2011, and 2012, my teams of REU students studied this question for specific families of trees using two different definitions of what it means for one tree to contain another tree. In this talk, I’ll discuss what we know about this problem and describe other variations that are open for exploration.

 

Getting Started in Sports Analytics Research

9:00 a.m. - 9:20 a.m.
Amanda Harsy, Lewis University

Abstract

Sports analytics is an exciting and assessable research area which draws student interest. Among the many mathematically inspired sports ranking systems, the Colley and Massey methods are relatively simple and can easily be introduced to undergraduate students who have taken a linear algebra course. At their most basic level, these methods are useful for sports rankings, but they are not particularly strong at predicting future outcomes of games. One way to improve these methods for ranking and predicting future outcomes is by introducing weights to these systems and using cross-validation to help determine the quality of our models. In this talk, we will share some of the undergraduate research projects done using linear algebra-based sports ranking models and share general advice on mentoring undergraduate research.

 

Data-intensive Undergraduate Research Projects

9:30 a.m. - 9:50 a.m.
Kumer Das, Lamar University

Abstract

To build the proverbial bridge between the mathematical sciences and the health sciences, one effective approach is to create resource-based research experience in data science. Study shows that undergraduate participation in data-science research projects has removed intra-institutional barriers encumbering access to data-resources and expertise for in-depth investigations. In particular, data dimension reduction approaches are being used to study many complex genomic and biomedical problems. This talk will present the design of a data-science research program and will share some of the resources.

 

Computer Driven Questions and Theorems and in Geometry

10:00 a.m. - 10:20 a.m.
Moira Chas, Stony Brook University

Abstract

Three numbers can be associated to a deformation class of closed curves on a surface S: the self-intersection number (this is the smallest number of times a representative of the curve crosses itself), the word length (that is the smallest number of letters, in a certain alphabet chosen a priori, one needs to describe the class ), and the length of the geodesic in the class (this is the length of the shortest representative of the class, where the way of computing length is chosen beforehand). The interrelations of these three numbers exhibit many patterns when explicitly determined or approximated using algorithms and a computer. We will discuss how these computations can lead to counterexamples of existing conjectures, to the discovery of new conjectures and to subsequent theorems in some cases. Many these results were discovered by or jointly with undergraduate and high school students.

 

Knotted Undergraduate Research

10:30 a.m. - 10:50 a.m.
Colin Adams, Williams College

Abstract

Knot theory is an excellent topic for undergraduate research, as the pictures are pretty, and you can involve the students in calculations right from the start to get them involved. Then they will be motivated to learn the relevant mathematics. We will talk about a variety of open problems in knot theory amenable to research by undergraduates.

 

Year: 
2020

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