Mathematics is all about solving problems, and research in mathematics is no different. Mathematical research is a creative process that starts with asking questions. Often our questions are guided by considering something that we already know and asking what happens if we change the hypotheses, similar to research in the sciences. These questions may be related to the world around us or they may be more abstract, related to mathematical structures or spaces.
Houghton math majors have the opportunity to do math research at Houghton through assignments in some classes, in our Mathematics Research Seminar course offered every spring, in Houghton's Summer Research Institute, and as an honors project.
Mathematics Research Seminar
Every spring, students in this course join a small research group (two to four students) with a professor to investigate an unanswered problem in mathematics. Here are some recent projects and the students involved:
- Spring 2020: Collatz Conjecture (Benji Marmor, Nate Parks, Sonny Ferri); Graph Invariants and Exponential Domination on Directed Graphs (Elise Pereira, Gwen Stokes, Micah McClatchey)
- Spring 2019: Combinatorics of Coadjoint Orbits (Gwen Stokes, Nate Parks, Caleb Lyon); Numerical Ranges Over Finite Fields (Amy Huddell, Aaron Monroe, Katelyn Cook)
- Spring 2018: Counting Hasse Diagrams II (Gwen Stokes, Nate Parks, Micah Coats); Exponential Domination on Directed Graphs (Caleb Lyon and Amy Huddell)
- Spring 2017: Exponential Domination on Spherical Graphs (Nic Loew and Ben Lawrence)
- Spring 2016: Product Field of Values (Penny Wu and Allison Larter); Counting Hasse Diagrams (Luke Duttweiler)
- Spring 2015: Game Theory: Cityscape (Maggie Kirkland, Ashley Schenk, Heidi Kroening, Sarah Rexroad); The Gaussian Moat Problem (RD Marek, Jonathon Yuly, Lynn McClatchey)
- Spring 2014 and 2015: Multiplicative Preservers of the C-Numerical Range (this also produced an honors project; Samantha Fairchild)
- Spring 2014: Exponential Domination on Graphs (Emily Bradley and Kyle Craft); Unknotting Games (Grace Baleno and Rachel Lynn McClatchey)
- Spring 2013: n-sato of the Numerical Range (Laura Ballard); Exponential Domination on Polygon Grid Graphs (Grace Baleno, Samantha Fairchild, Sarah Rexroad, and Emily Wendell)
- Spring 2012: Exponential Domination on Triangular Grid Graphs (Nathan Beiler, Nicholas Fuller, and Emily Wendell); Chutes and Ladders: Minimizing Game Length with Math (Winona Wixson, Kayla Gilbertson, Jacob Liddle, and Lauren Moss)
Summer Research Institute
For several weeks every summer, students from the Natural Sciences and Mathematics engage in research with our professors. The latest math projects are listed below.
- 2018: Coadjoint Orbits on Unipotent Groups (students: Caleb Lyon and Nathaniel Parks)
- 2017: Optimal Photosynthate Allocation Strategies for the Northern Pitcher Plant (students: Ben Reber and Brielle Kwarta)
- 2016: The Structure of a 2-adic Mandelbrot Set (students: Jonathon Yuly and Kyle Craft) (results published in peer-reviewed journal here)
- 2014: Applying Dynamic Amino Acid Interaction Preferences to Gaussian Network Model (students: RD Marek and Gus Gula)
Our students regularly present at regional and national mathematics conferences. Here are some recent presentations:
- Fall 2019: Fairness in Machine Learning by Amy Huddell, talk at Houghton College Science & Math Colloquium
- Spring 2019: Exponential Domination in Directed Graphs by Amy Huddell, talk at MAA Seaway Section meeting in Rochester, NY
- January 2019: Coadjoint Orbits for Unipotent Groups by Caleb Lyon and Nate Parks, poster at Joint Mathematics Meeting in Baltimore, MD
- January 2019: Modeling Impact of Thousand Cankers Disease in the Eastern U.S. in a Changing Climate by Ben Reber, poster at Joint Mathematics Meeting in Baltimore, MD, winner of "Outstanding Poster" prize
- Fall 2018: Economic Modeling of Free-Roaming Cats in Knox County, TN by Brielle Kwarta, talk at Houghton College Science & Math Colloquium
- Fall 2018: The Climes They Are A Changing: Modelling the Spread of Thousand Cankers Disease Under Future Climate Predictions by Ben Reber, talk at Houghton College Science & Math Colloquium
- Fall 2018: Coadjoint Orbits for Unipotent Groups by Caleb Lyon and Nate Parks, talk at MAA Seaway Section meeting in Toronto, ON
- Fall 2018: Automorphic Representation Theory by Caleb Lyon and Nate Parks, talk at Houghton College Science & Math Colloquium
Senior Honors Projects
Houghton students have the opportunity to do in-depth research during their senior year with a professor, resulting in an honors thesis. In Spring 2020, Caleb Lyon, currently a PhD student in mathematics at the University at Buffalo, completed an honors project entitled "Coadjoint Orbits for the Unipotent Group of Upper Triangular Matrices," a project that grew out of his work with Professor Brandon Bate in Houghton's Summer Research Institute in 2018. Also in Spring 2020, Amy Huddell, currently a Master's student in computer science at Villanova University, completed an honors project entitled "Exploring Numerical Range over Finite Fields," a project that grew out of her work with Professor Rebekah Yates in Mathematics Research Seminar in Spring 2019.
Research Experiences for Undergraduates
Houghton math majors have also regularly participated in external summer Research Experiences for Undergraduates (REUs) at institutions around the country, including Cornell University, Penn State, University of North Carolina at Asheville, and Hope College. you can read more about and see a list of REUs at the American Mathematical Society's Programs for Students page.