In 2023, more than 20 students were deeply engaged in undergraduate research projects; many went on to share their results in professional venues such as conferences and journals.  In what follows, we highlight two projects and share a sample of others and the students and faculty involved.

Justin Scuillo, supervised by Dr. Lora Bailey and supported by an Alayont Fellowship, built a way-finding app to help pedestrians navigate Grand Valley's Allendale campus.  Beginning with Google Earth images of campus and a measuring wheel, Justin painstakingly constructed a mathematical model of the campus sidewalk system as a weighted graph whose edges are sidewalks and whose nodes are sidewalk intersections.  Each edge is weighted by the physical distance between intersections.  Justin next constructed an app, somewhat similar to Google maps, in which a user can input two campus locations and determine the shortest route between them.  Readers may put Justin's app to use at this site. 

Justin next implemented several network analysis algorithms to determine various properties of this graph.  For instance, he could determine that the Little Mac bridge was one of the primary routes across campus, which explains the difficulties pedestrians faced when the bridge was closed last summer, and that the clock tower is the center of campus sidewalk network.  He also founded an approximate solution to the traveling salesman problem, which is the shortest circuit around campus that visits every building.

At the 2024 Centennial Celebration of the Michigan section of the MAA, Justin presented these results to an enthusiastic audience and was rewarded with the Ronald Mosier Award for the Outstanding Student presentation.

In a second project led by Dr. Bailey, Alaina Hogan applied a mathematical analysis to study the movement of dancers and non-dancers, a reflection of Alaina's passion for dance and her pursuit of a double major in mathematics and dance.  Alaina collaborated with other departments on campus to gain access to a lab with motion capture equipment, which was attached to participants who then performed a series of dance moves.  After collecting a large amount of data that she organized into a matrix recording the location of the sensors at various times, Alaina used a singular value decomposition to reduce the complexity of the readings and to create visualizations of the movements.  In this way, she could detect differences between the group of dancers and the group of non-dancers.

Dr. Feryal Alayont has been working with a large group of students on the topic of edge covers of graphs since February 2022. This topic investigates integer sequences arising from counting subsets of edges in a graph that satisfy the property that all vertices are included as an endpoint of at least one edge.

Evan Henning worked with Prof Alayont for several semesters starting in Winter 2022, and he gave multiple talks and co-authored a paper with Prof Alayont in the Journal of Integer Sequences; he even added some sequences to the On-Line Encyclopedia of Integer Sequences, including A358934, A363476.

Rachel Carpenter, Bradley Monarch, and Jacob Ritsema studied edge covers in Summer 2022 and each gave at least one presentation in the year following.  In Summer 2023, Professors Alayont and Drake supervised the work of several more students, including GVSU’s Rowan Kennedy, Mallory Price, and Syhming Vong on this topic, with several of the students funded by Kindshi Fellowships.  This work led to multiple presentations at such venues as the MSU Mid-SURE conference, the GVSU Summer Showcase, and the Joint Mathematics Meetings, as well as the 49th Annual Mathematics Conference at Miami University of Ohio.

Prof Alayont has also expanded the research group to include several students from Türkiye, Dokuz Eylul University, including Can Selek, Gizem Alkış, Ekrem Şimşek and Laden Nur Yılmaz. GVSU students Mallory Price, Bridget Rozema, Troy Conlay, Marshall Nicholson, Maisie Smith, and Ethan Woudwyk, joined in the collaboration.   All students presented their work at year-end events hosted by the GVSU Math Department and DEU.  In addition, several of the students have presented at conferences such the 26th Annual Nebraska Conference for Undergraduate Women in Mathematics, the spring 2024 Michigan MAA meeting, the 2023 Undergraduate Mathematics Day at the University of Dayton, GVSU Student Scholars Day, and the Joint Mathematics Meetings.  Some of the students are continuing their work with Professors Alayont and Drake this summer supported by significant funding from Michigan Space Grant Consortium and GVSU OURS.

Prof Alayont will be traveling to DEU while in Türkiye to recruit new DEU students for the fall 2024 independent study as well as to meet my fall 2023 students in person. This trip will be funded by an Internationalization Grant from the Padnos International Center.

In addition to the two projects described earlier, Dr. Lora Bailey mentored two more students on individual projects. 

For her honors senior project, Jenna Boelkins analyzed the effects of climate change on vegetation growth, connected to ecological research she did as part of the International Tundra Experiment in Utqiagvik, Alaska where she collected data on the vegetative landscape.  Jenna is a double major in applied math and ecology/evolutionary biology.

Paige McAloon, also working on her honors senior project, created a recommender system based on Goodreads books.  A user can input a book they read and enjoyed, and the system, which is based on the singular value decomposition, will recommend other books that may interest them.

In Winter 2023, Dr. David Clark and Lora Bailey co-taught two independent studies on “Minesweeper with Errors”. This game is played on paper, something like Sudoku crossed with the interactive Minesweeper game that you can play on your computer. The goal is to use numerical clues, placed in a grid, to identify where a certain number of “mines” are located. Students extended this game to situations where the clues are either the wrong number, or one clue is missing entirely. 

Both groups presented at Student Scholars Day and wrote a final report. The 8 students involved were Marshall Nicholson, Katie Mast, and Nicolas DeLibero (working with Prof Clark), plus Alaina Hogan, Rowan Kennedy, Kadence Rosinski, Lisa Shen, Izzy Zelenak (working with Prof Bailey).

Dr. Lauren Keough had 4 senior thesis students in Fall 2023--Sarah Zaske, Mallory Price, Rowan Kennedy, and Nick Simmons--all of whom went on to present at the 2024 Joint Mathematics Meetings (along with Alaina Hogan) and the Michigan MAA annual conference.  These students studied a process that begins with one graph and constructs an associated graph known as the Mycielskian and proved a novel result that relates what is known as the distinguished index of the Mycielskian and the original graph.

On top of all of this excellent work, many students have traveled to and attended regional and national conferences in the 2023-24 academic year:

• The University of Dayton (OH) for Undergraduate Math Day (8 students), 
• The Joint Mathematics Meetings in San Francisco (5 students), 
• The Nebraska Conference for Undergraduate Women in Math (7 students), and
• The 100th Michigan Section of the MAA meeting (16 students.

The mathematics department congratulates all of these students on their exceptional extracurricular work and the ways they are engaging with mathematics outside the classroom.  We also thank all faculty who devote time and energy to collaborating with and mentoring students, especially Drs. Alayont, Bailey, Clark, and Keough for the particular work noted in this article.