Math Mondays

Our first Math Monday of the new year is set for August 28. Please join us for a Math Nature Walk, which will start at 3:10 p.m. Plan to meet at the outside doors to Hayes Hall. We will leave shortly after 3:10.

A drink station will be available before the walk, but you are encouraged to bring your own water bottles. This is your chance to catch up with old friends and meet new ones as we say hello to all our fellow math and stats faculty and students. We hope to see you there!

Meet and greet with your fellow math/stat students and the math and statistics faculty at this year's First-Year Welcome Tea. Say hello to our math community and hear about all the exciting news in mant and statistics. Learn about exciting opportunities and our Math Monday series.

Join us on the Peirce Patio (weather permitting) at 3:10 p.m. on Monday, Sept. 4. We will be offering a variety of snacks with lemonade and iced tea. Celebrate another year of mathematics and statistics here at Kenyon. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. This week, we present a double feature from two of our juniors.

Kyle Kelley spent the summer researching addsub graphs. Addsub configuration graphs depict the relationship between ordered pairs of integers modulo n and a specified "move." We consider the structures of addsub graphs, their symmetries, and their relation to subgroup structures. We also investigate the number of weakly connected components in addsub graphs and their relation to the structure of the integers modulo n. Finally, we discuss possible generalizations of configuration graphs to other groups and to higher dimensions.

Sammy Shrestha worked extensively on research involving virtual reality. Virtual reality (VR), a branch of extended reality (XR), is the computer-generated simulation of a three-dimensional environment, which allows for immersive user interaction. Understanding user interactions and behavior within VR is necessary for creating meaningful and realistic VR experiences. This involves analyzing and interpreting behavioral data collected from VR experiences, which can provide valuable and unique insights for continuous improvement and practical design of immersive virtual environments.

Join us on Monday, Sept. 11, at 3:10 p.m. in Hayes 109 to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. This week, we present a double feature from one of our juniors and one of our seniors.

Vaughn Hajra worked this summer with research involving modeling recovery and fatigue in athletics. What factors are highly correlated with injury and fatigue? How can we apply statistical models in a practical way to benefit athletes? With an emphasis on bayesian hierarchical modeling, we can answer some of those questions.

Khue Tran spent the summer working on her research titled "Comparing Nonparametric Tests for Interaction in Two-way ANOVA with Balanced Replications." When the data are normally distributed, the F-test is the most powerful and recommended procedure for detecting interaction in two-way ANOVA. Previous research has shown that nonparametric test procedures are more powerful when the data are not normally distributed. We computed extensive null critical values for the aligned rank-based tests (APCSSA/APCSSM) in additional settings where the numbers of levels of the factors are between 2 and 6. The performance of these new procedures, the ANOVA F-test for interaction, the adjusted rank transform test (ART), Conover’s rank transform procedure, and the raov function in the Rfit package were compared using Monte Carlo simulations. There is no single dominant test that detects interaction effects for non-normal data, but nonparametric procedures APCSSM and ART are definitely more powerful than the F-test for Cauchy data. Our hope is that these recently developed nonparametric methods will be more widely considered.

Join us on Monday, Sept. 18, at 3:10 p.m. in Hayes 109 to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

Professor of Mathematics Noah Aydin was on sabbatical last year and spent six months in Algeria as a Fulbright scholar. In this informal presentation, he will talk about his experiences and his adventures there as well as some of his other activities during the past year. He will share some stories and many pictures from Algeria and Morocco.

Join us on Monday, Sept. 25, at 3:10 p.m. in Hayes 109 to hear this exciting presentation about Aydin's sabbatical. We hope to see you there!

Are you interested in a summer or mid-semester internship? Are you curious about what internships look like in math or related fields? Join us for a Student Internship Panel. Come hear your peers discuss their recent internships and share their experiences with you. Lori Gastin from Kenyon’s Career Development Office (CDO) will also share some details about how the CDO can support you in the process of securing an internship.

This year's panel includes students from our junior and senior years who have worked for a variety of businesses and institutions:

Viet Dang '24 - Data Management Consulting Intern at Infoverity

Kyle Kelley '25 - Moravian University's REU: Research Challenges of Computational Methods in Discrete Mathematics

Kate Lengel '24 - Platform Solutions Summer Analyst at Goldman Sachs

Connor Moss '25 - Data Science/AI Intern at Langar Holdings

Harshal Rukhaiyar '24 - Business Consulting at TietoEvry

Sammy Shrestha '25 - Research Intern in Statistics at the Ohio State University

Join us on Monday, October 2, at 3:10 p.m. in Hayes 109 to hear this exciting presentation about this year's student interns and how you too can get involved. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. This week, we present a full panel from some of our juniors and sophomores.

Jimmy Baker's research was to classify protein function by the geometric structure and chemical composition of the protein-ligand binding site using various mathematical and statistical methods. They classified the proteins according to a method we called CDPA.

Cael Elmore will discuss the research conducted at the University of Iowa on modeling healthcare worker behavior within hospital environments. Leveraging an extensive dataset comprising over 44 million observations from diverse healthcare facilities, they developed sophisticated models of healthcare worker interactions with patients and each other. Cael will share insights into the application of these models in driving simulations aimed at enhancing our understanding of hospital-acquired infection prevention.

Drake Lewis will share research done on optimizing pose graphs using the minimum cycle basis. In researching graph theory, the goal was to create code in Python and optimize a pose graph using the minimum cycle basis (MCB) and all pairs shortest path (APSP). Starting with all pairs shortest path, it was constructed using the lexicographical Dijkstra algorithm, ensuring a consistent APSP. Using only positive weighted graphs (a parameter of Dijkstra's algorithm), the true shortest paths for any undirected graph were found. With an accurate APSP checked with results from Networkx, the MCB was constructed by use of the Horton set and Gaussian Elimination. In doing so,  MCB for any given graph (the biggest one tested had 808 nodes and 827 edges) was computed, with its results also checked by Networkx. Now, while there wasn't enough time to learn the techniques necessary to implement code to optimize a pose graph using the MCB, we learned about its process and its influence in robotics because of its ability to minimize the error between predicted and observed data.

Join us on Monday, Oct. 16, at 3:10 p.m. in Hayes 109 to hear these exciting presentations and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

While Pascal's triangle is often taught within the context of elementary statistics, it holds great significance in subjects like combinatorics. In algebraic computation, Pascal's Triangle can be utilized to expand powers of binomials, but how exactly can an application like this generalize? We explore how triangles that generalize Pascal's hold secrets to efficiently computing everything from the betti numbers for projective hypersurfaces, to bounding the number points at which the partial derivatives of homogeneous polynomials can vanish in projective space.

Join us on Monday, Oct. 23, at 3:10 p.m. in Hayes 109 to hear this exciting presentation about Benjamin Castor's research. We hope to see you there!

Every summer, many of our students participate in the summer research program. Students work as full participants in the processes of creating a research plan, executing a research project, and preparing results for presentation in a public forum. Learn more about the research done by your fellow mathematics and statistics students. This week, we have Irina Beshentseva '24 and Michelle Polak '25 who worked with Professor of Mathematics and Computer Science James Skon this summer.

This project delves into the design and implementation of an open-source, cloud-managed Wi-Fi platform, featuring numerous functionalities typically exclusive to commercial managed enterprise Wi-Fi platforms. These capabilities encompass the centralized management of multiple Access Points (APs), the configuration of multiple zones and Service Set Identifiers (SSIDs), the establishment of per-user Virtual Local Area Networks (VLANs), and the implementation of user monitoring and control. The goal of this project is to develop a Wi-Fi system that extends enterprise-level networking features to households and low-income organizations, all at minimal to no cost. This section of the project focuses on the development of a web portal application and an API designed to interact with Skon's Raspberry Pi Wi-Fi software. This cloud-based web portal enables users to remotely manage various aspects of their network: access point and radio configurations, SSIDs, zones, individual network user-passphrase pairs, and per-user network data. The web portal is built using the Ruby on Rails framework and hosted on Amazon Web Services.

Join us on Monday, Oct. 30, at 3:10 p.m. in Hayes 109 to hear this exciting presentation and perhaps learn how you too can get involved in summer research programs. We hope to see you there!

Given a metric space, an isometry is a transformation which preserves the distance. I will be interested in isometries from a normed space X to another normed space Y. Translation, reflection and rotation are some well-known examples of isometries. 

On the other hand, we are familiar with projections. An operator P from a normed space X to X is a projection if P2 = P. Projections are building blocks of many otheroperators and are easy to understand.

This talk will explore the connections between the two operators described above. I will give plenty of examples of both types of operators on finite and infinite dimensional spaces.

Join us on Monday, Nov. 6, at 3:10 p.m. in Hayes 109 to hear this exciting presentation by Dey. We hope to see you there!