Mathematics Commons^™

Topological Data Analysis And Ant Interaction Networks, Adam Banatwala, Esther Rønn

Mathematics & Computer Science Student Scholarship

Adam Banatwala ’22, Majors: Mathematics and Finance
Esther Rønn ’23, Majors: Physics and Mathematics
Faculty Mentor: Dr. Laura Murray, Mathematics and Computer Science

Our research group used topological data analysis (TDA) to quantify the movement and behavior of ants in a colony.

We extracted higher dimensional networks from point cloud data collected from Dr. James Waters’ lab. Varying the proximity parameter in this construction gives a sequence of networks. We analyzed the enduring topological features of these networks, and how these features evolve over time as the ants move in the colony. Both the experimental and null model simulation data …

How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli

The Review: A Journal of Undergraduate Student Research

The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …

Classifications Of Transformations Of Km#Tn And Pm#Tn Via Symmetry Groups, Adam Banatwala, Jensen Barry, Mackenzie Maude

Mathematics & Computer Science Student Scholarship

Adam Banatwala ’22, Majors: Mathematics and Finance
Jensen Barry ’22, Majors: Biology and Mathematics
Mackenzie Maude ’22, Majors: Mathematics and Art History
Faculty Mentor: Dr. C. Joanna Su, Mathematics and Computer Science

One of the main topics in topology is the classification and comparison of shapes and surfaces. Since Spring 2020, our research group has been using symmetry groups to classify the 1- and 2-dimensional orientable and non-orientable closed surfaces.

First, the group worked on the symmetry groups of the 1- and 2-dimensional orientable closed surfaces; namely, the classification on V?? 1 (the one-point adjoint of n circles) …

Lines On A Smooth Projective Surface, Jordan Demoura

Mathematics & Computer Science Student Scholarship

Jordan DeMoura ’22
Major: Mathematics
Faculty Mentor: Dr. Su-Jeong Kang, Math

This research is to investigate lines on a smooth projective surface. A quadric surface contains two families of planes that provide a ruling of the surface. A cubic surface contains twenty-seven lines, and we provide a complete description of these lines for a Fermat cubic surface. Furthermore, under the Plucker embedding, we show that each family of the lines on a quadric surface corresponds to plane conic curves lying on complementary planes in the projective space of dimension five.

Reframing The Achievement Gap In Mathematics Education, Madeline Pavolovich '22

Posters

Much of math education research focuses on a so-called “achievement gap” measured by test scores and similar quantitative measures of “success.” By framing issues of equity in this way, methods to remedy the gap often require subordinated groups to become more like the “higher achieving” group. In other areas of study, we have been quicker to incorporate sociopolitical lenses into teaching and learning with an emphasis on identity and power. Such a sociopolitical turn could help us rethink what it means for math education to be truly equitable.

Bail Reform, Matthew Shang '22

Posters

The Public Safety Assessment (PSA) to assess the likelihood of pretrial risk. Then, the information is used to decide the conditions of release, including components like bail. The factors used are related only to age and criminal history. In short, the algorithm helps judges make more informed decisions.

Gender Discrimination In Ai, Nicole Papert '22

Posters

There are several studies revealing that AI tools used in job search applications and sites will promote different opportunities depending on the gender of the user. Specifically, men are typically shown more competitive job postings than women, given that the users have similar skills and qualifications. In this poster, I will closely examine why algorithms utilized for the job search process may present differently between men and women.

Tips For Success In Math Courses, Joshua Horowitz '22

Posters

Five steps in the development process for succeeding in mathematics.

Belonging In Math And How It’S Affected By Groupwork, Kara Mathes '22

Posters

Interactions in groups for class assignments are an important part of a student’s sense of belonging in mathematics and other academic disciplines. This sense of belonging has an impact on the student’s sense of self as well as their academic performance.

Cross-Sectoral Climate Change Modeling, Jeremy Gordon '22

Posters

Although climate data originates from various integrated sectors, it continues to be evaluated in isolation. By using cross-sectoral modeling, climate change modeling can more effectively represent data, and the possible consequences of misjudging future models.

Ranked Choice Voting: Who’S The Real Winner?, Brendan Magill '23

Posters

Ranked choice voting is a voting system in which voters rank candidates in order or preference. The winning candidate is determined by eliminating candidates and reassigning their votes until one has a majority. It provides solutions to some of the fundamental issues with traditional voting. But is it more fair? Should it be instituted in American democratic elections?

Racial Bias In Health Care Machine Learning Algorithms, Esther Akinpelu '22

Posters

Machine learning algorithms in healthcare are racially biased, especially when diagnosing patients and choosing candidates for care management programs.

Is U.S. News College Ranking A Weapon Of Math Destruction?, Zhipeng Kui '22

Posters

This poster presents Cathy O’Neil’s arguments from her book Weapons of Math Destruction and connects them with Columbia’s ongoing ranking scandal to show why we should view U.S. News college ranking as a WMD.

The Impossible Theorem Of Fairness, Man Nguyen '22

Posters

With the growth of machine learning, there has been an increase of machine biases that can cause wrongful discrimination. In the case of implementing “fairness,” several conceptions of bias were created to target a fair system. However, statisticians have found that these conceptions contradict one another. Thus, we run into an impossible conundrum of fairness in machine learning. In cases that high risk, we want to investigate the best fairness measures if one is possible. Moreover, we would like to determine when these fairness measures fail or what conditions must be met for them to succeed.

Accessible And Intuitive Mathematical Notation, Anthony Christiana '22

Posters

For math learners with disabilities, engagement with traditional mathematical notation can be difficult or impossible. Here, we explore two examples of the ways that notation can fail disabled students. We also note how accommodating for these disabilities allows us to imagine better ways of serving all students through notational practices.

Bias In Mortgage Approval Algorithms, Carter Steckbeck '22

Posters

In recent years, financial institutions are using machine learning algorithms for the mortgage approval process. Utilizing hundreds of complex variables, they decide whether an applicant gets approved. Recent studies have shown that people of color are disproportionately denied at higher rates for mortgages compared to White individuals.

The Effect Of Social Media On Polarization, John Burt '22

Posters

This poster attempts to look at the impact of social media on political polarization in the United States. Since the 2016 elections, there has been a shift in the political parties and their constituencies away from the center. Some have argued that a large part of this is due to the algorithms that social media use.

Experiential Learning In Mathematics, Lara Speer '23

Posters

The United States lags behind many other developed countries in math skills. The root of the problem lies not in mathematics itself, but in the way the United States approaches teaching math through memorization. One alternative pedagogical method to memorization is experiential learning, which is the process during which students acquire new knowledge through experience and is meant to reflect the way people learn in the real world.

Ethical Use Of Machine Learning In Higher Education Admission, Siqi Fang '23

Posters

A machine learning model called GRADE was used for PhD admission at UT Austin from the year 2013-2020. The model was trained a small set of past admission decisions which are already bias and was used immediately without further tuning or human validation. The model will score all applicants and the decision is made without further human assessment for applicants with the highest and lowest score. Only 362/588 full human reviews are conducted with a few people admitted and the majority of the rest being rejected by algorithm.

How Does Fico Score Discriminates People?, Stephana Lim '22

Posters

The FICO Score, the standard credit score, is used as a weapon of mathematical destruction as its algorithm creates a systematic discrimination against a disadvantaged racial group.

A New Metaphor: How Artificial Intelligence Links Legal Reasoning And Mathematical Thinking, Melissa E. Love Koenig, Colleen Mandell

Marquette Law Review

Artificial intelligence’s (AI’s) impact on the legal community expands exponentially each year. As AI advances, lawyers have more powerful tools to enhance their ability to research and analyze the law, as well as to draft contracts and other legal documents. Lawyers are already using tools powered by AI and are learning to shift their methodologies to take advantage of these enhancements. To continue to grow into their shifting role, lawyers should understand the relationship between AI, mathematics, and legal reasoning.

Exploration Of Piccirillo's Trick On Low Crossing Number Knots, Gabriel Adams

Honors Theses

Piccirillo recently discovered a process that can be applied to an unknotting number one knot to convert it into a different knot called a Piccirillo dual. Piccirillo duals have been shown to have the same n-trace and the same sliceness. However, exploration and knowledge of this process is limited. We were able to generate the Piccirillo duals for several low-crossing number knots. We offer the foundation for and explain how to follow the Piccirillo process and generate Piccirillo duals. This talk assumes little knowledge of knot theory and concisely gives newcomers a clear introduction to get started working with Piccirillo …

Linear Nearest Neighbor Flocks With All Distinct Agents, Robert G. Lyons

Dissertations and Theses

This dissertation analyzes the global dynamics of 1-dimensional agent arrays with nearest neighbor linear couplings. The equations of motion are second order linear ODE's with constant coefficients. The novel part of this research is that the couplings are different for each agent. We allow the forces to depend on the relative position and relative velocity (damping terms) of the agents, and the coupling magnitudes differ for each agent. Further, we do not assume that the forces are "Newtonian'" (i.e., the force due to A on B equals minus the force of B on A) as this assumption does not apply …

A Non-Euclidean Story Or: How To Persist When Your Geometry Doesn’T, Rami Luisto

Journal of Humanistic Mathematics

Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that a locally L-bilipschitz mapping f : X → Y between uniformly Ahlfors q-regular, complete and locally compact path-metric spaces X and Y is an L-bilipschitz map when Y is simply connected. The motivation for such a result arises from studying the asymptotic values of BLD-mappings with an empty branch set.

As far as the author is aware, the result is new, even though it would not be hard for specialists in the field to prove. The proof is essentially a modest extension of …

Alice’S Adventures In Wonderland: Carroll’S Symbolic Attack On Mathematical Symbolism, Firdous Ahmad Mala

Journal of Humanistic Mathematics

In 2009, a literature scholar, Melanie Bayley, proposed that Lewis Carroll's famous books about Alice visiting the magical and illogical Wonderland were attempts to mock and critique the modern mathematics of the day. In this short paper, I aim to support Bayley's thesis and expound upon Carroll's artful use of symbolism to attack excessive use of symbolism in mathematics.

The Hamster Diaries, Pamela B. Pierce

Journal of Humanistic Mathematics

When the pandemic hits, the author acquires a hamster, who provides some humorous anecdotes and some much-needed inspiration.

Makers Do Math! Legitimizing Informal Mathematical Practices Within Making Contexts, Amber Simpson, Signe Kastberg

Journal of Humanistic Mathematics

In this paper, we argue that making activities within non-formal learning environments (e.g., museums, libraries) provide opportunities to engage youth in what we define as mathematical practices for making, everyday mathematical practices within the context of making activities. The mathematical practices identified from two non-formal school-based contexts highlighted three mathematical practices for making: informal measurement, spatial reasoning, and curiosity. These practices are identified in prior scholarship as being beneficial and foundational for the understanding of mathematical concepts. As educators and researchers turn to non-formal and informal contexts, with an eye toward understanding ways youth engage in the activity of making, …

Mathematical Reasoning: Writing And Proof (Pretext Edition), Ted Sundstrom

Open Textbooks

Mathematical Reasoning: Writing and Proof is a text for the first college mathematics course that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics.

Mathematical Reasoning: Writing and Proof (PreTeXt Edition) was developed as part of the Accelerating Open Educational Resources Initiative at Grand Valley State University, with support from the University Libraries and the President's Innovation Fund.

Mathematical Reasoning: Writing and Proof was written by Ted Sundstrom, Professor Emeritus of Mathematics at Grand Valley State University. This textbook was converted into PreTeXt by Ian Curtis, Editorial Assistant for the …

The Effects Of Stem And Non-Stem Mathematics Corequisite Courses On Student Success At Public Institutions In West Virginia, Vanessa S. Keadle

Theses, Dissertations and Capstones

This study explored the differences in student success outcomes between students enrolled in non-STEM and STEM corequisite mathematics courses at 18 postsecondary institutions across five academic years in West Virginia, using de-identified student data. The researcher analyzed this extant data to determine if student characteristics were predictors of success, as defined as passing the mathematics corequisite course, retention to the next semester, and earning a GPA of 2.0 or higher. The researcher also conducted analyses to understand if the differences in those outcomes between STEM and non-STEM courses were significant. This study identified statistically significant gaps in success for students …

Math Department 2021-2022 Newsletter, Mathematics Department

Mathematics Newsletter

Welcome to our annual Mathematics Department Newsletter. As we are slowly coming out of the pandemic, we were able to resume many of our normal events.