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Peg Duotaire

Abstract: Peg duotaire is an impartial two-player combinatorial game where players alternate making hops to remove pegs. Based on peg solitaire, where a commonly known variant is the Cracker Barrel peg game, peg duotaire is a variation of this game that is played on simple graphs. We explore the winning strategies of peg duotaire on different graph classes and sizes and among different variations of the game such as normal, misère, and directed play, as well as multihop.

Analyzing Potential Effects of Ozempic on Polycystic Ovarian Syndrome Treatment

Intrusions of Warm Core Ring Water onto the Mid-Atlantic Bight Shelf Alleviate Ocean Acidification But Decrease Cold Pool Size
 

Abstract: Gulf Stream Warm Core Ring (WCR) activity has increased since the year 2000, and intrusions of WCRs into coastal shelf water of the MidAtlantic Bight (MAB) have been observed to contribute to recent warming and to alleviate ocean acidification, highlighting dynamic multistressor transitions. To gain a more comprehensive understanding of the effects of WCR activity on MAB carbonate chemistry and the Cold Pool, summertime (Jun, Jul, Aug) oceanographic data were obtained from several projects from 2017- 2022 using Slocum glider AUVs and analyzed. We found that increased frequency of WCR activity and coastal intrusions, which is projected to continue in the U.S. Northeast Shelf region that includes the MAB, may help to alleviate ocean acidification but will increase summer bottom water temperatures and decrease Cold Pool habitat that is home for many organisms, including the commercially important yellowtail flounder and Atlantic sea scallop.

Market Economics Internship in Healthcare Obtained Through a Background in Mathematics

Black History Month Keynote Lecture: No DMC

Quantitative Equity Strategy Crash Course

Abstract: Li Gordon-Washington (BMC ‘23) is currently working in an investment management rotational program at Vanguard. In her most recent role, she was on the quantitative equity trading desk. This team manages $39 billion dollars of assets in active funds. In this talk she will cover the basics of active vs passive investing, different quantitative approaches to generating excess returns, and discuss some of her project work on the team.

Spring Break - No DMC

Chloe Shupe '24

Raphael Small HC '15

Dylan Su '24

Alishia Nation '23

Math Major Alumnae Panel                                                                                           

Ziwei Tan '25

Malini Rajbhandari '24

Math Major Summer Experiences Panel

Find out about summer REU (Research Experiences for Undergraduates) and internship opportunities from some of our very own Math Majors. These students participated in exciting and enriching research and internships over the summer of 2023, and they are eager to share their experiences. Please join us! Student Panelists Katherine Clemens ’23: Texas A & M Math REU – Algebraic Methods in Computational Biology Ellie Lew ’25: SUMRY 2023 – Summer Undergraduate Math Research at Yale University Cordelia Li ’23: Capital Markets Intern in China and Summer Science Research Program at ������̳ Anna Nguyen ’25: Research Intern in Pediatric Genetics at the Children’s Hospital of Philadelphia Patriciah Ogombe ’24: Non-Profit Consulting Intern for Paragon One Abhi Suresh ’24: Private Equity Intern on the Fund Investment Team at Hamilton Lane Lucy Wilson ’25: Lafayette College REU in Agent-Based Modeling

Hermite Normal Form and Applications

Abstract: An introduction to Hermite Normal Form will be discussed. Computational examples will be provided. Then, we will discuss applications. We will conclude by examining an application to lattice based cryptography.

An Evening with Euler 

Abstract: Among history ’s foremost mathematicians is Leonhard Euler (1707-1783). In this presentation, we sketch Euler’s life, discuss his voluminous mathematical output, and survey a few of his discoveries from number theory, graph theory, and other branches of mathematics. We conclude with a proof – in full detail – of one of his greatest theorems: the solution of the “Basel Problem” from 1734. There, Euler found the exact value of the infinite series 1 + 1/4 + 1/9 + 1/16 + 1/25 + … in a brilliant display of analytic wizardry. Tradition has it that Laplace described Euler as “the Master of Us All.” This should show why such a characterization is apt. NOTE: The talk is accessible to any student who has had calculus.

Analyzing Eleven Bistable Gene Regulatory Networks for Hopf Bifurcations

Gene regulatory networks, also referred to as GRNs, consist of sets of genes that all interact to perform many important cellular functions, including cellular differentiation and cell cycle control. By cataloguing the behaviors of these networks under various initial conditions, we learn more about how these networks function, and therefore gain some insight into cellular functions as well. The focus of this talk is the behavioral analysis of 11 small bistable GRNs that all interact to form over 40,000 important larger biochemical networks. To be more specific, we searched for the presence of Hopf bifurcations in all 11 networks, as well as the location and parameter values required for this behavior to be expressed. Of the eleven networks in question, we verified that 4 do not have Hopf bifurcations, while the remaining 7 may still exhibit this behavior. The Routh-Hurwitz stability criterion was used to exclude the possibility of Hopf bifurcations in certain networks. If this criterion did not exclude the network, the location and parameter values of the possible Hopf bifurcation will be calculated using other methods.

Digitally Restricted Ostrowski Expansions

The standard middle-thirds Cantor set is the set of having baseexpansions which do not contain the digit 1. The Hausdorff dimension of the Cantor Set is log 2/log 3. In fact, any Cantor-like set with digital restrictions in base b > 1 has Hausdorff dimension log a/log b, where a is the number of allowed digits. We will discuss recent work where we determine the Hausdorff dimensions of analogously defined sets. Our sets consist of real numbers whose “Ostrowski digits" have been restricted. Fix an irrational with continued fraction , and denote where are the convergents of . The Ostrowski expansion of a real number with respect to is an expression of the form subject to the condition that if , then . In the sets we investigate, there are restrictions on the digits appearing in the Ostrowski expansions of real numbers with respect to a fixed . In the simplest case where we find that our digitally restricted sets have dimension , where is a real number which is naturally related to the number of allowed Ostrowski digits. On the other hand, if the coefficients of ’s continued fraction are allowed to grow, then the digitally restricted sets have a dimension which depends on that growth. We also study “fractal percolation” in this setting, where the digital restrictions are determined by a random process. These results have applications in metric Diophantine approximation.

Fall Break - No DMC

Exploring Voter Behavior, Turnout, and Apathy: An Agent-Based Model

In recent decades, voter turnout in U.S. elections has fluctuated. Here we present an agent-based model (ABM) to study several factors contributing to voter apathy; specifically, we ask how voters weigh their individual demographic characteristics against their community’s political opinions to inform their likelihood to participate in an election. We examine how varying initial settings—such as party breakdown and the degree to which voters tend to communicate in echo chambers—impacts election results and voter turnout. Using sensitivity analysis, we deduce which of our input parameters have the greatest effect on turnout, as well as the extent to which the electorate is represented in the election results. Our model shows that turnout rates are tied to the level of political similarity in an agent’s surroundings, as well as the degree to which individuals are swayed to abstain or vote based on their interactions within the community. Furthermore, we find that the minority party’s level of mobilization can skew the breakdown of election results, allowing for an unexpected winner to emerge.

Summer Experience: Internship and Summer Research

Arithmetic Progressions of Integers that are Relatively Prime to their Digital Sums

A positive integer b ≥ 2 is called b-antiNiven if it is relatively prime to the sum of the digits in its base-b representation. We explore the maximum lengths of sequences of consecutive b-anti-Niven numbers and arithmetic progressions of b-anti-Niven numbers. This research was done in Summer 2023 as part of the Moravian University Math and Computer Science REU Program.

Ethnomathematics in Action: Insights from the Malekula Community

Ethnomathematics, as defined by Marcia Ascher, is the study and presentation of mathematical ideas of traditional peoples. This talk will highlight how various communities, both small-scale and large, have employed mathematics to guide their daily lives and shape their societal and cultural interactions. In particular, we will focus on the Malekula people and their unique method of determining section memberships within their community, shedding light on the intersection of cultural rules and mathematical concepts.

Summer Experience: Internship and Summer Research

Over the summer, I interned at a wealth management firm and participated in a summer science program at ������̳ with Professor of Mathematics Leslie Cheng. In this DMC talk, I will talk about what I did in my internship and summer research and how I found these opportunities.

Tetris, Tri-Ominoes, and De Bruijn Polyominoes

A polyomino is a connected shape on the plane constructed by gluing together unit squares edge-to-edge. There are 16 ways to color the cell of a fixed square tetromino either black or white. Can you find the smallest polyomino with cells colored black or white that includes all sixteen ways of coloring? This research conducted in Polymath REU 2023 answers this question. In the talk, we will look at De Bruijn numbers and how it helps to construct a solution. We will also explore “nprismatic polyominoes” building upon the problem.

Math Candidate Talk - No DMC

Approaches to Energy Consumption: A Mathematical Analysis