Session Index
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Undergraduate Session 1
2:15pm--3:15pm, Roessner 201
Speakers: Yiqi Ye, Yunke Li, Bohong(Max) Zheng, Tech Oh, Kendall Heiney
Undergraduate Session 2
2:15pm--3:15pm, Roessner 202
Speakers: Arsiama Gebreyesus & Allison Donnelly, Chloe Sanchez, Daniel Vanco, Sean Cesarini , Madison Whipple and Brigid Limarzi, Abdullah Alshamrani, Jerome Grant
Undergraduate Session 3
2:15pm--3:15pm, Roessner 203
Speakers: Eilis Casey, Catherine Bartushak and Rebecca Jackson , Nathan Ngaleu, Brian Pan
Undergraduate Session 4
2:15pm--3:15pm, Roessner 204
Speakers: Nevaeh Sisco, Raj Mamidala , Jacqueline Coval
Undergraduate Session 5
2:15pm--3:15pm, Roessner 205
Speakers: Catherine Barrish, Malia Nauman, Lucas Schwartz
Undergraduate Session 1
Roessner 201
2:15pm, Yiqi Ye, Yunke Li (Franklin & Marshall College )
Optimal Meal Selection Strategies through Linear Integer Programming
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Power Packs Project (PPP) provides a weekly meal to families experiencing food insecurity, ensuring children are prepared for educational success. We used mathematical optimization strategies to help PPP select future recipe rotations and food procurement, reducing costs while maximizing nutrition. We created multiple objective functions to quantify the cost and benefits of each recipe: the retail cost, the actual cost to PPP given its discounted supply networks, and the nutritional value. We then utilized integer programming to identify an optimal recipe schedule. We found an optimal set of 7 recipes out of 20 converted manually in Summer 2023. New team members are working this semester to streamline this process, including improved string matching as well as automated extraction of ingredients from recipe PDF files using a specialized Python package.
Close Abstract2:30pm, Bohong(Max) Zheng (Franklin & Marshall College)
Cosine Similarity for String-Matching of Food Databases
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The nonprofit Power Packs Project provides a box of food and dinner recipe each week to needy families in Central Pennsylvania. We are using applied mathematics approaches to help Power Packs carry out its mission. In this talk, we describe our novel use of string- matching processes for food product identification. Focusing on the critical task of comparing a list of Power Packs’ ingredients against food product names in an extensive nutritional database, we utilize a method based on cosine similarities to achieve our objectives. The process uses an embedding function to transform raw text strings into vector representations, allowing for a more nuanced comparison than traditional string-matching techniques. Our method then computes the cosine similarities between vectors, identifying the best matches between the ingredient lists and product names. Our method is an accurate and highly effective approach for string-matching against large-scale retail product databases, with the potential to improve inventory management and consumer searches.
Close Abstract2:45pm, Tech Oh (F&M College)
Who is math? Do you want to play with them?
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I like math because playing with math feels like playing with a person: in thinking about patterns, I get to know more about who math is. I will show how patterns in multiplication, like commutativity (eg. $1\times 2=2\times 1$) and associativity (eg. $(1\times 2)\times 3=1\times(2\times 3)$), are like ways of describing the personality of multiplication, and this will hopefully give you an idea of what I mean by "who" math is, and why I want to be friends with math. There are no prerequisites for this talk.
Close Abstract3:00pm, Kendall Heiney (Cedar Crest College)
Generalized Cullen-Sierpinski Numbers
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A Sierpinski number is a positive integer $k$ such that $k\cdot 2^n+1$ is composite for all positive integers $n$. The Cullen sequence is defined by $C_t=t\cdot 2^t+1$. In this talk, we show the there are infinitely many Sierpinski numbers in the Cullen sequence. We then generalize the concept to show that there are base-b Sierpinski numbers in the base-b Cullen sequence.
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Undergraduate Session 2
Roessner 202
2:15pm, Arsiama Gebreyesus & Allison Donnelly (Saint Joseph University)
The Father of Numbers
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However, some problems are left unproved and understandable in mathematician history, even though others have discovered them already. The father of numbers, Pythagoras tends to remain an important pillar as the first mathematician to prove the existence of the pythagorean theorem and numbers. Pythagoras studies and proves these challenging problems that bear his name, believing the entire world could be explained and learned by numbers. The schools he went to tried to use numbers to understand the world’s universe. Back then, numbers were strongly thought to have their special nature and ways of living ethically because of Gods. During this presentation, we will mainly focus on and discuss the life of Pythagoras, and the discovery of numbers. Pythagoras travels to some country to learn about his mathematician and other beliefs. It’s impressive that a lot of the stuff Pythagoras did still play a big and significant role today, especially in the mathematics field because it’s used for practical applications and much more.
Close Abstract2:30pm, Chloe Sanchez, Daniel Vanco, Sean Cesarini (Saint Joseph's University)
Fibonacci Sequence
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In this presentation we will be talking about Leonardo Fibonacci is a great mathematician who was born in late 10th-century Italy. He wrote the Liber Abaci or the “Book of the Abacus” which was the first European book written on Indian and Arabian mathematics. We will talk about his life and his great contributions to mathematics.
Close Abstract2:45pm, Madison Whipple and Brigid Limarzi (Saint Joseph's University)
The Life of Carl Friedrich Gauss
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Thousands of famous mathematicians have contributed to theorems that we use in our daily lives. Although, one of the most famous would be Carl Friedrich Gauss. He was a mathematician and astronomer who discovered the theory of magnetism, the fundamental theorem of algebra and derived the function of representation of the normal distribution, amongst many other achievements. Without his astonishing accomplishments, technology and our society alone would never have advanced to the point it has today. Gauss was the child prodigy to parents of the poor working class who was able to dedicate his life to discovering the unthinkable and altering the world of mathematics. In this presentation, we will discuss and expand upon some of Gauss' greatest achievements and the upbringing that makes him stand out from the ordinary.
Close Abstract3:00pm, Abdullah Alshamrani, Jerome Grant (Saint Joseph's University)
The Mathmatics of Machine Learning algorithms
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This presentation delves into Data Science and Machine Learning, starting with the basics before exploring the historical evolution of these fields. It highlights the mathematical backbone essential for algorithms like Linear Regression and Neural Networks, emphasizing their practical applications in Data Science.
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Undergraduate Session 3
Roessner 203
2:15pm, Eilis Casey (Villanova University)
Arithmetical Structures on Complete Graphs
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This project focuses on the study arithmetical structures on graphs, which is the integer labeling of the vertices that satisfies some divisibility requirement. For this research, each integer label must divide the sum of its neighbors. We will focus on complete graphs, which are graphs in which every vertex is connected to every other vertex. Tor each arithmetical structure on a complete graph, there is an associated matrix that contains information about labels and adjacent vertices. For this study, we are trying to find the structure that maximizes and the one that minimizes the spectral radius of this matrix.
Close Abstract2:30pm, Catherine Bartushak and Rebecca Jackson (Villanova University)
Non-recursive description of the Tower of Hanoi
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The Tower of Hanoi is an old puzzle that consists of a collection of disks of different sizes that have to be moved from one tower to another without violating two basic properties. There is a well-known recursive description of the most efficient solution (least number of steps) of the Tower of Hanoi. In this talk, we will provide a non-recursive description of this solution.
Close Abstract2:45pm, Nathan Ngaleu (Albright College)
Domination and Independence Numbers For Cylindrical Honeycomb Chess Boards
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The age and popularity of chess has made it an appealing topic of study for mathematicians. In particular, the diversity of piece-movement has led to the development of several popular questions, including the following: What's the fewest number of queens on a chess board that attack every square? What’s the largest number of non-attacking queens that can be placed on the board? Our research focuses on answering these questions for the five main chess pieces on a hexagonal honeycomb and a cylindrical honeycomb chess board. The answers to these questions are known as the domination and independence numbers, respectively, of the associated graphs.
Close Abstract3:00pm, Brian Pan (Albright College)
Quantum Advantage in the Modified Penny Flip Game
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As humanity attempts to keep up with Moore’s Law, computer chips are getting smaller and smaller to increase the speed of information processing. But chips are now approaching a limit in size, or else they will be affected by quantum mechanics. If the transistors of computers get small enough, a particle’s wave function (in this case, electrons) can tunnel though, also known as quantum tunneling. This will cause our logic gates to register a one instead of a zero, causing errors. The effects of quantum tunneling will render the memory storage of our computers ineffective. One can use an electron’s spin up and down state as an analog to the ones and zeros of binary code. However, quantum objects can be in multiple states simultaneously, thereby an increase in computational power. So, perhaps, embracing the strange effects of quantum mechanics may be a solution to this information conundrum. My research with Dr. Buerke investigated the potential advantages of quantizing information through game theory as a medium.
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Undergraduate Session 4
Roessner 204
2:15pm, Nevaeh Sisco (Penn State Brandywine)
Infinite Series and Fractals as Displayed Through Crochet
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In this talk, we investigate applications of infinite series to fractals – or, geometric shapes with self-repeating patterns. Infinite series can be used to calculate properties such as the perimeter and area of certain fractals, such as the Koch snowflake and Sierpinski triangle. We will also show some crocheted physical models of these fractals and describe how calculus can be used to study their interesting properties.
Close Abstract2:30pm, Raj Mamidala (Penn State Brandywine)
Calculus and Machine Learning
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In this project, we investigated applications of calculus to machine learning. In particular, we focused on how the chain rule and partial derivatives apply to neural networks. Neural Networks simulate learning in machines, similar to brains activating layers of firing neurons. In a Neural Network, a set of inputs travel through layers of activation that determine a most likely output. A neuron is composed of a set of inputs, each of which is assigned a weight. The wights are adjusted through backpropagation, which relies on the gradient descent algorithm. Using training data, the machine determines appropriate weights that should be assigned to a set of inputs by minimizing the error between the expected and actual values.
Close Abstract2:45pm, Jacqueline Coval (Chestnut Hill College)
Markov Chain Monte Carlo
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Markov Chain Monte Carlo, also referred to as MCMC, is a branch of modern mathematics that grew popular in the 1990s specifically in the field of statistics. MCMC is a mathematical modeling process that samples high-dimensional distributions by combining Monte Carlo simulation and Markov chains. This presentation will investigate Monte Carlo simulation and Markov chains individually. A random walker example will be utilized to explain the process behind a simple Markov chain. Finally, an exploration of the Gibbs sampler will demonstrate one of the main methods for running MCMC itself.
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Undergraduate Session 5
Roessner 205
2:15pm, Catherine Barrish (Muhlenberg College)
An Extended Approach To Algebraic Voting Theory
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In the late 1990s, economist Donald Saari wrote a series of papers on a geometric approach to voting theory. In these papers, he analyzed two common voting methods in this context: Condorcet’s method (a pairwise method) and the Borda Count (a positional method). Following Saari’s work, Zajj Daughetry extended his work by transitioning from the geometric model of voting theory to an algebraic model. In her work, Daugherty also takes into consideration the possibility of partially ranked ballots. In my talk, I will give a brief overview of these approaches as well as discuss how I am extending Daugherty’s work to examine different “shapes” of partially ranked data.
Close Abstract2:30pm, Malia Nauman (Millersville University)
Analyzing Drug Concentration Dynamics in the Bloodstream Over Time Using Mathematical Models and Numerical Methods
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Throughout history, medical professionals have struggled with safely administering and readministering drugs to their patients. The emergence of new medications raises questions about determining appropriate dosages and monitoring changes in drug concentration in the bloodstream over time. Inaccurate dosing can have life-threatening consequences. Thus, we must treat every situation concerning drug concentration with careful consideration. In this study, we used a mathematical model to characterize drug concentration in the bloodstream over time and developed various numerical methods to identify optimal drug release dosages within patients. Our findings indicate that for safety, the initial dosage should not exceed 0.9 mg. Subsequent doses of 75% of the initial dose should be administered approximately 11 hours after the first dose, and again approximately 10 hours after the second. By leveraging these insights, healthcare providers can prescribe treatments with precision, ensuring maximal efficacy while minimizing risks to patients.
Close Abstract2:45pm, Lucas Schwartz (Millersville University)
Analyzing the Probability of a Shut-out in Racquetball
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Racquetball is distinct from many other racquet sports because players are not separated by a net that they need to hit the ball over. Instead, both players are on the same side of a court surrounded by walls, and have to hit the ball into the front wall. A player only scores a point after winning a rally if they serve the ball. If the player who wins the rally does not serve, they now serve and the score is not changed. The first player to score 21 points wins. Previous models have determined that the probability of a player winning 21 - 0, P, follows the equation
P(p) = ((1+p)/2)(p/(1-p+p2))^(21)
where p is the probability of the player winning any given rally. In this project, we derive this model, and then use it to approximate the smallest p such that a player will win 21 - 0 at least half the time. We will use four different numerical methods to accomplish this: the Bisection Method, Newton’s Method, the Secant Method, and Fixed-Point Iteration. We determined with an error ε = 10^(-4) that if player A wins any given rally with probability p ≈ 0.842304791125858, they will shut out player B at least half the time.
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