Mathematics Research - Worcester State University

Research

Mathematics Research Opportunities at Worcester State

Within the Mathematics Department, you’ll have the opportunity to participate in faculty-led undergraduate research in a wide range of areas. Recent topics include the sequence of Fibonacci numbers, the role of mathematical analysis in the SIR model, and statistical analysis of Worcester’s temperature data. If you are pursuing our statistics and modeling concentration, you’ll work directly with faculty members to collect, analyze, and report on data related to our programs and gain proficiency with IBM’s SPSS Statistics software.

Recent Mathematics Research Presentations

Mathematics in Major Sports Compared to Field Hockey

The mathematics involved in sports around the world often goes unseen. Because field hockey is not a popular sport worldwide, many people also do not recognize how the mathematical aspects of sports can be connected to field hockey. Putting these two elements together forms the purpose of this paper, which is to identify the mathematics utilized in baseball, basketball, and golf, and relate them to the mathematics behind field hockey.

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Modeling Basketball Free Throws

In basketball, a free throw can be considered an easy scoring opportunity because the ball is thrown from a fixed distance from the basket. In order to score, the ball cannot be thrown too high, too hard, or too low. The goal of this problem is to use the mathematical modeling process to determine and explain which ball path, out of all the paths, will score.

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Optimizing Performance in a Triathlon

Training for a triathlon and other multidiscipline sports has proven to be quite the athletic feat. I aim to dissect each element of triathlon to come up with some valuable advice for athletes training for their first race. I have grouped the information by the three different legs of the race consisting of swimming, biking, and running and in each section, there are multiple mathematical analyses that aid in providing helpful training recommendations.

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Investigations of Mathematical Logic

First-order logic, intuitionistic logic, and constructivism are introduced, and their impact on mathematics is discussed via axiomatic set theory.

The Math department at Worcester State played an important role in my success as they provided me with all the right tools to build a competitive resume.

— Meighan Casey '20

The skills I gained from Math make me confident in pursuing an array of fields which I would otherwise not have–like data science, machine learning, and artificial intelligence.

— Marcos Felipe '21

Teaching 7th grade Math is an endlessly rewarding career that makes a positive impact on our youth.

— Rachel To '20

Mathematics Research at Worcester State

Cryptography

The field of cryptography studies and practices the techniques used to encode and decode secured information. In this presentation, I will explain how cryptography is based on mathematical theory and computer science, and how symmetric-key and public-key cryptography are used to encrypt and decrypt information.

Faculty Advisor: Michael Winders, Ph.D.

Taxicab Geometry

My goal of this project is to deepen the understanding of people’s knowledge about a non-Euclidean geometry known as Taxicab geometry. I will explore the similarities and differences of triangle congruences as well as the properties of triangles in both Euclidean and Taxicab geometry.

Faculty Advisor: Maria Fung, Ph.D.

Mathematics of Serial Crime

Serial crimes capture the attention of the public along with the valuable resources of police forces. This project looks at a formula developed by Kim Rossmo, the creator of the field of geographic profiling.

Faculty Advisor: Maria Fung, Ph.D.

The Effects of Self-Driving Vehicles on Auto-Insurance Markets

Self-driving technology will shortly become a prominent feature in our everyday lives. This project is an exploration via probability and statistics into the effects that self-driving vehicles will have on auto-insurance markets.

Faculty Advisor: Maria Fung, Ph.D.

The Product of Primes is Prime

Prospective teachers frequently express anxiety and resistance to teaching mathematics. Many of them also have similar mathematical misconceptions. This project studies the benefits of training, tutoring, and micro-teaching for prospective teachers as they confront these misconceptions and build their confidence.

Faculty Advisor: Maria Fung, Ph.D.

Climbing Shoe Efficiency

Serious rock climbers swear by brand-name rock-climbing shoes that claim to help with overall performance. We challenge this assumption by testing these shoes against tennis shoes. Our experiment tests subjects with different abilities and backgrounds.

Faculty Advisor: Tim Antonelli, Ph.D.

RSA Encryption

The RSA Encryption algorithm was created to encrypt and decode messages asymmetrically by using public and private keys. A user of RSA shares a public key, which is the product of two prime numbers and an auxiliary value, but does not share the value of those two prime numbers.

Faculty Advisor: Michael Winders, Ph.D.

RSA Encryption

RSA encryption is designed to allow people to use encryption, and decryption, on messages sent via computer. Most people don’t even realize that RSA encryption affects them every day and that the majority of websites use RSA encryption because it helps them protect people’s personal information.

Michael Winders, Ph.D.

Modeling the U.S. Water Supply

The United States holds approximately 8 percent of the entire world’s freshwater supply, but we use that water recklessly. In this project, we took into account the amount of water used per person, as well as that used by industry to develop a model that could predict how long we can stretch our current water supply.

Faculty Advisor: Maria Fung, Ph.D.

Mathematics and Music

This work will depict some of the relationships between mathematics and music. It is intended to analyze the construction of musical scales, among them the Pythagorean Scale, which is based on integer numbers, and the Tempered Scale, which is based on the concept of geometric progression.

Faculty Advisor: Maria Fung, Ph.D.

The Parking Lot Problem

We will show how a paved parking lot that measures 100 ft. by 200 ft. can be designed while aiming for maximum efficiency and space. We will depict the advantages and disadvantages of positioning the stalls at different angles, and also consider the benefits of one-way traffic versus two-way traffic.

Faculty Advisor: Tim Antonelli, Ph.D.

Group Theory and the Quantum World

This project explores one of the many fundamental relationships between abstract mathematics and physics: the application of group theory as it pertains to quantum mechanics. We begin by reviewing both separately at an introductory level and then delve into the application of groups to the quantum world.

Faculty Advisor: Michael Winders, Ph.D.

Sabermetrics and Linear Regression to Determine Most Valuable Player from Contract Value

My project uses multilinear regression to statistically evaluate each baseball player’s value and determine which batter and pitcher had the most productive 2016 MLB season.

Faculty Advisor: Hansun T. To

High School GPA and College Success

High school grade point averages (GPAs) are one of the major factors that are considered in college entry. Taking data of more than 2,600 students at Worcester State University over three semesters, I analyzed the correlation between the reported high school GPA and subsequent college GPA.

Faculty Advisor: Maria Fung, Ph.D.

Mathematics of Sudoku

From solving strategies to identifying how many unique boards exist, the puzzle game Sudoku has many mathematical elements that combine logic, combinatorics, graph theory, and much more.

Faculty Advisor: Maria Fung, Ph.D.

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