Undergraduate Student Speakers

Undergraduate Student Presentations

Friday 3:15-5:00 PM

Session 1

3:15-3:30 The Story of George Dantzig: A Mathematician with a Sense of Humor

Abraham Holleran, Gordon College

Join me as we uncover the lore of Operations Research with the tales from the life of George B. Dantzig, the father of linear programming. Dantzig, with the knowledge that computers were soon to be valuable and accessible tools, developed an algorithm for solving linear programs to help solve practical problems. Linear programs and their extensions are used worldwide to help with problems like scheduling airplanes or allocating vaccines. I focus on Dantzig as a collaborator and tell some humorous stories from his life.

3:30-3:45 Lattice Point Sets

Kathryn Anderson, Keene State College

The set of lattice points, L, in the xy-coordinate system consists of all points whose coordinates are integers. A pattern of lattice points, C, is a finite subset of L. A translation [m,n] of C is defined as [m,n](C)={(m+p,n+q) for each (p,q) ∈ C}. This presentation will investigate translations of C such that the translation contains at least one point of C, and the subsets of C that result from these translations. We will also discuss various conjectures about lattice point sets.

3:45-4:00 Investigating Open and Closed Mathematics

Olivia Clinkscale, Keene State College

There are many alternative approaches when teaching mathematics. Many educators fear that students are completely unable to use the mathematics they have learned throughout their education in situations outside the classroom context. This has led many to rethink the way math is taught in schools. We will investigate two different mathematical teaching methods, open and closed mathematics. Open mathematics being the inclusion of open-ended activities at all times, project based learning, and closed mathematics being the traditional textbook approach to teaching.

4:00-4:15 Godels First Incompleteness Theorem and Mathematical Truth

Joseph Clark, Worcester State University

Godels' first incompleteness theorem is considered one of the most important results in modern logic and mathematics. It concerns the limits of provability in formalized axiomatic systems and implicitly touches on the concept of mathematical truth. This projects scope involves understanding the philosophical content behind the idea of mathematics and discussion of Godels' first incompleteness theorem both in terms of its proof and the implications it has on the concept of truth in mathematics. Often times we claim the view that mathematics is one of, if not the, most pure description of the world we can formulate as human beings. But we must also come to understand that mathematical truth has its limits. The goal of this project is to lay down a general understanding of the philosophy of mathematics and truth, prove Godels' first incompleteness theorem and discuss the relevant meanings this has on the idea of mathematical truth at large.

4:15-4:30 The Golden Ratio: Beautiful Mathematics

Gavin Koehler, Keene State College

We will observe the numerical value of the golden ratio, it's properties, occurrence in nature, and relationship with the Fibonacci numbers.

4:30-4:45 Congruent Triangle Partitions of Scalene Triangles

Jackson Turni, Keene State College

Given a scalene triangle $T$, for which values of $n$ can mutually congruent triangular partitions $T_n$ be constructed such that no area of $T$ is left unused? We investigate the rules in which $T$ can possibly be partitioned, and consequently the domain of $n$. We then use these findings to compose a method of geometric construction that generates any $T_n$ for valid inputs of $n$.

4:45-5:00 Preferential and $k$-Zone Parking Functions

Christopher Soto, Queens College of the City University of New York

Parking functions are vectors that describe the parking preferences of $n$ cars that enter a one-way street containing $n$ parking spots numbered 1 through $n$. A list of each car's preferences is also compiled into vectors in which we denote as ($a_{1}, \ldots , a_{n}$), such that $a_i$ is the parking preference for car $i$. The classical parking rule allows cars to enter the street one at a time going to their preferred parking spot and parking, if that space is unoccupied. If it is occupied, they then proceed down the one-way street and park in the first available parking spot. If all cars can park, we say the vector ($a_{1}, \ldots , a_{n}$) is a parking function.

In our research, we introduce new variants of parking function rules with backward movement called k-Zone, preferential, and inverse preferential functions. We study the relationship between k-Zone parking functions and k-Naples parking functions and count the number of parking functions under these new parking rules which allow cars that find their preferred spot occupied to back up a certain parameter. One of our main results establishes that the set of non-increasing preference vectors are k-Naples if and only if they are k-Zone. For one of our findings we provide a table of values enumerating these new combinatorial objects in which we discover a unique relationship to the order of the alternating group A_n+1, numbers of Hamiltonian cycles on the complete graph, K_n, and the number of necklaces with n distinct beads for n! bead permutations.

Session 2

3:15-3:30 Quaternion Rotation and Why We Use It

Linnea Caraballo, Sacred Heart University

Quaternions are an extension of the complex number system and have a large presence in various applied fields. The most common way quaternions are used is for the rotation of three-dimensional objects. In this talk we will discuss why quaternion rotation is the preferred method for rotation by highlighting common issues with other forms of rotation. We will then analyze original data depicting the speed at which quaternions can be calculated versus other forms of rotation.

3:30-3:45 Application of Matrix Theory in Business and Finance

Makinzie Youngblood, Sacred Heart University

This talk will address a few of the applications of matrix theory to business and finance. We will go into detail of the use of Markov chains as well as linear regression. We will apply Markov Chains to predicting if a market is bullish or bearish. We will also apply linear regression to determine the volatility of a stock.

3:45-4:00 Counting the Number of Proper Skolem Labelings with the Skolem Number (Part 1)

Abigail Allen, Southern Connecticut State University

Alyssa Haskins, Southern Connecticut State University

Building on existing results for counting Skolem arrays, we will explore how to count proper Skolem Labelings of Ladder Graphs. When relaxing constraints on the number of times a label can appear on a graph, the number of Skolem Labelings increases significantly. In this presentation, we will look deeper into counting the Skolem Labelings of Ladder Graphs as it relates to Skolem arrays. In part 1, we will discuss how a Skolem Labeling works for both sequences and arrays. We will provide examples and a case analysis for labeling a ladder graph as we begin to explore the idea of counting the number of distinct Skolem Labelings. In part 2, we will discuss strategies and ways to count the total number of distinct labelings.

4:00-4:15 Counting the Number of Proper Skolem Labelings with the Skolem Number (Part 2)

Alyssa Haskins, Southern Connecticut State University

Abigail Allen, Southern Connecticut State University

Building on existing results for counting Skolem arrays, we will explore how to count proper Skolem Labelings of Ladder Graphs. When relaxing constraints on the number of times a label can appear on a graph, the number of Skolem Labelings increases significantly. In this presentation, we will look deeper into counting the Skolem Labelings of Ladder Graphs as it relates to Skolem arrays. In part 1, we discussed Skolem sequences and arrays, along with labeling and beginning to count the number of Skolem Labeling for Ladder graphs. In part 2, we will discuss ways to count and determine to the total number of distinct labelings using multiple strategies. On top of this, we will show an analysis of a specific size ladder graph and display our results to this point.

4:15-4:30 Data Analysis of TRMM Data Set

Erica Juliano, Sacred Heart University

The Tropical Rainfall Measuring Mission (TRMM) was a satellite mission launched in 1997 that lasted until 2015. The TRMM satellite was responsible for collecting information on rainfall distributions across the world, but primarily focused on the Tropics. In this presentation, an analysis of the TRMM data set is given to identify the following trend over tropical islands: a weakening of storm strength with an increase in island elevation. We will attempt to explain the trend.

4:30-4:45 The Lorenz System

Sophie Pindrys, Sacred Heart University

The Lorenz equations, a system of differential equations, are often used as an introduction to Chaos Theory, as they drew attention to the field with the famous quote: "a butterfly flapping its wings in Brazil can produce a tornado in Texas" . The stability of the system's equilibrium points delivers us a fascinating story of the system's behavior that leads to the remarkable discovery of the Lorenz attractor. Examining the Lorenz attractor, we will explore the meaning of Chaos to explain why weather systems appear to be so unpredictable.