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Math Senior Portfolio Presentations

Time: 11:45am - 1:25pm CST November 30, 2020

Location: Online

The Mathematics Department invites you to attend the final presentations for our seniors finishing up their work in Senior Research. (Presentations will be in the order given below).

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Meeting ID: 991 7384 8347
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The first two days, Monday, Nov. 30 and Friday, Dec. 4, are presentations of students’ third paper for their thesis portfolio. This paper is meant to be based on a journal article: students both explain the math in the article and also do some work themselves — extending, applying, or proposing a more elaborate project based on what they’ve read and studied.

The third day of presentations, Monday, Dec. 7, features our students who have been working on a research project the whole semester and are writing up their work in a formal thesis paper.

Monday, Nov. 30

11:45 a.m.-1:25 p.m.

(Paper three presentations, 15 minutes for talk + Q&A)

  • Olivia Masso ’21: “Mathematical Modeling in the Healthcare field”
  • Molly Guagenti ’21: “Math in The Spirograph”
  • Lexy Jensen ’21: “Do Dogs Know Calculus?”
  • Syanne Thomason ’21: “Is Time a Problem?”

Friday, Dec. 4

11:45 a.m.-1:25 p.m.

(Paper three presentations, 15 minutes for talk + Q&A)

  • Sean Johnson ’21: “Can Point Spread Ratings Predict the Winner of This Year’s Super Bowl?”
  • Cassie Curtis ’21: “Puzzles and Matrices”
  • Dan Mutter ’21*
  • Ronny Onano ’21*
  • Elizabeth Ryan ’21: “A Study of Gangs in America”
  • Sandra Masibayi ’21*

Monday, Dec. 7

10:30 a.m.-12:30 p.m.

(Formal Thesis presentations, 20 minutes for talk + Q&A)

Ben Levicki ’21: “Changes to Approach and the Effects of Approach on Hitting Trends”

The purpose of this study is to determine the effects of a player’s approach on the hitting trends of MLB players in the 2019 season. The players in this study are the qualified starters for the Cleveland Indians from the 2019 campaign. The problem that this study intends to solve is the specific changes in a player’s approach at the plate and how it affects a player’s hitting ability. This study will determine if and what correlation there is between the approach of a hitter and their hitting performance. The methods that will be utilized in this study are moving averages for the batting statistics to show trends. Then, using correlation, we will determine the association between hitting and a batter’s approach. Furthermore, using multiple regression analysis to determine the highest influence in the changes to approach to a player’s slump. We will see that there is a significant correlation between the approach of a player and their batting performance. We will prove that there is a statistically significant relationship between performance and approach. Lastly, we will look into the future applications and improvements on the model for future research.

Andrew Dorst ’21: “Scrutinizing Strategies for Secret Santa”

In this paper, we investigate different randomization strategies for Secret Santa. We create probability trees that map out each possible outcome in a game of Secret Santa and use these to calculate the probability of a given number of cycles occurring within the game when a certain number of people are playing. From this, we determine the relationship between the probabilistic outcomes of each strategy and the results from previously conducted work.

David Waitley ’21: “Determining an NBA Champion with Numbers”

In this paper, we predict an NBA champion based on team performance in multiple categories, including both traditional and advanced statistics. Traditional statistics, familiar to a casual NBA fan, can easily be compared from team to team. Some examples include points per game, rebounds per game, field goal percentage, and more. Advanced statistics, used by the analytics departments of NBA teams, truly dive deep into what causes teams to win. Examples include true shooting percentage, turnover percentage, net rating, and more. By looking at each individual statistic in depth, we then create models with this data to determine which statistics are more important than others in both the regular season and the NBA playoffs. Data studied in this research includes the 2010-2011 NBA season all the way up until the 2018-2019 NBA season.

Alexandria Wheeler ’21: “Identifying Z-Groups up to Isomorphism”

Suppose G is a finite group. According to the Sylow theorems, for every prime factor p of |G|, there exists a Sylow p-subgroup of order p^n. Furthermore, if each of these p-subgroups is cyclic then we call G a Z-group. In this thesis, we seek to prove that a Z-group is determined up to isomorphism by its order and signature. Previous work by Jensen and Lewis proves that sequences of kth powers of Froebenius complements can be determined up to isomorphsim — this proof will provide the final stepping stone needed to extend their results to all Z-groups.

Calvin Raymond ’21: “A Study of Three Dimensional Coincidence Isometries”

In this paper, we explore a process for generalizing coincidence reflections non-singular n × n matrices. The group of coincidence reflections is a subgroup of the group of coincidence isometries. We will be looking at the standard forms representative of the conjugacy classes of matrices in GL_n(R. A given matrix can be considered a structure matrix of a lattice, and there may be an orthogonal matrix acting on it as an isometry. Furthermore, that isometry will be considered a coincidence isometry if the intersection of the lattice and its coincidence site lattice forms a sublattice of both the original lattice and the lattice under the isometry. We demonstrate vectors of specific forms that define coincidence reflections in the lattice.

Marquell Williams 21*

* Students with an asterisk are tentatively scheduled, but may not be prepared to present due to illness or other factors. 

SPONSORING DEPARTMENT, OFFICE, OR ORGANIZATION:

Mathematics Department

FOR MORE INFORMATION, CONTACT:

Haley Yaple, hyaple@carthage.edu 

By: Haley Yaple

Location: Online