Background

Mathematics


I am pursuing my Bachelor of Arts in Mathematics at Occidental College. I am fascinated how math surrounds us in everything we do, especially in the intersection to computer science. My coursework is focused in applied and computational mathematics.

Data Science


I want to continue building my mathematical and computational acumen by pursuing a career in the field of data science. Processing, interpreting and communicating data correctly can influence big business decisions. I plan to eventually pursue a graduate degree in this subject.

Health & Fitness


In addition to Mathematics, I am also a double major in Kinesiology. Being a former student athlete, I was drawn to the subject based on how applicable it was to my life. I am intrigued by the inner workings of the human body and have a deep knowledge of biomechancis, human anatomy and physiology.

Project Highlights

"Optimized Conversion of Categorical and Numerical Features in Machine Learning Models"


While some data have an explicit, numerical form, many other data, such as gender or nationality, do not typically use numbers and are referred to as categorical data. Thus, machine learning algorithms need a way of representing categorical information numerically in order to be able to analyze them. Our project specifically focuses on optimizing the conversion of categorical features to a numerical form in order to maximize the effectiveness of various machine learning models. Of the methods we used, we found that Wide & Deep is the most effective model for datasets that contain high-cardinality features, as opposed to learned embedding and one-hot encoding.

PDF Github

"Utilizing Mathematical Modeling Techniques to Optimize Athletic Footwear for Sports Performance"


This paper will analyze the application of mathematical models onto biomechanical systems, specifically running gait mechanics and the foot/ground interaction, as well as its application to long distance running footwear and sports performance. A literature review was conducted by collecting research articles through Science Direct, Web of Science and Pub Med. The purpose of this research was to highlight the process of mathematical modeling and how it can be applied to human dynamics to improve performance. Multiple models are analyzed that incorporate different aspects of gait mechanics, including simulating dampening of shoes and the spring like effect of the arch of the foot and the metatarsophalangeal joint. Many breakthroughs have already been made in this field, but what this paper brings is the connection between the theory and the application and how these models can show which factors influence performance the most. What is concluded is that these highlighted factors do lead to improved sports performance specifically when looking at the Nike Vaporfly 4% running shoe and both men’s and women’s world record marathon time.

PDF

About Me

A snapshot of who I am and what I do,

Connect with me!

Tom Butler

Student

Age: 22
Hometown: Seattle, WA
Current Location: Los Angeles, CA
Goals:
  • Learn something new everyday
  • Attend graduate school

Occidental College

(2016 - 2021)

  • Degrees: BA Mathematics, BA Kinesiology
  • Focus of Study: Applied and Computational Mathematics, Biomechanics
  • Awards: Deans List (2017-2021), Kinesiology Department Ambassador
  • Involvement:Varsity Baseball: Player (2016-2020), Team Captain (2019-2020), Assistant Pitching Coach (2020-2021)

  • Operations Research Intern
  • Mathematics TA (Linear Algebra, Partial Differential Equations)
  • Human Anatomy and Biomechanics Tutor

  • Lifting
  • Surfing
  • Computers
  • Gaming
  • Sports

Full Portfolio

Undergraduate Research Projects

Co-Authored, PDF, Code: GitHub

Summary: While some data have an explicit, numerical form, many other data, such as gender or nationality, do not typically use numbers and are referred to as categorical data. Thus, machine learning algorithms need a way of representing categorical information numerically in order to be able to analyze them. Our project specifically focuses on optimizing the conversion of categorical features to a numerical form in order to maximize the effectiveness of various machine learning models. Of the methods we used, we found that Wide & Deep is the most effective model for datasets that contain high-cardinality features, as opposed to learned embedding and one-hot encoding.

Authored, PDF

Summary: This paper will analyze the application of mathematical models onto biomechanical systems, specifically running gait mechanics and the foot/ground interaction, as well as its application to long distance running footwear and sports performance. A literature review was conducted by collecting research articles through Science Direct, Web of Science and Pub Med. The purpose of this research was to highlight the process of mathematical modeling and how it can be applied to human dynamics to improve performance. Multiple models are analyzed that incorporate different aspects of gait mechanics, including simulating dampening of shoes and the spring like effect of the arch of the foot and the metatarsophalangeal joint. Many breakthroughs have already been made in this field, but what this paper brings is the connection between the theory and the application and how these models can show which factors influence performance the most. What is concluded is that these highlighted factors do lead to improved sports performance specifically when looking at the Nike Vaporfly 4% running shoe and both men’s and women’s world record marathon time.

Authored, PDF

Summary: Traumatic brain injury is one of many types head injuries that occurs in sports, but it is also one of the most dangerous due to the possible long-term consequences on brain function. This has prompted sporting leagues such as the NFL and the UFC to alter rules and invest large amount of money into further research to increase the safety of its athletes. Our knowledge of brain injuries is slowly evolving because of the complexity and the vast inner mechanisms of neural tissue. In this paper I will evaluate how impact location, kinetics and interface with the head/headgear change the rotational and linear kinematics of the head in two specific sports: American football and Boxing/Mixed Martial arts.

Authored, PDF

Summary: Major League Baseball pitchers have been becoming bigger and stronger with the average height and weight of MLB pitchers increasing from 6’1” 189 pounds in 1955 to 6’3” 205 pounds in 2014 (12). Since Major League Baseball has begun recording velocities of pitches with their Statcast data tracker, the average fastball velocity of pitchers has increased from 90.9 MPH in 2006 to 93.5 in 2016 with a record high of 106 MPH being clocked in during the 2010 season by Aroldis Chapman. This has coincided with a sharp increase in the amount of Tommy John Surgeries performed. The number of pitchers who have received this procedure has grown immensely from the first surgery in 1974 to 2003 when approximately 1 in 9 MLB pitchers had received Tommy John to today when officially 26.2% of MLB pitchers, or a little more than 1 in 4 have had their UCL reconstructed. These trends pose the question, what about pitching puts players at such high risk for UCL tears and does the reconstruction surgery enhance the pitchers elbow from a biomechanical perspective?

Personal Projects

  • - JavaScript based browser BlackJack table game, Code: GitHub
  • - California Covid-19 Data Dashboard utilizing The Covid Tracking Project API and Chart.js, Code: GitHub
  • - This Website, Code: GitHub
  • - More to come soon
  • - "Optimized Conversion of Categorical and Numerical Features in Machine Learning Models", PDF, Code: GitHub
  • - California Covid-19 Data Dashboard utilizing The Covid Tracking Project API and Chart.js, Code: GitHub
  • - More to come soon
  • - Sports Betting: Kelly Critereon resource management using max heap data structure. Code: GitHub
  • - Partial Differential Equations: Using the explicit finite difference method to numerically approximate the 1D heat equation. Code: GitHub
  • - More to come soon

Contact

Send me a message and I will get back to you as soon as I can!

Los Angeles, California tombutler368@gmail.com
Connect With Me: