Undergraduate Research

I am happy to work with you to pursue an area of study that goes beyond our current catalog offerings. Anyone interested in pursuing additional study or research should

My office hours are posted on my door, and you are welcome to drop in any time I am in my office.

Research Topics

I am interested in the many connections between mathematics, human reasoning, and computer science. I am influenced by the "two systems" framework from Thinking, Fast and Slow. Mathematics and computer algorithms implement careful "System 2" reasoning, whereas LLM's better match fast and unconsicous "System 1" reasoning.

  • Foundations of Mathematics (♾️)
    • Understanding the (many) things people mean when they talk about 'proofs' or 'randomness'
    • Connecting 'proofs in words' with 'algebra like computations'
    • Advanced Study in other areas of mathematics
  • Algorithms and Programming ( 💻 )
    • Understanding mathematics by implementing algorithms
    • Writing code to perform a specific task
  • Modern AI and Large Language Models ( 🌐 )
    • Testing model abilities through benchmarking
    • Developing AI powered applications
    • Training models that have specific abilities
    • Understanding the mathematics behind LLM's

Past Projects

  • Larger Projects (Honors Thesis and Funded Undergraduate Research)

    • The Role of Surprise In Guessing Games, Fall 2020 - Spring 2021. ♾️ 💻
      An exploration of Information Theory and Randomness in games.

    • Analysis of Emergency Responder Patrolling Techniques through Agent-Based Modeling, 2019-2020. 💻
      Supported by a Summer ATP Grant.
      Developed an Agent-Based Model in NetLogo

  • Formal Directed Study (Math/Comp 499)

    • Foundations of Mathematical Logic, Fall 2025. ♾️

    • Retrieval Augmented Generation for Learning Assistants, Summer 2025. 💻 🌐

    • Hyper Real Numbers and Nonstandard Models of Arithmetic, Fall 2024. ♾️
      Nonstandard Analysis uses Mathematical Logic to create a number system that contains Infinitecimal Numbers that can be used to develop calculus without the use of limits.

    • Designing and Prototyping a Computer Algebra System, Fall 2016 Semester. ♾️ 💻
      Supported by a Semester ATP Grant.
      Explore and implement portions of a Computer Algebra System

  • Informal Directed Studies

    • Introductory Measure Theory, Fall 2018 - Spring 2019. ♾️
      Graduate level Measure Theory through the first two chapters of Folland.