Handouts

Personal handouts written, and some stuff. If you find a typo, please contact me.


PROMYS 2025 Seminar Notes

TAMU Projects

  • Rational Normal Scrolls (with Quentin Holmes)

    Introductions to Rational Normal Scrolls and the combinatorial approach of finding the number of hyperplane sections of a given scroll. Presentation for the Computational Algebraic Geometry (MATH 648) taken in Spring 2026.

  • Quadratic Excess Theorem

    Theorem stating if p is a 3 mod 4 prime, then more quadratic residues lie on the interval (0,p/2) than on the interval (p/2,p). Presentation for the Directed Reading Program (MATH 285) taken in Spring 2025 (mentored by graduate student William Taylor).

  • The Wavelet-Galerkin Methods for PDEs (with Colin Neaville)

    Method of using wavelets and scaling functions to approximate the numerical solution of a PDE. A paper written in the course Fourier Series and Wavelets (MATH 414) taken in Spring 2025.

  • Compact Sets

    The open cover definition for compact sets, which is unnecessary for the real line but used in general metric spaces. Written in the course Analysis on the Real Line (MATH 409) taken in spring 2025.

  • Dirichlet's Theorem on Arithmetic Progressions

    Theorem that there are infinitely many primes in any arithmetic progressions if the first term and the common difference is relatively prime. A paper written in the course Foundations of Mathematics (MATH 300) taken in fall 2024. Uses basic analytic number theory.


Other Stuffs