Personal handouts written, and some stuff. If you find a typo, please contact me.
Minicourse for returning students. The full rigorous proof of the Quadratic Excess Theorem.
Minicourse for students. Introduction to elliptic curves, the group law, and some applications. Solves the infamous fruit problem "95% of people cannot solve this!".
Counselor Seminar. Introduces Agoh's conjecture, Giuga's conjecture, and prove their equivalencies.
Minicourse for students. Introduction to functions with one complex variable (without complex analysis), and how to graph them.
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.
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).
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.
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.
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.
A rigorous introduction to elementary differential equations, written mainly for mathematics majors.
Approximating the solution to the Laplace’s equation. Presentation in the course Applied Mathematics Project taken in Korean Minjok Leadership Academy, fall 2023.
Laplace transforms for ODEs, covers all topics covered in elementary engineering mathematics.