Personal handouts written, and some stuff. If you find a typo, please contact me.
Intermediate counting on AMC to low-AIME level. Includes complementary counting, PIE, circular permutations, and stars and bars.
Sequences on AMC to AIME level. Includes basic sequences, telescoping and recursions.
Coordinate bashing on AMC to AIME level.
Techniques to solve complicated (mostly nonlinear) systems of equations.
Complex numbers on AIME level. Includes roots of unity and relationships to trigonometry.
Useful techniques of bashing and guessing for the AIME.
My solutions of AMC 12A 2023 after taking the exam, with the help of Ian Baek.
My solutions of AMC 12B 2023 after taking the exam, with the help of Ian Baek.
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). There are two separate slides as I presented this in two different talks.
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 (TAMU 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 (TAMU MATH 300) taken in fall 2024. Uses basic analytic number theory.
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.