The Rising Sea Solutions — A self-contained write-up of exercises and results from Vakil’s The Rising Sea.
[PDF]
[GitHub]
The Arithmetic of Elliptic Curves Solutions — A collection of expanded proofs, remarks, and exercise solutions from Silverman’s The Arithmetic of Elliptic Curves.
[PDF]
[GitHub]
Formalizing \(n = a^2 + b^2 \) in Lean — A formalization that \(n = a^2 + b^2\) has a solution if and only if the p-adic valuation \(\nu_p(n)\) is even for each \(p \equiv 3 \mod 4\) using the Gaussian integers.
[GitHub]
Describing a Hyperbolic Surface: From Lengths and Twists to Matrices — UW–Madison MxM Undergraduate Research Seminar, Fall 2022.
We constructed explicit generators in \( \mathrm{PSL}(2, \mathbb{R}) \) for Fuchsian groups representing hyperbolic surfaces (e.g. pairs of pants), using twist and length parameters.
[program link]
A Proof of Quadratic Reciprocity by Galois Theory — A complete Galois-theoretic proof of quadratic reciprocity, expanding on a sketch by Prof. Ana Caraiani.
[PDF]
[GitHub]
Segre & Veronese Algorithms in Macaulay2 — Macaulay2 code for computing presentations of Veronese subrings and Segre products of graded rings.
[GitHub (Segre)]
[GitHub (Veronese)]
Original Number Theory Problems — A collection of 9 self-authored problems with complete solutions exploring Diophantine equations and modular arithmetic.
[PDF]
[GitHub]