My Projects
Welcome to my projects page! Here you'll find a collection of my work in mathematics, computer science, and machine learning. Each project represents a unique challenge I've tackled or random problem I decided to persue.
Mathematics & Theory
- Sum of Uniform Random Variables - Finds the expected number of i.i.d variables uniformly distributed betweeen 0 and 1 needed to be sumed in order to exceed one. Very satisfying answer.
- Hartogs' Extension Theorem - A study of extending holomorphic functions in several complex variables.
- Conformal Mapping Techniques - Comformal invarience proof and applications of conformal mappings of Complex Brownian motion.
- Expected Value of A Random Point in Square to it's Nearest Edge - Finds the expected distance between a point chosen at random in a unit square to the nearest edge.
Software Development
- Claude Code Reimplementation - An AI-powered development assistant reimplemented with Gemini AI for Python development and file system operations.
- Story Teller AI - An interactive AI-powered storytelling application featuring Boop Boop the Storytelling Elephant for children aged 5-10.
- Gator RSS Aggregator - A command-line RSS feed aggregator written in Go with multi-user support and automatic content aggregation.
Each project page contains detailed explanations and the mathematical foundations behind my work. Feel free to explore these topics and reach out if you have questions.