My name is Jeremy Kun. I’m currently a mathematics PhD student at the University of Illinois in Chicago. I am part of the Mathematical Computer Science group there, my advisor is Lev Reyzin, and I did my undergraduate at Cal Poly San Luis Obispo in mathematics and computer science. I have a thorough background in computer science, but my most exciting experiences there always stemmed from elegant (and uncoincidentally mathematical) solutions to programming problems. This blog is a presentation of the interesting solutions I come across, and an exploration of the deeper mathematical ideas therein. Most often this means exploring the mathematical structure of a problem to lubricate the cogs of algorithm design. In seldom cases, this involves using programs to reason about mathematical theory.
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For potential employers, grant-givers, or research partners, think of this blog as a three-fold portfolio: it contains code I’ve written in multiple languages, has a wealth of technical writing samples, and displays my ability to integrate and explain (or intentionally simplify) ideas from various mathematical and software fields. Most of the work on this blog has followed the recipe:
- Stumble upon a topic that sounds fascinating, or become fed up with my own ignorance of some area of mathematics or programming, or come up with an original question or idea.
- Read books, papers, blogs, and watch lectures online about the topic.
- Come up with a small software project that uses the idea in a nontrivial way.
- Write a main content post explaining and demonstrating the project.
- Write a primer post explaining the background mathematics.
- Look for ways to expand, generalize, or relate the idea to projects past and forthcoming.
While I don’t put my largest software projects here (indeed, I feel a large code base would take away from exploring relationships with mathematics), there are plenty of examples of my own written code. I include snippets in my main content posts, and include the entire source for each project on this blog’s Github page. This includes the programs I use to generate images and animations.
Here is a list of the languages used in some nontrivial capacity (using nontrivial features of the language) on this blog so far:
- Standard ML
Here is a list of the main mathematical areas explored so far:
- Linear algebra
- Graph theory
- Abstract algebra
- Probability theory
- Machine learning and learning theory
- Theory of computation and computational complexity
- Algebraic topology
- Category theory
Here are some other of my online profiles:
Math ∩ Programming by Jeremy Kun is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.