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Andy Parrish APM 6434

Current teaching
I am a teaching assistant for these courses in Winter 2012.

• Math 20A — Differential Calculus. I am TA for sections A03 (noon in U413 #2) and A04 (1 PM in U413 #2). My office hours are W 9-10 AM in my office, and F 9-10 AM in the Calc Lab (APM B402). Homeworks are due Fridays at 4 PM.
• Math 186 — Probability and Statistics for Bioinformatics. My office hours are Th 9-11 AM in my office. Homeworks are due Thursdays at 11:59 PM.

Research
I am a PhD student in the Math department of UC San Diego. I am working in combinatorics, and specifically trying to discern necessary structures within large graphs, sets of integers, and anything else I can wrap my head around. This leads to some buzzwords like "extremal combinatorics," "Ramsey theory," and perhaps "the study of natural numbers larger than infinity." I am working with Ron Graham, with additional guidance from Fan Chung.

Papers
Here are some papers I have worked on. They are in various stages of submitted, in-progress, and not-fit-to-publish.

• Toward a graph version of Rado's theorem (2012). This is a follow-up to the previous paper. Call an equation graph-regular if every r-coloring of the complete graph on the natural numbers contains a monochromatic complete subgraph whose vertices solve the equation. This paper gives two Rado-like conditions for an equation which are respectively necessary and sufficient for graph-regularity.
• An additive version of Ramsey's theorem (2011). This is a combination of the two flavors of Ramsey theory: additive and graph-theoretic. In short, Ramsey's theorem guarantees that any edge-coloring of a large complete graph will give large monochromatic complete subgraphs. In this paper, We show that we can get more: if the vertex set is the natural numbers up to n, we can guarantee some additive structure of the vertices in the monochromatic subgraph. Specifically, we prove that, for all r and k, there is an n = n(r, k) so that, for any r-coloring of the complete graph on vertex set {1, 2, ..., n}, there must be a solution to x₁ + ... + x_k = y₁ + ... + y_k by distinct numbers, so that all edges among those values have the same color.
• Van der Waerden's Theorem: Variants and Applications. I am working on this book with Bill Gasarch and Clyde Kruskal. It is a collection of combinatorial proofs of results in additive Ramsey theorey. This is built on my senior thesis at the University of Maryland. The original motivation for the book is its detailed combinatorial proofs of the Polynomial van der Waerden theorem and the Polynomial Hales-Jewett theorem, expanding on proofs in a short paper by Mark Walters.
• There is no "large van der Waerden theorem" (2009). This is a minor negative result in Ramsey theory from a question of Bill Gasarch: the Large Ramsey theorem does not translate directly to a "Large van der Waerden theorem."
• Exploration of the three-person duel (2006). This was a problem I worked on as an undergrad at the University of Maryland. Under the guidance of Bill Gasarch, I formulated the equations governing the probabilities of winning in a three-person duel, and explored the conditions for the three players to be evenly matched.

Past teaching
I have been teaching assistant for these courses:

• Math 10A (Fall 2011) — Differential Calculus. I was the instructor for this course.
• Math 152 (Spring 2011) — Game Theory. I was a co-lecturer for this course assisting Fan Chung, in addition to being the TA. (evaluations)
• Math 20B (Winter 2011) — Integral calculus (evaluations)
• Math 153 (Fall 2010) — Geometry for Secondary Education (evaluations)
• Math 202 (Winter/Spring 2010) — Applied Algebra (Here are some selected homework solutions)
• Math 163 (Winter 2010) — History of Mathematics (evaluations)
• Math 20D (Fall 2009) — Differential equations (evaluations)
• Math 20C (Spring 2009) — Multivariable calculus and analytic geometry (evaluations)
• Math 20B (Winter 2009) — Integral calculus (evaluations)
• Math 20A (Fall 2008) — Differential calculus (evaluations)

Past course webpage
In summer 2009, I studied random geometric graphs with some other students. I maintained the course website.

Jobs
Here are some jobs I have held outside of teaching. If you have any jobs you would like to see added to this list, the process begins with my résumé.

• Google — I am working for Google's Cambridge office in summer 2011. I attempt to optimize local storage for YouTube by understanding video request patterns.
• Johns Hopkins University Applied Physics Lab — I worked for two summers (2007-2008) investigating a new protocol for Private Information Retrieval, with the goal of attaining practical algorithms with low communication costs.

Some links
Here are some things which do not quite fit into other categories.

• Here is some advice for how to manage grad school applications. It is a detailed account of the specific things I did to avoid being overwhelmed by applications.
• Here is a list of every group of order up to 30. This list was created by John Pedersen at the University of South Florida, but has since been taken down. I still wanted to use it, and maybe you do, too.
• I made a Dinosaur Comics Graphics Randomizer. For those unfamiliar, Dinosaur comics is a really wonderful webcomic, which happens to use the same six panels (of dinosaurs!) for every strip. The strip's creator Ryan North built in a way to replace the dinosaurs with other characters, and set up seventeen different skins for the comic. My tiny contribution was to write a script which randomly generates one of these skins, for maximum enjoyment. Warning: one of the skins replaces the text in panel six. If you aren't careful, you could miss the intended punchline!
• Detexify is the best thing to happen to LaTeX since Donald Knuth and Leslie Lamport! Here's how it works: you draw a math symbol, and it tells you how to type it in LaTeX. It's far from perfect, but farther still from neutral.
• I spent Fall 2006 in Budapest, in the Budapest Semesters in Mathematics program. It was an incredible experience both culturally and academically, and I encourage all math majors to consider it. Please contact me if you want to know more.

Is Katie awesome?