courses I am teaching

Fall semester 2012, I am teaching Math 160, Introduction to Applied Statistics, sections A, K, and I.

information about my research

I finished my PhD at the University of Minnesota in 2006. Here’s my thesis, and here’s the known errata list.

associated Hermite polynomials

At FPSAC 2007 I gave a talk on the combinatorics of associated Hermite polynomials. I have slides from the talk, and a preprint of the paper is available at arXiv:0709.0987. The paper appeared in the European Journal of Combinatorics: doi:10.1016/j.ejc.2008.05.009 (here is citation info).

k-distant noncrossing matchings and set partitions

Jang Soo Kim and I have a preprint: k-distant crossings of matchings and set partitions, which was accepted as a poster at FPSAC 2009 and appears in the proceedings.

Higher-order matching polynomials and d-orthogonality

See arXiv:0909.1655. This paper was published in Advances in Applied Mathematics: doi:10.1016/j.aam.2009.12.008. I gave a talk on this paper at the 2012 Combinatorial Potlatch in Vancouver; here are the slides.

Bijections from weighted Dyck paths to Schröder paths

See arXiv:1006.1959. In the k-distant noncrossing matchings paper above, Jang Soo and I proved that little Schroeder paths are equal to the generating function for certain weighted Dyck paths; this paper presents a bijective proof of that fact and examines its consequences. This appeared in the Journal of Integer Sequences. I gave a talk on this bijection at the Korea Combinatorics Workshop at Yeungnam University; here are the slides. I also gave a talk on the bijection at the fall 2010 KMS meeting at Postech: here are those slides which are an improved version of the Yeungnam ones. The Sage demo I used is here.

I talked about this bijection at the KPP combinatorics seminar, in the larger context of the combinatorics of Chebyshev, Hermite, and Charlier orthogonal polynomials. Here are the slides.

Generating functions for plateaus in Motzkin paths

This is joint work with Ryan Gantner and appears in the Journal of the Chungcheong Mathematical Society; see their page or arXiv:1109.3273.

other stuff

2012 PREP workshop on Sage

Karl-Dieter Crisman and I organized an MAA PREP workshop on Sage during the summer of 2012.

SageTeX

I’m the main author of the SageTeX package, which allows you to easily pull the results of Sage computations and plots into your LaTeX document. And since Sage is based on Python, you can write Python that writes LaTeX for you. This is really useful! SageTeX is a (admittedly small) component of an NSF grant for “integrating open mathematics software and open educational materials into the mathematics curriculum and classroom”.

Here’s the documentation and the typeset example file.

Try it today. If you’re really curious, you can follow SageTeX development at bitbucket.

KAIST Sage server

I maintain the KAIST Sage server(s). If you are interested in an account on the Memorial Day server, please email me. Otherwise, anyone can use the Groundhog Day server. (Read about the difference between the two servers.)

Archimedean solids via truncation, expansion, and snubification

In 2007, I developed some Java applets that demonstrate the geometric operations of truncation, expansion, and snubification on the Platonic solids. My goal was to get all of the Archimedean solids this way; it turns out to be impossible, but I enjoyed making the applets and you may find them interesting.

That page also includes a little mini-essay on the freedoms and restrictions that mathematical software affords and imposes on you.

GeoGebra applets

GeoGebra is a Java program with which you can easily make very cool interactive geometry demonstrations. Its focus is on elementary Euclidean geometry, but I’ve discovered that you can use it for an impressive variety of 2-dimensional graphics. It’s also extremely easy to make web pages with GeoGebra – see my pages on the complex cosine or polar plotting or Riemann sums for definite integrals. Try double-clicking on the applet to open the full GeoGebra program!

I’ve also published a (IMHO) very nice applet demonstrating the epsilon-delta definition of limits.

TikZ/PGF

TikZ is a graphics system for TeX and friends. It’s very powerful, and somewhat similar to PSTricks. I highly recommend TikZ (and its lower-level engine, PGF) for all your graphics needs when writing LaTeX documents. Here are some examples of things I’ve made with TikZ:

• A document describing stability behavior of linear differential equation systems near the origin. The main diagram is basically copied out of Zill and Cullen, but my version is more complete and more colorful. Here’s the source file so you can see how I did it.
• The Borromean rings. The source is here.

Old notes and other writeups

Here are some old notes and other things I wrote back in grad school; according to server logs, they’re relatively popular and I should update and improve these sometime, but for now, here they are:

• Fifty ways to find the volume of a torus.
• Finding the size of a conjugacy class in the symmetric and alternating group. Includes a proof that A₅ is simple.
• The size of SL(n, q) and GL(n, q) – the sizes of the special and general linear groups over a finite field of order q.

links to various people, places, and things

Sage

I use and contribute to Sage, an open-source mathematics computing system whose mission is to create a viable free open source alternative to Magma, Maple, Mathematica and Matlab. Read about why you should use Sage and download it today!

I’ve set up a public Sage server here at KAIST: you can access it at http://sagenb.kaist.ac.kr.

Zotero

Zotero is a web service that is a great tool for helping research. It keeps track of your references, makes it super easy to capture information, search and sort that information, and then put references into your documents. It has synchronization features that make it super easy to have access to all your data everywhere you go.

Zotero works mostly as a Firefox plugin, but is now available as a standalone program. When it was only a Firefox plugin, I initially thought putting a citation manager into your browser was not a great idea, but think about it: if you are using a computer to look up information about a reference, what kind of software are you using? You’re using a web browser – so put the citation manager where the action is. Zotero is open source and works very well. I recommend it.

CiteULike

CiteULike is a great service for keeping track of all your references. It stores PDFs, lets you add notes, and is moving towards some useful social networking features. Have a look at the things I’ve bookmarked. I’ve mostly abandoned CiteULike in favor of Zotero, but it’s still a nice service.

Ubuntu Linux

I’ve used Linux in some form or another so long that it’s surprising my beard is so short. I recommend installing Ubuntu (or another Linux distribution). It works really well, doesn’t crash, and is easy to install. Get it today!

Graduate Student Combinatorics Conference

I was one of the organizers of the inaugural Graduate Student Combinatorics Conference at the University of Minnesota in April 2005. I’m delighted to see that the conference is continuing, and even getting NSF funding!

• 2006, University of Wisconsin
• 2007, University of Washington
• 2008, UC-Davis
• 2009, University of Kentucky
• 2010, Auburn University
• 2011, Penn State
• 2012, University of Illinois at Urbana-Champaign
• 2013, back to the University of Minnesota!