Dan Drake

Department of Mathematics ∙ University of Wisconsin–Madison

I’m a lecturer in the mathematics department of the University of Wisconsin. I study combinatorics, specifically the combinatorics of orthogonal polynomials. I was previously at the University of Puget Sound, KAIST, and the University of Minnesota. Here’s how to contact me.

email: ddr...@math.wisc.edu. I digitally sign my messages with GPG; my key is here (key id 58C2E4BA). The digital signature is the little text attachment you see on emails from me.
office: Van Vleck Hall 407.
snail mail:
Department of Mathematics
480 Lincoln Dr
Madison, WI 53706

Here’s my CV.

courses I am teaching

Spring semester 2015, I'm teaching Math 340, Linear Algebra.

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.


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 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:

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: