Professor Dresden's Home Page

Department of Mathematics

The College (of Arts & Sciences)

Washington & Lee University


Welcome to my web page. For academic info about me, be sure to check out my somewhat-up-to-date Curriculum Vitae [pdf file]. For class or research info, read on!

How To Reach Me

Office Hours

For winter term 2015-2016 (starting January 11, 2016). These are subject to change, and you can always make an appointment to see me.

Fun with differential equations

I had a tremendous amount of fun this last term with my Math 332 class (Ordinary Differential Equations). We took some rather simple differential equations and created lovely stream plots that depict the behavior of the solution over time, given a certain initial condition. Here are two pictures from computer labs we did in class.

StreamPlot1 StreamPlot2

On the left, we see a traditional stream plot for the equation dx/dt = x2 - t with various initial conditions, and on the right we see the same stream plot but run through this special Mathematica filter that gives it that lovely coffee-toned look. We also did some animations, although that took up a lot of computer processing time.

This term, I'm teaching Math 333 (Partial Differential Equations) from Stanley Farlow's book. Although it's only ten dollars (yay!), the textbook has an unfortunate number of typos, misprints, and so on (boo!). I've written up a list of errata, hints, solutions, and commentary; here's Part 1, and here is Part 2. Feel free to copy and distribute this file to your own students, but please drop me a line and let me know that you're using it (so that I can brag about it to my colleagues).

Newsweek photo

This photo (of me and student Scotty Groth) appeared on the Newsweek/Daily Beast website for W&L (which was ranked #11 on the list of Most Rigorous Schools).

Mathematical Research

I work in an area of mathematics called number theory, and in particular on the subject of the Mahler measure of a polynomial. I also study other topics from both number theory and abstract algebra (on polynomials, groups, algebraic extensions, etc). Here are some of the articles I have written: I'm rather fond of my three articles that were published in the MAA Monthly, partly because two of them were jointly written with other mathematicians (which is a tremendous amount of fun), and partly because the MAA Monthly (as seen here) is the most widely read mathematics journal in the world.

Thanks to my joint articles, I have an Erdös number of 3. This means that I'm only three co-authors away from Paul Erdös, the most prolific mathematician in history (biographical links to Wikipedia here and to the MacTutor history of mathematics site here). The MathSciNet database gives the chain as Dresden -- Art Benjamin (at Harvey Mudd) -- Phyllis Chinn (at Humboldt State) -- Paul Erdös. How cool is that! (Some famous people with Erdös number 3 include Larry Page, Sergey Brin, Kurt Gödel, and John von Neumann.)

Some of my articles have been referenced in AT&T's On-Line Encyclopedia of Integer Sequences, which is always nice to see. For example, check out 0, 0, 1, 0, 1, -1, ... (reference number A094754) and 1, 1, 2, 6, 4, 2, ... (reference number A008904), among others. Thanks to Jacob Siehler for providing the Mathematica code!

Some of my articles have also been referenced in books. For example, my two papers on the last non-zero digits of various sequences are quoted on page 32 of the book, "Numbers and Functions: From a classical-experimental mathematician's point of view" by Victor H. Moll of Tulane University, as seen here.


Along with Professor Siehler, my Abstract Algebra students and I worked on finding natural representations for finite rings. Please visit our Small Rings page for examples.

I've given many presentations on mathematics and one on teaching mathematics, at local and national conferences. Also, Art Benjamin (mentioned above) gave a presentation on our joint work at MIT in December of 2004, and fellow W&L professor Wayne Dymacek gave a talk on our joint paper here at W&L. Recently, I gave a talk at JMU on the Mahler measure and again on the Look-and-Say sequence, and a student of mine gave a talk at Loyola (in Maryland) on her senior honors thesis (on the subject of factor rings).

Math Information for Washington & Lee Students (and others)


For general mathematical information, here are some of my favorite links:

The Trail

As you no doubt know, the Appalachian Trail is only a few minutes from campus. I don't think I'll ever actually walk the whole thing, but I do like to get out and hike for a few hours on parts of the trail, accompanied occasionally by our faithful trail dog, Mr. Puppy. Here's a pair of nice pictures from up on the Blue Ridge Parkway (also a few minutes from campus), with the Peaks of Otter in the background of the first shot and the James River in the second.

trail dog Dresden

This page was written in HTML by Prof. Dresden, using a template originally borrowed from UT-Austin. It's been up, in one form or another, since 1997. It's likely that some of the information and links here are out of date; I'm not as diligent in updating things as I should be.