Advising

Potential research students

Interested in doing research or writing a thesis? I currently have a handful of research problems that have great potential for a thesis at all three levels -- undergrad senior thesis, masters thesis, and Ph.D. thesis. If you think you might enjoy working on a project on discrete dynamical systems, combinatorics, Coxeter groups, discrete mathematical biology, or scheduling problems in operations reserach, drop by and see me. I'll give you some papers to read and some things to think about. Not sure which of those you might like, if any? Come on by anyways.

Words of wisdom

On the remainder of this page, I've compiled a collection of advice and tips that I've accumulated throughout the years. It is grouped by target audience.

Everybody

The following applies to everyone, from high school students to Emeritus Professors. Even if you've seen these before, they are well worth revisiting.

Fundamental axioms of mathematics, by Federico Ardilla
The Lesson of Grace in Teaching, by Francis Su. Also available as a YouTube lecture.

Undergraduate students in STEM fields

I have several pieces advice that everyone who gets a degree in math, science, or engineering should follow. I list them in order of importance.

• Learn a computer programming language. Even if you hate it. Take the intro class if you need it, but also that one class on object-oriented programming that takes up a ton of time. As a job skill, computer programming in the 21st century is like what typing was back in the 1950s. There are many technical jobs these days where if you apply without any programming experience, there will be 10 people just as qualified, but who know how to program who will get the nod above you. And fortunately, you don't need much (usually just that one object-oriented language / data structures course) to get by.

• Get good at linear algebra. Take it as early as you can -- preferably before differential equations, and even before or concurent with vector calculus. It comes up everywhere, and you'll understand your upperdivision classes much better. Think of it as laser eye surgery for the math part of your brain.

• Spend at least one summer doing research. This can be with a professor in your department, or even better, and NSF funded Research Experience for Undergraduates (REU) program. As an undergraduate, most professors would be thrilled if you are interested in pursuing this. They might not have funding for you, but most would love to help, and could give you some great advice on where and how to find these programs. Don't be shy. This is a great way to prepare for graduate school, a career in industry, or to figure out which one of those two directions you want to take after graduation.

• At some point, years after taking a class, you might want to email one of your former professors. It might be about a question, an update about the great job or graduate school you got, or nothing in particular. You'll wonder: Does he she remember me?, or even Would he or she even care? Now, I can't speak for everybody, but for me, the answer to both questions is an immediate YES! I suspect the vast majority of your professors would feel the same way. We love hearing back from former students.

Undergraduate math majors

• Everything mentioned above, obviously.

• Take Intro to proofs (MATH 3190 at Clemson) as early as possible -- 1st semester sophomore year at the absolutely latest.

• Take Linear Algebra (MATH 3110 at Clemson) as early as possible -- 2nd semester sophomore year at the absolutely latest. Pay no attention to the course number, it could (and probably should) come before Differential Equations (MATH 2080 at Clemson).

• Take Advanced Calculus / Real Analysis (MATH 4530 / 4630 at Clemson) as early as possible -- ideally no later than 1st semester junior year. This is the most fundamental undergraduate advanced math course, and is quite difficult. However, it will be just as hard your senior year as in your junior year, but the benefits you gain from taking it early will pay off in your later courses much more so than any upper-division math course we offer.

Graduate students in mathematics

Obviously, this is in addition to the list above. But this time, in no particular order. It's amazing how many graduate students don't do some of these, or in many cases, all of these.

• Make a webpage. Put your CV on it. Summarize your research. It's easy to do, and it's professional. It's also a great way to network.

• Respond to emails promptly. Again, it's professional. And if you get in the bad habit of blowing them off in grad school, you're probably not going to fix it later.

• Learn how to use UNIX / Linux. You don't have to become an expert at it. But get competent. You are in academia, and there is a reason why it's prevalent here.

• Subscribe to the daily arXiv mailings. This takes a minute or two of your time to browse each morning (or night, if you stay up as late as I do). If you don't know what this is, go to www.arxiv.org and figure it out.

• Do NOT feel intimidated to approach a professor about his/her research. It's natural to feel shy or even scared about this, and to think that they know much more than you. Well, they probably do. So what? But here's an inside secret: Professors like it when students express interest in their research! And as much as grad students need good advisors, professors need good grad students.

• Take topics / reading courses early and often. There is absolutely no commitment in doing a topics course or a reading course with a professor with regards to writing your thesis with him/her. There is also nothing wrong with doing several reading courses at once with several different professors. See what types of problems you enjoy. It's a great way to get exposed to new areas and see what you like.

• Learn the LaTeX typesetting language. Get good at it. If possible, write up your assignments in LaTeX. That way you'll always have copies down the road, and you can correct any errors.