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.
Advice for undergraduate students in math, science, & engineering
I have several pieces advice that everyone who gets a degree in
math, science, or engineering should follow. I list them in order of
• 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.
Advice for (undergraduate) math majors
• Everything mentioned above, obviously.
• Take MthSc 119 (intro to proofs) as early as possible -- 1st
semester sophomore year at the absolutely latest.
• Take MthSc 311 (linear algebra) 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 MthSc
208 (differential equations).
• Take MthSc 453 (advanced calculus / real analysis) 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.
Advice for 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's 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
• 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.