Opportunities for
Undergraduate Research in Computational Algebra
Links that connect
to an non-USM website will open a new window.
What is the goal of
undergraduate research?
- A risk-free ("not graded") opportunity to stretch yourself
and make
yourself more marketable to potential employers or graduate schools.
The end result should be a well-written thesis that will summarize your
study, and perhaps a publishable paper.
- A chance to get a taste of how "real" mathematics is done.
How do I get
started?
- Look over the list
of possible projects/topics below. If something strikes you
as interesting, contact
me.
- If you don't find anything that appeals to you, take a look
at these USM
math department professors' pages instead:
- Dr.
Ding (numerical analysis, optimization, ergodic theory,
dynamical systems)
- Dr.
Kolibal (fractals, differential equations, numerical analysis)
- Dr.
Lee (algebraic geometry, differential geometry, symplectic
geometry, noncommutative geometry)
- If you have your own ideas, you can talk to me (or any professor), and see if I am (s/he is) interested in working on it with you.
- You can also try
- Google's Summer of Code
- AMS' listing of summer Research
Experiences for Undergraduates (REUs)
- AMS' listing of internship opportunities for
undergraduates
- NSF's listing of REUs
What are
some possible projects or topics with Dr. Perry?
- Problems from MAA journals
These tend to be relatively easy and short term (days or weeks, instead
of months). Solving them requires a bit of time and creativity. Once
you finish a solution, you can submit it to the journal and see your
name in print. The short-term nature of these problems means that you
cannot use this for an Honors Thesis. However, it is a good
introduction to research, and you can sometimes generalize the problem
to something suitable for an Honors Thesis.
- Projects leading to original
results and/or software,
designed for math majors with some computer experience or comp sci students
willing to learn a bit of math
- User interfaces for mathematical research
(Obviously you need some programming skill for this.)
- Programming projects available for students able to work
in Eiffel (both ISE Eiffel and SmartEiffel),
Java,
Python
(SAGE actually), or Maple.
Such projects will be useful either for mathematical research (a
problem I'm interested in) or of education (the common benefit of
elementary and secondary schools).
- Theoretical projects available for students who have
taken Modern Algebra I. A familiarity with combinatorics is a plus.
- Projects that won't lead to original results, but will
supplement or round out your undergraduate mathematics major (or minor)
- Galois Theory
- Applied Algebra
- The Fundamental Theorem of Algebra
- Theory of Computation
- Computer programming for mathematicians
What are
the benefits and costs?
- Benefits:You
stretch your mind, gain a lot of experience with problem-solving
outside the classroom, and end up with another item to add to your
resume, CV, job application, etc. If you want to travel, you might have
an opportunity to do that, too. REUs at other institutions have
enough money to pay for your travel and lodging. Google's Summer of
Code 2007 offers a $4500 stipend to students, and you don't have to
travel.
- Costs:
All research takes a lot of time, patience, determination, and a
willingness to deal with hard problems that have unexpected or even
undesirable results. If you work with me, you also have to be willing
to put up with my quirks.
What
if I'm not that good at math (or algebra, or programming, or...)?
The
only way to get better at it is to work at it and keep at it! I wasn't
very good at them either once. I have memories of getting so
frustrated that I was sure
I'd never try programming or mathematical research again. Now I do it
for a living and
enjoy it. You can too, if you're willing to plug at it hard enough.
Current students
- Courtney Bright (Factors impacting the poor performance of mathematics students in the United States)
- Deanna Leggett (Dodgson's method of computing determinants)
- Ashley Sanders (Problems from MAA journals, A new user interface for computer algebra systems)
Past students
- Lenton McLendon (Introduction to Gröbner bases)
- Jonathan O'Rourke (Universal Algebra, with Dr. Lee)