Undergraduate Research in Computational Algebra
Links that connect
to an non-USM website will open a new window.
and Lyx files
for typing an Honors Thesis according to the Honors College guidelines.
is the goal of undergraduate research?
How do I get started?
What are some possible projects
or topics with Dr. Perry?
What are the
benefits and costs?
What if I'm not that
good at math (or algebra, or programming, or...)?
What is the goal of
- A risk-free ("not
graded") opportunity to stretch yourself
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
- Look over the list
of possible projects/topics below. If something strikes you
as interesting, contact
- If you don't find
anything that appeals to you, take a look
at these USM
math department professors' pages instead:
Ding (numerical analysis, optimization, ergodic theory,
Kolibal (fractals, differential equations, numerical analysis)
Lee (algebraic geometry, differential geometry, symplectic
geometry, noncommutative geometry)
- Make a habit of visiting the library every month and perusing math journals. Reading others' work often stimulates ideas.
You probably can't understand everything in most articles, but you can
certainly understand at least something in most articles; if you find
an article that interests you, you can take it to a member of the department who specializes in that area and ask her or him to work through it with you. Two good journals that target undergraduates are:
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
- The College Math Journal
- Math Magazine
- Google's Summer of Code
- AMS' listing of
Experiences for Undergraduates (REUs)
- AMS' listing of internship opportunities for
- NSF's listing of REUs
some possible projects or topics with Dr. Perry?
- Problems from MAA journals
These tend to be relatively easy and short term (days or weeks).
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.
- Projects leading to original
designed for math majors with some computer experience or comp sci students
willing to learn a bit of math
- Problems in Linear
Algebra and Modern
Algebra I. Specific problems I have directed, or am willing to
These projects generally require at least a small amount of proof.
- Fixing Dodgson's method
for matrix determinants
- Other fraction-free methods to compute determinants
- Techniques to triangularize a sparse matrix
- Methods to represent a polynomial on a computer: lists, matrices, geobuckets, ...?
- Programming projects
available for students able to work
in C/C++, Eiffel (both ISE Eiffel and SmartEiffel),
(SAGE actually), or Maple.
Such projects will be useful either for mathematical research (a
problem I'm interested in) or for education (the common benefit of
elementary and secondary schools).
- Projects that won't
lead to original results, but will supplement
or round out your undergraduate mathematics major (or
- Galois Theory
- Applied Algebra
- The Fundamental Theorem of Algebra
- Theory of Computation
- Computer programming for mathematicians
- Note for students of the Honors College: The Honors College now discourages theses that do not include original results of some kind.
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
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. Unfortunately, I can't offer you any kind of stipend
at the moment.
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 put up with
if I'm not that good at math (or algebra, or programming, or...)?
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. Sometimes I still feel that way, but now I do it
for a living and
I enjoy it. (most days) You can too, if you're willing to
plug at it