Undergraduate Research Group: FAQ
Table of Contents
This page is aimed at students interested in getting involved in one my
undergraduate research projects.
If you want to know what it will be like
(short answer: very intense,
demanding, challenging, frustrating at times, but also highly rewarding),
what I expect of the students in my group
(short answer: a lot -
especially in terms of motivation, work ethic, and commitment), and
you can expect to get out of this experience
(short answer: a whole lot!), read on!
About this page
What does it take to get in? Prerequisites and qualifications
What will it be like? How it works in practice
What do I get out of it?
Rewards and benefits of undergraduate research
I'm interested. What do I do next?
Note: This page reflects my own approach to guiding undergraduate
research, which I'd like to think of as providing an honors
version of an undergraduate research experience: More intense and
more demanding, with more direct professor/student interaction, but also
- I hope - ultimately more rewarding than the typical such experience,
with added benefits including individualized career support, help with
graduate school and REU/internship applications, and support for
Just like honors classes, this approach is not for everyone. I expect a
lot of my students, but I will also do my best to make the research
experience a worthwhile and rewarding one, and to help them make the most
out of it.
My 2012/2013 IGL Group is an excellent
model for the kind and mix of students I am looking for. The students
ranged from freshmen to seniors and represented a broad range of majors
and academic interests. All were highly talented and exceptionally
motivated and had strong academic records (several had previously taken,
and aced, Math 241 Honors or Math 347 Honors). They worked great
together as a team, they put in the long hours and and the extra effort
needed to meet the project deadlines, and they were happy to volunteer at
open houses and outreach activities. Thanks in large part to this great
group of students, the projects turned out to be wildly successful, they
have garnered the students all-expenses-paid invitations to national
conferences, presentation awards, and invitations to REU programs, as
well as local publicity in the University's
postmarks newsletter and the Mathematics Department's
Math Times newsletter.
My goal for each project is to put together a similar "dream team" of
students that not only have the skills and academic background necessary
for the given project, but also have the right mesh of personalities, and
team work and communication skills that are needed to make a group
project a successful one.
Students must have a very strong academic record, with math grades in
the A range, and ideally some honors level math classes.
Students can be of any major as long as they have the appropriate math
background. My 2012/2013 group included students with majors in Math, CS,
Physics, ECE, and Linguistics, all of whom did a fantastic job!
Some projects have specific requirements on course work and programming
experience; see the
page for details. However, these requirements are somewhat flexible;
a strong overall academic record, and special skills such as those
described below are more important than having taken a particular course.
A typical project will involve a team of 2-5 students, and the
work is a collaborative effort by the whole team. Each team member is
expected to contribute his or her fair share to this effort.
Usually, a natural division of labor emerges, with each
team member focusing on tasks that best match his or her interests,
strengths, and particular skills. For example, some may focus on the
theoretical side, studying relevant literature and working on proofs,
while others may do the programming needed to explore the problem
Undergraduates involved in any
Illinois Geometry Lab (IGL) project
must commit 5-10 hours per
week. Students in my IGL groups probably fall at the upper end of this range,
i.e., averaging closer to 10 hours per week than 5.
These numbers are averages, and some
weeks are a lot busier than others. We will typically have two
full team meeting each week, lasting around 2 hours. During busy periods
(e.g., in the days before a presentation is due), we will likely need
additional meetings to get everything ready and beat the deadlines.
Everybody is expected to chip in and should be prepared to work overtime
during crunch times. I am very flexible with scheduling meeting times
and can make pretty much any reasonable hour/day. In past years, we had
most of our crunch sessions on evenings or weekends as this worked best
with everybody's schedule.
The following special skills are helpful for many projects, though are
not absolute prerequisites. Many students in my group start out with
little or no programming skills at the outset, but often pick up some of
these skills over the course of the project. For students who do already
have very strong programming skills in the areas listed, I can be
flexible with some of the academic requirements, such as specific course
At the beginning of a project, we typically have a specific problem that
we want to attack, some possible directions to take, and some vague goals
to aim for. This gives us a starting point and some ideas to try out and
things to experiment with. How the project will evolve from there is hard
to predict, and impossible to plan out. We will take things one week at a
time, adjusting directions and goals as needed. Research is full of
surprises and unexpected turns. For example, in my "n-dimensional volumes"
project from Fall 2012, a problem (the "Broken Stick Problem") that I
intended as an easy warm-up exercise before moving on to the advertised
project, proved to be so interesting in itself that we turned it into a
second full-fledged research project, and kept working on in for the rest
of the year. Such is the nature of research!
The following is an approximate run-down of what a project might involve in
terms of meetings and work.
- Advanced programming skills in C/C++ and/or Python. In
particular, experience with large scale software projects in a Unix/Linux
environment is helpful for certain projects. We have access to high
performance computing facilities on the campus computing cluster, but to
take full advantage of these capabilities will require a very solid, low
level, knowledge of C/C++. Python is an all-purpose scripting language
that is useful for many projects.
- Advanced Mathematica skills.
Most of my projects use Mathematica for experimentation and visualization,
and to create interactive tools such as those at the Wolfram Demonstrations
Project. Students often pick up Mathematica programming skills as
part of the project, and some manage to become highly proficient in a
short amount of time. However, having at least one team member who
already has advanced Mathematica programming skills is helpful.
- Strong communication and leadership skills.
Communications skills---both written and oral---are important in many
aspects of a research project, from preparing posters and technical
reports to giving oral presentations at conferences and outreach events,
to communicating with other team members. I'd like to have at least one
student with outstanding communication skills on each team. Equally
useful are leadership skills; having a team member who has experience
organizing projects and serving in leadership positions can be a
tremendous boost to a group project.
Research means venturing into the unknown, working on problems whose
solution is unknown, and discovering something that had not been known
before. In regular math courses you mostly work textbook problem,
whose solution is known (at least to the author!) and which are
"doable" in a short amount of time - minutes, rather than days, or weeks,
or months. In honors classes you may encounter more difficult problem
sets or mini projects that may take a few weeks to complete, but even
those normally involve problems that have already been solved. By
contrast, here you will be working on a genuine research project with a
strong potential of leading to new mathematical discoveries or interesting
new applications of mathematics.
Students in my group will learn technical and programming skills, such as
LaTeX (the standard tool for mathematical typesetting), Beamer (the
standard tool for mathematical presentations), and Mathematica or other
mathematical software. These skills can be useful for many of your math
classes, and they are essential if you plan to go on to graduate school in
math. However, they are also useful in many fields outside mathematics,
they boost your resume, and they make you more attractive candidates for
summer programs and technical internships. Developing these skills is an
ongoing process that will take time and effort,
but that will pay off in the long run.
Regular team meetings (twice a week).
These are meetings with the entire project team,
held at regular time slots, and lasting around 2 hours or so. At these
meetings we will discuss progress and share any results, do some
brainstorming, plan the next stage, and assign tasks
to complete until the next meeting.
Project-related assignments (weekly).
This is our version of homework, though - I hope - it will be a lot more
fun, more challenging, and more rewarding than the homework you have to
do for regular classes. The nature of these assignments varies from
project to project, and from week to week. They might include reading and
studying papers in the literature, trying to prove a result, running large
scale computer experiments, or writing code for Mathematica demos. We
will divide up the various tasks among the team members (or possibly small
subgroups), and I will try to match the tasks to the particular strengths
and skills of each team member.
Learn the basics of LaTeX and Mathematica (ongoing).
Students in my group are expected to develop some basic technical and
programming skills. In particular, we will usually use LaTeX/Beamer to
produce presentations and posters, and Mathematica for visualizations.
Prepare presentations, posters, and other materials (twice per
For IGL projects,
there are two key points in the semester at which various materials such
as posters, beamer presentations, reports, and widgets, have to be
completed and submitted to the IGL. The first is the IGL midsemester
meeting, and the second is the end-of-semester IGL Open House. These
events are a bit like a midterm and a final, and the days before the
deadlines are hectic, with additional meetings needed to get everything
ready and delivered in time.
- Participate in outreach activities and open houses (optional).
The IGL provides a variety of opportunities to engage in outreach
activities. Students in my group have given presentations to high
school students at Urbana High School, to middle school students at Leal
School, and to prospective university students at the LAS College's
Admitted Student Day. Participation in such activities is entirely
voluntary, but it would be great if we could continue contributing to
these outreach efforts.
Prepare conference presentations and rehearse talks (optional).
I encourage my students to take advantage of
opportunities to present the results of their research,
I assist with the application
process, and I organize prep sessions and talk rehearsals in the weeks leading up
to the conference. Conference opportunities usually arise after the project has
been completed since one needs to have results ready before one can apply to a
conference. For fall projects, the earliest opportunities are at spring
conferences, and for spring projects, the main conference opportunities are in
the summer and fall.
Students in my group have given over one hundred
presentations at local, regional, and national conferences.
In addition to developing such technical skills, I also put great
emphasis on developing communication and presentation skills. Over the
course of a typical semester, we will need to prepare presentations of
various kind - from internal presentations at IGL events, to
presentations at local and national conferences (see below). The days
before these presentations are usually very intense periods and typically
require additional evening, late night, or weekend sessions to get
everything ready and in as perfect a shape as possible, and to practice
and rehearse talks.
Another extremely valuable skill you develop in the course of a research
project is team work. Each project will involve a group of 2-5
undergraduates - all highly motivated students with strong academic
backgrounds, but representing a broad range of majors, interests, and
skill sets. (My 2012/2013 group included students ranging from freshman to
senior level, with majors in Math, CS, Physics, ECE, and Linguistics, and
representing five different ethnic backgrounds. They formed a fabulous
team, with each participant bringing his or her particular strengths and
interests to the projects, and the results went way beyond anything I
could have anticipated!)
Once you have completed a project and obtained
interesting new results, you can present these results to a wider audience
local and national conferences. These conferences are fantastic
opportunities to get broader exposure for your work, to gain experience
and confidence in giving presentations, to see other presentations by
undergraduates, and to network and meet professors from other schools and
perhaps even recruiters for graduate schools and REU programs. Giving a
talk at prestigious national conferences is also a great resume booster.
Best of all, many of these conferences pay all or most expenses to their
presenters, so you will likely get a free trip if your application is
I strongly encourage my students to take advantage of such opportunities,
I assist with the application process, and organize prep sessions and talk
rehearsals in the weeks leading up to the conference.
Students in my group have given over over forty
presentations at local, regional, and national conferences
since 2012, and
presentation awards in the process.
REUs (Research Experiences for Undergraduates) are 6-8 week
summer research programs for undergraduates, offered at dozens of
universities and colleges throughout the U.S.
Participants are recruited nationally, and usually receive full
funding for housing, meals, and travel, plus a stipend. REU programs have
been around since the 1980s, and for a long time were the primary (and
often the only) opportunity for undergraduates to get involved in
research. REU programs are great to have on one's resume when applying to
Unfortunately, these programs are very hard to get into, and international
students have an even greater challenge as most programs are restricted to
U.S. students. A typical program will receive hundreds of applications
for 5-10 slots. Almost all of these applications will have outstanding
academic records with near-perfect GPAs and strong letters of
recommendation, and there is very little to differentiate these
applications based on the academic record alone. In order to have a
realistic chance of getting into an REU program, you need some additional
evidence that you will be a successful participant in this program and a
strong contributor to the REU team. The ideal qualification is prior REU
experience, along with a strong letter of recommendation by the REU director,
but to gain that experience, you have to get into the REU in the first
An in-semester research project at your own university provides a way to
break this cycle by offering an accessible, entry-level REU-like research
experience, and an opportunity to distinguish yourself and show your team
work skills. This can dramatically increase your chances of getting into
a nationally advertised REU program the following summer.
I have experience with REU programs, both from the perspective of a
director (I ran NSF REU programs in 2001, 2002, and 2009,
and since 2015 am directing the NU-UI REU Program),
and from that of a frequent
letter writer for applicants. As REU program director, I have seen the
kinds of applications and recommendations these programs get, and I have
had the difficult task of choosing candidates for offers from a large pool
of applicants, all highly qualified. As letter writer, I know how
difficult it can be for a student - especially international students -
to get into an REU if they don't have prior research experience. I have
known students who had a fantastic resume with a perfect GPA, lots of
advanced/honors courses, and local awards or scholarships, but still
didn't get into an REU. I believe this was largely because of their lack
of research and team work experience, which made them too much of a risk
for an REU program director!
I am happy to work with students in my group who are interested in REUs
and similar programs, help with the application process, and write recommendations.
Members of my group have had some success getting accepted by highly
competitive REU programs, and I believe the research experience itself, and
the outstanding performance by these students in the team, was critical to
Getting involved in research at the undergraduate level is a unique
experience that makes you stand out of the crowd and helps with
applications for summer research programs, internships, scholarships, and
graduate schools. It can lead to a great letter of recommendation,
especially if you distinguish yourself in the project, outperform
expectations, and prove yourself as a key player on the team.
It can open up
further opportunities, such as
outreach activities, which help you stand out even more and which look
great on a resume. The general skills you will learn in the process
- technical skills such as LaTeX, Beamer, and Mathematica,
communication skills, and team work skills - further enhance your resume.
All in all, a year-long research project can add half a dozen or more bullet
points to your resume!
A standard IGL project requires registration for 3 hours of Math 492
("Undergraduate Research in Math"); upon successful completion,
you will receive 3 hours of credit. The course credit is a nice bonus,
but it should be the least of your motivations, and it would be one of
the hardest ways to get 3 hours of credit. If you need a couple of hours
of course credit, this is not the way to go; take an easier route! (Most
students in my group had the opposite problem: They were taking so many
classes already that they had to get special overload approval to
register for Math 492 credit!)
Contact me: If you are interested in joining my group or have
questions about my projects, I'd be happy to discuss this with you;
email me at email@example.com, and attach your cv/resume and
Check out my
Undergraduate Research Page.
Current news, descriptions of the projects I'm offering, links to
reports on past projects, conference presentations, awards, etc.
Check out the
Illinois Geometry Lab (IGL)
In particular, take a look at the lists of past and current projects
under the "Projects" tab. Applications for semester-long projects typically
open up near the end of the previous semester. Watch for announcements
on the main IGL website.
Check out the
Actuarial Science Undergraduate Research Program.
A recently established program with many opportunities for
undergraduate research in Actuarial Science.
Check out the
Illinois BioMath Program.
This interdisciplinary program offers semester and summer research
opportunities, seminars, and courses in the field.
Check out our Math Contest program.
If you are interested in math contests, be sure to check out our
Program. It is among the most comprehensive programs of
this sort, it has been considerably expanded in recent years, and
it is enjoying unprecedented popularity.
Check out other exciting new opportunities in math.
In particular, you might be interested in
the challenging courses offered in the
Math Honors Sequence, and our extensive program of
Math Scholarships, Awards, and Prizes.
Last modified: Mon 09 Aug 2021 12:47:54 PM CDT