Undergraduate Research Group: FAQ
A.J. Hildebrand

Table of Contents

  1. About this page

  2. What does it take to get in? Prerequisites and qualifications

  3. What will it be like? How it works in practice

  4. What do I get out of it? Rewards and benefits of undergraduate research

  5. I'm interested. What do I do next?

1. About this page

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 what you can expect to get out of this experience (short answer: a whole lot!), read on!

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 conference opportunities. 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.

2. What does it take to get in? Prerequisites and qualifications

2.1. A role model: The 2012/13 group

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.

2.2. Academic background

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 Projects 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.

2.3. Ability and willingness to work in a team setting

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 experimentally.

2.4. Willingness to commit a significant amount of time

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.

2.5. Special skills

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 work.

3. What will it be like? How it works in practice

3.1. Overview

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!

3.2. Meetings and work schedule

The following is an approximate run-down of what a project might involve in terms of meetings and work.

4. What do I get out of it? Rewards and benefits of undergraduate research

4.1. Gain a unique learning experience, something completely different from anything you encounter in regular courses

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.

4.2. Develop valuable general skills that are useful in many situations, regardless of your career goals

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.

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!)

4.3. Gain opportunities to travel to conferences to present the research

Once you have completed a project and obtained interesting new results, you can present these results to a wider audience at 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 accepted!

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 won several presentation awards in the process.

4.4. Boost your chances of getting into summer research programs and internships

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 grad schools.

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 place!

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 this success.

4.5. Enhance your resume and boost your career

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 conference presentations and 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!

4.6. Get course credit

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!)

5. I'm interested. What do I do next? More information and related opportunities

Last modified: Mon 09 Aug 2021 12:47:54 PM CDT A.J. Hildebrand