VIGRE Research Experiences for Undergraduates:
Student Comments

"In my research experience in the Summers of 2006 and 2007, I feel I was given an excellent opportunity with the VIGRE REU Program.  In 2006 I had the privilege of working with Seshadri Thiruvenkadam and Tony Chan on Occlusion tracking with Logic Models, which was later published.  It was exciting to be a part of such prestigious research as an undergraduate, I know I will parlay this experience to my future graduate study.

In Summer 2007 I was honored to be selected as an assistant mentor where I worked as team lead on the videotracking project.  Again, working with Seshadri Thiruvenkadam I feel I was given a great opportunity in research and leadership.  I thank Professor Andrea Bertozzi and the VIGRE grant for providing such a valuable experience to myself and other undergraduates."

"As a mathematics major, I was very excited about the chance to participate in undergraduate research.  As I was a transfer student, I was to participate in VIGRE during the Summer before my first quarter at UCLA, and I did not know what to expect.  At first I was a bit intimidated since I didn't have any Upper Division mathematics courses at all under my belt.  However, Professor Miech was able to ease me into the project at just the right pace.  Best of all, I was always treated with respect and my ideas were always considered.  It was this positive attitude, as well as the privilege of getting to know a Professor well, that I will always remember.  We can't always prove the next huge theorem, but we can sure spend an invigorating Summer trying!

Thanks Professor Miech, and thanks VIGRE for actually paying students to learn!"

"Summer research is a great way for undergraduates to gain experience and to have fun. In particular, I had a great summer working on implementing mathematical algorithms for swarming motion of robots at CalTech.

Thanks to VIGRE and especially Prof. Bertozzi for providing this opportunity. I have gained knowledge in numerical computing, equations for physics based motion, experience in programming, and hand-on engineering. I also learned how to write a research paper and to work in a team with graduate students and postdocs from Prof. Bertozzi's research group. Additionally, we had the generous hospitality of Prof. Richard Murray, the director of the Multi-vehicle Wireless Testbed, and the helpful guidance of the grad students at Caltech. All in all it was an awesome experience."

"During the summer of 2004, I had the privilege of working with Prof. Bertozzi on a research project involving the cooperative control of autonomous robots. I implemented a cooperative decentralized search algorithm for locating a list of spatial targets on the Caltech Multi-Vehicle Wireless Testbed.

It was a very rewarding experience to implement an algorithm from Prof. Bertozzi's group and make it work on a physical platform. Special thanks to Prof. Bertozzi for her guidance. She met with us regularly and provided us with all the support we needed."

"The summer program is a really exciting experience in research and meeting students from other universities"

"Can Mathematics really play a profound role in our everyday society? To some, this may seem quite unrealistic, but through the Summer 2002 REU Program, I found that math is indeed a key factor in understanding critical issues that consequently affects us all. My partner, Janelle Rodriguez, and I decided to study the Population Dynamics of Parasitemia in Malaria through the basis of mathematical models. Since malaria is a deadly disease amongst many foreign countries, we were able to understand the causes and effects of it through the models as related to population dynamics. What captivated me most about this research project is the fact that we were able to show the progression of these models from the 1980s to present day and thusly provide other models for further study. Thanks to my advisor, Ronald Miech, Janelle, and the Summer REU Program, my passion for learning mathematics has reached its ultimate high, and now I am a Math Teacher!"

"My research experience over the summer was unlike anything I was expecting. As an REU, I was expecting to assist a professor in an area that he/she had already designated. Professor Miech on the other hand offered something far more valuable and personal compared to the usual research most undergrads are exposed to.

When I first signed on with Professor Miech he explained that his interest was in Mathematical Physiology (M.P.). He never focused on a specific topic. Instead, he exposed us to various applications of Mathematics in M.P. through a series of lectures we were actively involved in. At the end of the series, we had been familiarized with enough areas of study to be able to conduct individual research projects. As the primary researchers, we were given the opportunity to explore our own knowledge, interest, and imagination. Under the guidance of Professor Miech, everyone part of the research team walked away with both a learning and fulfilling experience."

Comments by Isaac Goldbring (Third Year Mathematics Major)
"On the Success of the Competitive Exclusion Principle"
Advisor: Prof. James Ralston; Summer 2002

"For my Summer Research Project, I studied the Competitive Exclusion Principle and, more specifically, on the proof of its truth for the case of n species competing for 1 abiotic resource. The competitive exclusion principle, in its crudest form, states that when n species compete for fewer than n resources, some species will become extinct. The growth and decline of the species are described by ordinary differential equations and the entire system as a whole is then modeled by a system of ordinary differential equations.

Professor Ralston was my mentor and he guided me through the process of, first: learning the necessary terminology and theory necessary to analyze systems of differential equations and equilibria behavior; two: pointing out pertinent papers on the topic; and three: a weak spot in one of those papers in which my improvement upon could be my thesis for my paper.

After completing the project, I felt a great sense of satisfaction. This project confirmed my desire to pursue a higher degree in mathematics and to do research in this field. Another benefit of this project was my exposure to a new field that I had no previous interest. Currently, my main interests were in logic and set theory. However, I now have a curious new side hobby in the theory of Differential Equations and this project allowed me to view a topic I would otherwise not have pursued any further. Overall, this research experience was extremely worthwhile and beneficial to my undergraduate mathematics education here at UCLA."

Comments by Michael Montgomery
"A Moving Beta Analysis of the S & P 500"
Advisor: Prof. Bryan Ellickson, Professor of Economics; Summer 2002

"My summer research project focused on the topic of financial economics. While taking a year-long sequence in financial mathematics through the Economics department, I learned what a integral part mathematics plays in modern finance theory. This research project gave me the chance to take a deeper look at this area of Applied Mathematics. I am grateful to Professor Ellickson for giving me the opportunity to conduct this independent research and help in the designing of analytic tools for future sections of the financial economics course. I would definitely recommend students take on at least one major research project during their undergraduate career whether they are considering graduate school or not. A project like this opens the door to future research opportunities and helps students get beyond the daunting thought of a long-term research project. Working closely with a faculty member is an incredible opportunity as well. Learning from the experiences of one of your professors is something that you cannot find in the classroom."

Comments by Sarah Hipschman
"Elliptic Curves and the Mordell-Weill Theorem"
Advisor: Prof. Don Blasius; Summer 2002

"This summer I participated in two summer research projects here at UCLA. One of them, completed with Dr. Blasius, was an official paid REU. The other, with Dr. Miech, was on a volunteer basis.

The project that I did with Dr. Blasius was on elliptic curves over finite fields. I found this topic challenging. It was also very interesting because it showed me how so much of the theory and techniques I have been learning in abstract algebra can be put to use to solve some really difficult problems.

The other project that I worked on with Dr. Miech was on differential equations. This started out as a large group, split into pairs, looking at different aspects of how differential equations could be applied to life sciences. I found this really fascinating. For a few weeks, the whole group met twice a week and one set of partners would present what they were studying. It was a great way to see some of the applications of math to biology, ecology, and physiology. Later in the project, the pairs worked independent of the group on specific subjects towards the goal of the final paper. I enjoyed this part also, although I was paired with someone who had a bit less prior training in the subject."

"Firstly, I would like to thank Prof. Miech, and the VIGRE Program for giving me the opportunity to work directly under a professor here at UCLA. The project in which I (and my partner) worked on was Bifurcation Through Ordinary Differential Equations. During these 8 weeks I learned a lot about ODE, and more importantly I learned a lot about myself, in learning how to teach myself ODE.

Our research project was separated into two sections, 1) bifurcation, and 2) ODE. My partner handled bifurcation, while I took on ODE. In specific, I studied Lotka-Volterra’s Models. Within these Models, I looked into all cases the models contain and its geometric interpretation. I also started to delve into nonlinear equations.

In the ladder of the two things that I learned, I discovered a wealth of information on myself! Before I started this research I thought pulling any mathematics book from a shelf and reading it cover to cover would be an easy task. NOT TRUE. I was also disillusioned that not all the answers (to my questions) are in one book. I also learned that it is very difficult to find a topic on what to write about. Lastly, I learned that there cannot be any ego when it comes to learning a new subject, especially with a partner who is more experienced then you are.

In closing, I would again like to thank everyone who helped me in this research and I also would like to thank myself! (Thanks Johnny Boy!)"

"As an undergraduate electrical engineering major, I do not have much opportunity to gain hands-on experience in research. The REU program which I participated in during summer 2002 provided me with an insight into what it is like to write a scientific research paper. Under the guidance of Professor Miech, I was able to do research on a topic relevant to mathematics; this is something I have never done. Not only did the research make me realize that there is more to college than classwork, but it also allowed me to develop independence through my self-study on the research topic. I hope the undergraduate student body will become more aware of this great program in the near future."

"My senior year in college, I decided I wanted to apply to Ph.D. programs in math, despite the fact that I was getting a degree in the entirely unrelated field of romance languages. I signed up for the REU program because, of course, it would be a wonderful opportunity to gain new experience, but also as a test to see if I was making the right decision. I studied elliptic curves over finite fields with Professor Blasius, which was my first time really working with mathematics. I had to work just to get to the point where I understood what the phrase "elliptic curves over finite fields" even meant. Over the course of the summer I discovered, to my surprise, that not only was I able to do mathematical research, but I actually enjoyed it. Although this was merely a glimpse of what life would be like as a graduate student, I feel more confident in my decision to pursue a graduate degree in mathematics than I did at the beginning of the summer. "

"For the summer REU program, I interned in the human genetics department, under the guidance of Dr. Rita Cantor. Her work involves the mapping of simple and complex disease genes using statistical analysis, and, as an intern, I was responsible for handling most of the data and calculations. However, the real benefit of the program was that I gained first hand experience in the research environment. Dr. Cantor was very patient in making sure I understood what I was doing, and the overall methodology of the process. By the end, I felt I had a firm grip on the fundamentals of heredity, as well as the logic behind the statistical approach to the subject of genetics. I would highly recommend that undergrads who are thinking about attending grad school participate in a program which introduces them to the research environment, such as REU. "

Comments by Julia Nudel, "A Polytope,"
Advisor: Prof. Christoph Thiele, Summer 2001:

" In my summer research, I had partaken a part of active research with Prof. Thiele. I was working on a part of his current paper. It was interesting in a sense that we had to justify our findings and come up with our own definitions of polytopes and proofs of thereof. This was the first time I witnessed the originality of research where I actually had to solve an original problem that no one has worked on before, but which was very useful in the context of the paper. I also learned a lot from observing Prof. Thiele at work. We didn't know whether we'll find the solution to the problem, and it was more rewarding when we did. We had to use a lot of originality, which one does not witness in an ordinary undergraduate curriculum.

The experience showed me how uncertain and exciting research in mathematics can be. It furthered my desire to pursue my studies in mathematics. "

Comments by Cheng Ly, "Analysis of a qubit system,"
Advisor: Prof. Russel Caflisch, Summer 2001:

"I participated in a REU program at UCLA, during the summer of 2001, under the guidance of Professor Russel Caflisch. This experience was extremely valuable for me. I have always liked math as a subject, but this opened up my eyes to how directly applicable mathematics is. It was very exciting to actually help publish a paper, "Analytic Model for Electron Confinement of a Layered Material" cam report # 01-30. This project entailed modeling of a qubit, used possibly for quantum computing. I was a little uncertain about graduate studies in mathematics, but after that summer, I knew this is what I wanted to do. My relationship with Professor Caflisch grew, it became more than just the usual student-teacher relationship. I talked to him about many issues concerning graduate school, what classes to take, and where to apply. I feel indebted to him for his extreme generosity."

Comments by Edward Fan
"On the Discussion of Curvatures of Polygons and Polyhedrons"
Participants: Xiaopeng Hu, Kim Ha and Edward Fan; Advisor: Prof. Peter Petersen; Summer 2000

"We did the REU program in the Summer of 2000. Our research was about some geometric properties of polygons and polyhedrons. Now as a Graduate Student in Mathematics, looking back, I feel the REU program gave me a very valuable experience. The summer of 2000 is one of the most meaningful summers I spent at UCLA.

REU makes students experience what doing research is really like. In classes, the material we learn has pretty much been around for at least fifty years or even a century. They are all well formulated and complete. The class homework assignments were all correct and clear. (At least, most of them were!) However, in our research, everything was different. The material in our research is totally new and no one has done it before. As a result, we didn't have a clear problem to solve. We had to formulate the problem along the way. We actually found out that our original conjecture was incorrect through the research. As the research came to end, typing the final paper was also new and challenging experience. We had to thank Xiaopeng for his excellent typing. To communicate your idea well to an audience is not an easy task. Professor Petersen made a lot remarks about how to use proper articles in a sentence. I never thought proper English would place such an important role in mathematics. Believe it or not, it does! A student will never get this kind of experience in classes. REU makes students think seriously about whether they want to choose a research-oriented career. I really enjoy this kind of work. The REU strengthened my determination to be a mathematician who can do research for his or her whole life.

REU also provides a good opportunity for students to interact with professors. In classes, it was very hard for professors to know students personally and vice versa, especially, in a large public school such as UCLA. At the beginning of the summer, Prof. Petersen gave a two or three-hour lectures three times a week. The listeners were just three of us. This provided us an excellent opportunity to know Prof. Petersen better and vice versa. Frankly, I had no knowledge of geometry and I was not interested in learning it before I did the REU. It happened that it was the only proper topic for us to do that summer. But after doing the REU, and getting to know Professor Petersen better, he asked me to learn more geometry. The more geometry I learned, the more I became interested in it. Now geometry is very likely to be my research field in graduate school.

There is no such thing as a "free lunch", but REU is free in the prospective of students. We learned new things, we had new experiences and we got to know Professor Petersen much better. On the top of all these benefits, we got well paid too! Can anyone do better than this?"

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