Testimonials from VIGRE Participants
Many mathematicians report that they chose their career as a result of some invigorating mathematical experience, often a course taken from an especially stimulating teacher. One of the goals of our VIGRE program is to get students excited early about mathematics as a career option. Through our VIGRE seminar courses, we hope to give students opportunities to discover mathematics for themselves and to gain an understanding of and appreciation for the rewards of research.
Such intangible goals are not subject to quantitive analysis. Although we do track objective data, as indicated in our assessment page, we think that subjective comments from participants are important too in evaluating the success of our VIGRE program. The following are some reflections by VIGRE participants on how VIGRE has made a difference to them personally.
Comments from undergraduate students
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As a freshman, I enjoyed working with advanced students and
hearing their ideas. Possibly most beneficial to me was the
experience of formally writing on a math topic. This helped
me see the value of rigorous exploration and evaluation. ...
This VIGRE course has stimulated in me some interest for
applied mathematics and the subsequent career opportunities.
In line with that, I plan to pursue an APMS [applied
mathematics] major with the hopes of working in industry or
research.
-
I really enjoyed my VIGRE experience .... this has been a
glimpse as to what I might do with my math degree. Although
I am used to small classes, I've never [before] really had
one-on-one talks with a professor.
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This course has given me a good chance to see how the
professor/student relationship works when doing research.
The problem I worked on was pretty interesting, and I
learned a few new methods for approaches to problem solving.
It was also a good experience because of the presentation
and paper we did. ... This fall I am starting on my
Master's in Computational Math .... After that I am
planning on going into industry to do computer-intensive
math or problem solving.
-
This experience helped me understand what research is like.
[A VIGRE postdoc] is helping me understand how to write up my
results, and also taught me things about the research
process along the way. ... My future plans are ... to be a
professor of mathematics at the university level.
Near-term, I am ... working this summer with
Johns-Hopkins CTY program, teaching a course of my
own.
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As an undergraduate, I [worked] hand in hand with a
graduate student. It was exciting as we solved and invented
mathematics never before done. This relationship I made
through this course has stretched outside of the course,
and he has helped me mature in mathematics and as a
person. ... We plan to publish our results in a refereed
journal, and we are currently in the process of writing our
paper. ... My decision to attend graduate school has been
solidified by this experience.
-
This past year has been great since I got my first taste of
mathematical research [in a VIGRE seminar]. This year I have
researched and studied the topics of wavelets, wavelet
sets, frame theory, and sampling theory. ... Just recently
I completed a project for my oceanography class [in which]
I used my theoretical knowledge of wavelet analysis and
applied it to solve problems dealing with data compression
and signal processing of sea surface temperature data. So
this VIGRE seminar has really opened my eyes to a whole new
world. I feel that I am one step closer to being ready for
graduate study.
Comments from graduate students
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This has been the most engaging course I have
ever been in. I have engaged in original
research on the construction and classification
of all wavelet sets which are finite unions of
intervals, leading to three talks, one at the
AMS conference in San Francisco in Fall 2000, a
[Graduate
Student Organization] talk here at Texas
A&M, and a talk at the approximation theory
seminar. ... [An undergraduate VIGRE
participant] and I are an example of a
graduate-undergraduate team. We have asked
original research questions and have answered
some of them. We have used all of the languages
Maple, Matlab, and C to perform integer
programming and other computations. ... I feel
that this course ... and my relationship with
[a senior faculty member] was pivotal in my
acceptance to the University of California at
Berkeley in Mathematics.
-
I gave a talk on [my VIGRE seminar work] in the
[Graduate
Student Organization]
series.
... I also collaborated with [another graduate student] to write a
Java applet that can automatically give the interpolation
map between two arbitrary bounded finitely-many-intervals
wavelet sets. ... I took a leave of one week to
the IMA
for a workshop in Geometric Design.
- Until I took these VIGRE courses and tried a
couple of the problems, I didn't have a good feel for
what research in mathematics really was. Thus these
courses helped me decide that I would like to continue
graduate work in mathematics, and I will enter the PhD
program in math at the University of Washington next
fall.
- My experience as a VIGRE student modeling
arterial wall elasticity was enjoyable. I did try to
coordinate with the other students in our group (about
5 of us) and organize the work load. I helped upgrade
the Matlab tools that we developed, and showed the
students how to solve non-linear-least squares
optimization. So, it helped me in that regard. ... I
presented a poster at a SIAM Math in Industry Workshop
back in October. ... I have an opportunity to work at
Lawrence Livermore National Lab for the summer.
- I was able to be more of a mentor to the more
junior graduate students. Out of the students in the
class, I probably knew the most about the material
coming in. As an undergraduate, I participated in an
REU [Research Experiences for Undergraduates]
program in which we studied this
program. Therefore, I was able to lend some expertise
to the other students in the class. I presented many
times and several times helped others understand the
material. ... Next semester, I will be a faculty member
in a small department.
Comments from postdoctoral fellows
For the postdoctoral researchers at the beginning of their career, VIGRE has helped foster their excitement about teaching as well as enhance their interactions with senior faculty. It has also helped advance their careers by providing flexibility and support -- for instance for travel. Here are some of their remarks.
- Each of the students [in the VIGRE seminar I
ran] showed noticeable improvement over the course of
the semester, and the feedback I received from the
students was quite encouraging. This was my first
professional experience in the role of advisor and I
found it rewarding. I enjoyed the opportunity to give
students one-on-one instruction and closely monitor
their progress. I hope to do some further work with one
of the participants to prepare a paper for a college
mathematics journal describing our results. ... The
summer VIGRE support is allowing me to maintain my
research program and to travel to visit a colleague.
-
The VIGRE travel money has been very
valuable. For most of the conferences and seminars
where I was invited to give a talk, I was given support
from the institution that invited me. The VIGRE
travel money allowed me to travel to almost every
conference in the US that related to [my field],
even if I was not invited. It also paid for my plane
ticket to [Europe] for 3 weeks where I have an ongoing
collaboration with [an eminent senior researcher].
... I am also part of a
group NSF grant.
- I participated in VIGRE seminars on
Mathematical Models in Biomedical Engineering. In
these seminars I gave many of the lectures on
background material in continuum mechanics and
nonlinear elasticity. Preparing these lectures helped
me greatly to consolidate my knowledge in these areas.
... My participation ... led to research in
collaboration with [senior faculty in mathematics and
in engineering]
on some of the
mathematical issues that arise when modeling soft
tissues as nonlinear elastic materials. [One of these
collaborators] and
I have had one paper accepted for publication ... I
will attend the SIAM Annual Meeting in July to present
a talk on this research. Also ...
co-organizing a minisymposium on Biomechanics and
Nonlinear Elasticity.
-
There was much excitement during the
... seminar. ... First and foremost we had many
students involved with original research; most of the
students worked in small groups. ... This work has
resulted in a manuscript and several student
presentations at meetings and seminars.
Comments from senior faculty
Some of the faculty involved with VIGRE remarked on its contribution to enhancing interdisciplinary aspects of their own research programs.
-
Two VIGRE classes were devoted to modeling soft tissue
with the help of colleagues in Bioengineering. ... The
students investigated the existence archival literature
and then studied new models. They had access to
experimental data from the lab of [a Bioengineering
professor]. ... Though dealing with very messy data, we
were able to do a better job of modeling it than
previous researchers did. The group modeling the lamina
cribrosa had no data with with to work since such data
is much more difficult to collect. However, they did
develop a model showing the correct qualitative
properties. The goal of the eye model was to test a
conjecture of [another Bioengineering professor] as to why
the elevated pressure difference inside the eye causes
damage for patients suffering from glaucoma. Her
conjecture requires knowing how much the lamina
cribrosa bulges out. That's where nonlinear elasticity
enters the picture. Previous researchers used linear
elasticity to do the estimates, whereas it's pretty
clear that the lamina cribrosa is a very complicated
structure exhibiting highly nonlinear
behavior. [A postdoc] ... and I discovered
some interesting mathematical questions about the
nonlinear elastic models some people had previously
proposed for soft tissue that had not been adequately
addressed in the literature. We've now gotten one paper
accepted and are finishing a second paper on the
subject. This work came directly out of the VIGRE
courses.
The students showed great initiative and interest in the problems. They put in many hours outside of class working on the models and writing and testing computer codes to do simulations of their models. I've never had students in a regular class put in such dedicated effort. They were motivated by the (clinical) importance of the applications.
-
[A summer VIGRE seminar] was devoted to studying a
new method for ultrasound modulated laser tomography
developed by a colleague in Bioengineering. The
students, which included an REU student along with
graduate students from Math and Bioeng, studied models
for ultrasound wave propagation in soft tissue, laser
light diffusion through soft tissue, and how the two
interact with the former being able to "focus" the
latter. The problems proved to be too difficult to make
much progress in just five weeks. However, one of the
students has ended up doing her
Ph.D. dissertation ... on the tomography
problem coming from this VIGRE class.
-
What was rewarding: The topic intertwined very
different mathematical subjects, which both gave the
students an appreciation for breadth and allowed the
course to play to different students' strength. For
instance, the class rediscovered a certain
combinatorial equality on cell complexes through the
work of computer-science-oriented students using a
computational viewpoint to get lower bounds and
topologically-motivated students getting upper bounds,
which eventually converged. Each group came away with a
new appreciation for the other set of tools.
What could have been improved: at the time we hadn't really offered appropriate courses to build up an audience for the course. Now that the department's regularly offering combinatorics courses that are popular and successful, I expect future VIGREs in the area to be able to focus more time on research rather than background.