Ramesh designed a PDE visualization tool for use in the AMATH 403 course, which he is teaching Spring 2006. The tool is based on Matlab GUIs and is called PIVOT. The website for this tool is http://www.amath.washington.edu/~ramesh/PIVOT/. He will be describing this project at the International Conference on Teaching Undergraduate Mathematics in Istanbul, Turkey in July 2006.
Beth as designed a sustainable template for helping a local elementary school with math enrichment at the end of the school day. Beth organizes 3 undergraduates and 3 graduate students to prepare interested elementary school students at TOPS Elementary for the Math Olympiad.
Chris developed an honors course in computational finance for undergraduates. To supplement the course, he has under development an R/S-PLUS library that can be used with the text, Ruppert, Statistics and Finance: An Introduction.
This VIGRE committee has created a sustainable template for a weekly seminar for undergraduates. They are advised by Werner Steutzle, the present ACMS Undergraduate Program Director. The graduate fellows are each responsible for a portion of seminar organization each week. The attendance was been terrific and this seminar is a place for announcing and co-organizing other events. For example, the Undergraduate Projects committee has organized within this forum on April 27th where undergraduates will discuss their research.
Sponsor: Mix Ice Cream on University Avenue
This VIGRE committee has created a sustainable template for a weekly problem of the week. Please see the web site http://www.ms.washington.edu/challenge
The Statistics for this site shows the problems being solved mainly by undergrads with substantial graduate student and faculty participation across departments.
The Examples seminar is a forum for undergraduates and graduate students to share mathematical folklore, discuss advanced ideas and enhance mathematical intuition in a free-form environment which is supportive of students at many different levels of mathematical sophistication. The format of the seminar supports this goal by offering a "show and tell" approach to presentations, in which participants spontaneously present material that they have been thinking about, or present material which resolves questions that have previously been raised in the seminar. The main feature of the seminar is the concept of using examples from topics in higher mathematics to convey the broad sweep of mathematical ideas without getting overwhelmed by detail, as well as developing mathematical intuition in the technical sense of being able to discern subtle differences in definitions and hypotheses. During the current year, some of the areas that we touched on using this approach included: tools to visualize higher dimensional spaces, ideas at the foundation of algebraic geometry, some recent ideas in the combinatorics of the symmetric group, and an introduction to Lie groups.
See the Examples seminar web site at http://www.math.washington.edu/~bahuaud/examples
As my VIGRE project, I am organizing an introduction to the UW's Combinatorics and Geometry Seminar. At 2:30pm on the days of seminars, we give a group of about 10 undergraduates (and other interested parties) an introduction to the research topic of the day. The speaker presents the subject and the audience is encouraged to participate to understand.
The speakers have presented at various times background material, key ideas, and examples that help this audience better understand the talk at 4pm. This pre-seminar is geared to an undergraduate audience, although others may attend as well. Each seminar brings its participants new ideas, new questions, and new answers to problems in combinatorics.
We have been developing workshops to encourage students in the 124/5/6 to consider math as a major. We promote them through the TA's for the classes. As an example of such a workshop, we invited people to learn how to make various geometric origami models.
A note of warning: We have found it difficult to encourage many people to come to our workshops. If somebody wants to do a project like ours, they need to figure out an effective way to advertise.
I am running two projects: A `Topics in Analysis' seminar aimed at primarily at advanced undergraduates (though several graduate students have taken an interest as well), and an undergraduate research project in stochastic differential equations.
The seminar meets once a week for an hour. My aim is to give a broad overview of some of the directions that analysis goes after the undergraduate and beginnning graduate level. When finished, we will have covered a diverse collection of topics, including real analysis, functional analysis, harmonic analysis, harmonic measure, and geometric measure theory, and the theory of partial differential equations. Mostly I present the topics, but participants are encouraged to find topics that interest them and create their own short presentations for the group.
The undergraduate research project is in its beginning stages. My student, Marcus Hodges, and I are reading the lecture notes `An Introduction to Stochastic Differential Equations' by Dr. Lawrence C. Evans at the University of California at Berkeley. (The notes are wonderful and are available from Dr. Evans' web page.) Dr. Krzysztof Burdzy of our own department has agreed to help us find an appropriate project for Marcus to complete after we finish learning about stochastic differential equations together.
My project involved creating an undergraduate research project with Steffen Rohde. We recruited two teams of students who are working to understand SLE(k) well enough to write computer programs that will display accurate sample pictures of these random curves. In addition, I am working part-time with GK-12.
I worked on a website with my advisor designed to help beginning graduate students in algebraic geometry find references using a system of volunteer mentors.
When graduate students first start looking at a topic, they often run into questions that they feel "ought to have been studied before" but perhaps is too simple to be the main result of an article. It may thus be hard to find any sort of reference. This site is designed to facilitate students finding the answer to such questions by having a collection of mentors in specializing in various aspects of algebraic geometry. Questions would be forwarded to appropriate experts and the students would be asked to track down the references provided and type up an answer which would be archived on the site.
***(Hopefully it will be up within a month or two. When we get it up I will happily provide a URL).***
I also organized and ran the Algebraic Geometry seminar. This year we covered topics of vanishing theorems, motivic integration and tight closure.
The purpose of my VIGRE project is to create a website: specifically, an online archive of UW mathematicians' experiences, with special emphasis on those of women. It will contain anecdotes, personal stories, and advice about all the various phases of a career in mathematics, from undergraduate through post-doctorate and beyond. In particular, the website will be organized around the transition points in a math career: getting into and choosing a graduate school, passing prelims, choosing a research area and an advisor, finding a post-doc, and so on. All mathematicians in the department (of all levels, and of both genders), as well as those in statistics and applied math, will be invited to share their stories about these periods and others in their careers, both positive and negative.
To this end, I and six others, ranging from undergraduate to post-doc, have formed the Mathos Project, and we're currently working on building the website. The backend team is setting up a MySQL database and designing the website, while the content team is going about interviewing various mathematicians in the department. We plan to get the website up and running by the end of Spring quarter.
UW VIGRE <vigre@math.washington.edu>