THE UNIVERSITY OF CHICAGO 2009 Summer VIGRE Program for Undergraduates

This announcement describes an eight-week summer program of research and teaching for undergraduates at the University of Chicago. Its first year of operation was 2000, and details of its past operation may be found at

http://www.math.uchicago.edu/ may/VIGRE/index.html.

In this program, students have the opportunity for study and research in mathematics together with work in two of the outreach programs of the Department of Mathematics. Students participate in at least one of four courses taught by Department of Mathematics faculty members. They also work as counselors in either the Young Scholars Program (YSP) or the SESAME teacher development program.

The purpose of the summer VIGRE program is to provide an opportunity for students to be involved in a deeper experience in mathematics than is usually available during the academic quarters and to allow them to be effective partners in the educational outreach programs of the Mathematics Department. This program is especially beneficial for undergraduates who are considering graduate study and research in mathematics and for those who are interested in teaching mathematics at any level.

DATES: June 22–August 14, 2009; June 22–July 17 for the Apprentice Program. Participants in the full program are required to be in residence for all eight weeks. Apprentices are required to be in residence for the first four weeks and are welcome to participate in the program for the full eight weeks.

STIPENDS: Each student will receive a stipend of $3000, payable in two equal installments at the end of July and the end of August. Please note: taxes will be deducted from these paychecks. It is not permitted to hold a part-time job while participating in the REU without explicit permission from the program director. Participants in the four week apprentice program will receive a stipend of $1500.

ACCOMMODATIONS: Students are expected to find their own accommodations. Graduate students and past participants will offer advice and assistance.

APPLICATIONS: Students must be currently registered students at the University of Chicago and, to be eligible for financial support, must be United States citizens or permanent residents. Foreign University of Chicago students are welcome to participate in the program, but cannot receive financial support. Application forms for the summer of 2009 will be available in Eckhart 211 and 212 by Friday, February 21, and are due Friday, March 13, 2009. Late applications will not be considered. Completed applications should be returned to Ryerson 350; if nobody is in this office, applications should be slipped under the door. Applicants will be notified of acceptance or possible wait list status by e-mail no later than March 23.

THE PROGRAM OF STUDY AND RESEARCH: Students attend courses taught by Department of Mathematics faculty. The courses consist of lectures and problem solving sessions; graduate student assistants run help and problem sessions. Some research problems and some problems aimed simply to aid understanding are introduced by the professors. No previous knowledge or study in the areas taught is required. In addition, opportunities for reading and research with graduate students and/or faculty are offered, and regular meetings with graduate student mentors are required.

The apprentice program is similar, but includes material aimed at those with less mathematical experience. It lasts four weeks. Its participants are typically freshmen and sophomores who have not been in advanced mathematics courses, and they often participate in the full program the following summer.

Participants in the full program serve as counsellors in either the YSP program for high schools students, which takes place during the third through sixth weeks, or the SESAME program, which takes place the seventh and eighth weeks.

The first two weeks have a larger proportion of lectures than the later weeks, setting up background in some areas, giving self-contained presentations in others, and offering many problems. There will be student presentations on days (and/or evenings) near the end of the program, with the dates to be determined later. It is hoped that many will make presentations. These can be made by individuals or by groups working together. All participants, whether or not making presentations, are required to write a short mathematical paper on some problem or topic of their own choosing.

Graduate student counsellors will be on hand ready and willing to offer help throughout the program. Moreover, each student will be paired with a graduate student mentor, who will meet with the student on a regular basis and will be available to offer tutorials. Topics for papers should be discussed with the mentors.

The program offers a wide variety of material at various mathematical levels. Some is problem oriented, some introduces areas that are not ordinarily encountered in the undergraduate curriculum. There will be lots of problems, including research problems, that students can work on in groups or alone throughout the program — and later!! Students are encouraged to work together and to organize evening and weekend sessions. Students are expected to spend substantial amounts of time working on projects or problems outside of classes.

The program for 2009 has not yet been firmly established. As always, we plan to offer a variety of courses at various levels, arranged into several “sequences”. The program will be frontloaded in intensity in order to minimize scheduling problems with respect to YSP and SESAME and to maximize opportunities to get started on research problems and papers. In addition, there will be a special course for apprentices in the second, third, and fourth weeks. Abstracts of all course offerings will be made available no later than March 9. At this writing (January 10), faculty participants have not yet been finalized, but they are expected to include Laszlo Babai, Gregory Lawler, Benson Farb, Miklos Abert, and Peter May; Abert will teach the apprentice program. To give some idea, the following gives the full list of 2008 faculty speakers and the topics they presented.

1. LASZLO BABAI. DISCRETE MATHEMATICS. Eight weeks.

2. Miklos Abert. PROBLEM SOLVING COURSE. Weeks 2–5.

3. GREGORY LAWLER. PROBABILITY AND THE HEAT EQUATION. Weeks five and six.

4. BENSON FARB. TOPOLOGICAL METHODS IN GROUP THEORY. Weeks 1–4.

5. PETER MAY. FINITE TOPOLOGICAL SPACES AND RELATED TOPICS. Weeks 1–8.

6. BEN McREYNOLDS and BEN SCHMIDT. TOPICS IN GEOMETRY. Weeks 6–7.

5. MIKLOS ABERT and LACI BABAI. APPRENTICE PROGRAM: LINEAR ALGEBRA AND THE SPECTRAL THEORY OF GRAPHS. Weeks 2–5. Abstracts of courses from the 2002 – 2008 REU’s can be found at

http://www.math.uchicago.edu/ may/VIGRE.

THE COUNSELOR PROGRAM: Each VIGRE student in the full program serves as a counselor in either YSP or SESAME.

YSP is a four-week program for mathematically talented seventh through twelfth graders. There are three components: one for students in grades 7-8, one for students in grades 9-10, and one for students in grades 11-12. The YSP consists of lectures in number theory, problem solving sessions led by VIGRE counselors, and computer sessions. Counselors are assigned to a particular component and to a small group of students for problem solving and computer sessions.

SESAME is a two-week program for elementary school teachers from the Chicago Public Schools. VIGRE Counselors work in one of several courses in the SESAME program (number theory, geometry, history of mathematics, physics for teachers, etc, and serve in much the same capacity as they do in YSP.

Applicants will be asked to state a preference for which outreach program, YSP or SESAME, they would prefer to be assigned to, but there is no guarantee that students will get their first choice. Typically, experienced counsellors from previous VIGRE REU’s and experienced Junior Tutors are assigned to YSP. Computer experience is a plus.

WEEKLY YSP and SESAME WORK SCHEDULE: Week 1 (June 22 – 26) Free Week 2 (June 29 – July 2) Preparation and training: 9 – 12 M-F Week 3 (July 6 – 10) YSP duties: 9:30 a.m. - 2:30 p.m. Week 4 (July 13 – 17) YSP duties: 9:30 a.m. - 2:30 p.m. Week 5 (July 20 – 24) YSP duties: 9:30 a.m. - 2:30 p.m. Week 6 (July 27 – 31) YSP duties: 9:30 a.m. - 2:30 p.m. Week 7 (August 3 – 7) SESAME duties: 9:00 - 4:00. Week 8 (August 10 – 14) SESAME duties: 9:00 - 4:00.