University of Georgia, Summer 2002
Summary
The VIGRE Research Experience for Undergraduates in Mathematics at UGA will run for four weeks, June 10 - July 5, 2002. Students will work in teams guided by faculty mentors. Research teams will meet approximately 30 hours a week. The research experience is open to all majors, and it is not restricted to University of Georgia students.
Twelve $1500 stipends will be awarded to United States citizens and permanent residents. Participants may register to receive course credit. A final research report is required of all students. Students are responsible for the cost of tuition, fees, and housing.
This program is funded by a VIGRE grant from the National Science Foundation.
Research topics
Derivatives on different sets
Dr. Jo Hoffacker, johoff@math.uga.edu
We all know that the derivative of x2 is 2x ... or is it? It turns out that the derivative is very dependent on the set of variables x you care about. Our team will explore what happens on other sets, as well as different ways to calculate the derivative. We will also try to decide how best to measure the accuracy of our calculations. This is a relatively new idea, so our team will be searching for answers to problems that no one else has done yet. More detailed research plan
Computer algebra and geometry
Dr. Bill Rulla, rulla@math.uga.edu
Computer software allows the exploration of many interesting examples in algebra and geometry. We'll use the textbook Ideals, Varieties, and Algorithms, by Cox, Little, and O'Shea to develop algebraic tools and to pursue geometric applications.
At its most basic level, algebraic geometry is the study of the common zero locus of a bunch of polynomials in several variables. There is a dual point of view - the study of ideals of polynomial rings. The advent of computer software such as Macaulay allows the investigation of intricate examples which historically may have been prohibitively computational.
Possible topics: singularities of algebraic sets, tangent cones, elimination theory, Hilbert polynomials, rings of invariants under the actions of finite groups. The Cox, Little, O'Shea book is very accessible, and anyone with linear algebra (and preferably some knowledge of abstract algebra, though this is not absolutely necessary) should be comfortable. More detailed research plan.
Program details
Schedule and requirements
The program will run during Short Session I of the UGA summer school. Classes meet Monday, June 10 through Friday, July 5, 2002. Research teams will meet approximately 30 hours a week. Participants may not enroll for other classes or hold other employment during the period of the program. Every student must submit a final report.
Financial support
Twelve stipends of $1500 will be awarded to students who are United States citizens or permanent residents. Every qualified applicant will automatically be considered for this stipend.
Other sources of financial support are available through the UGA SURP and CURO programs.
Housing and meals
Students can arrange to stay in a double occupancy room in a campus residence hall for approximately $12 per night. A Monday through Friday meal plan is also available in the summer for about $12 a day. Program participants are responsible for the cost of their housing and meals. Please contact Jennifer Peterson if you would like assistance in arranging these details.
Course credit
Program participants have the option of receiving 3 semester hours of college credit for the VIGRE Research Experience by registering for MATH 4950, Research in Mathematics. Students who register for course credit are responsible for the cost of tuition and fees (UGA Bulletin).
If you are not already a student at UGA, you must apply for transient admission (UGA Undergraduate Admissions) to receive college credit. Transient students for the summer semester should apply for admission by April 1.
Application
Deadline March 1, 2002
Required documents
Mailing address
VIGRE Summer Program
Department of Mathematics
University of Georgia
Athens GA 30602-7403
Contact information
Dr. Clint McCrory
VIGRE Director
clint@math.uga.edu
(706) 542-2576Dr. Malcolm Adams
adams@math.uga.edu
(706) 542-2546Jennifer Peterson
Educational Program Specialist
jennifer@math.uga.edu
(706) 542-2577
This page was created November 19, 2001. It was last modified May 9, 2002.