The PCMI 2008 Program

Undergraduate Faculty Program (UFP)

Co-sponsored by Chautauqua Programs
Application Deadline is
January 20 2008

For the faculty members whose main focus is teaching undergraduate students, PCMI offers the opportunity to renew excitement about mathematics, talk with peers about new teaching approaches, address some challenging research questions, and interact with the broader mathematical community. Each year the theme of the UFP bridges the research and education themes of the Summer Session.

Algebraic geometry is one of the richest areas in all of mathematics and also has the somewhat legitimate reputation for being one of the most difficult. Still, undergraduates can learn and do research in algebraic geometry. For faculty, knowing even a little algebraic geometry can lead to insights in teaching from calculus to the highest level courses. This workshop will have four goals:

  1. Participants will be able to teach an undergraduate course in algebraic geometry.
  2. Participants will work on research type problems in algebraic geometry.
  3. Participants will see how to use algebraic geometric ideas in other courses and fields.
  4. Participants will survey current work in algebraic and analytic geometry, allowing participants to interact with the other parts of the Institute.
In essence, algebraic geometry studies the zero loci of polynomials. Thus it links algebra and geometry. Without much effort, topology and analysis arise naturally. In fact, algebraic geometry likely lurks in the background of most areas of mathematics.

Used in class, algebraic geometry can highlight connections between traditionally segregated areas of undergraduate mathematics. This workshop will give participants the needed tools to make these connections.

Tom Garrity was an undergraduate at the UT Austin, a graduate student at Brown and a post-doc at Rice.  He joined the faculty of Williams College in 1989, where he has been ever since, save for sabbaticals spent at the University of Washington in Seattle and the University of Michigan in Ann Arbor.  

At Williams, Garrity is the William R. Kenan Jr. Professor of Mathematics, department chair and the director of the Williams College Project for Effective Teaching (Project PET).  His research has been in algebraic geometry, differential geometry and, more recently, number theory.  He is the author of All the Mathematics You Missed [But Need to Know for Graduate School]  and  appears, against Colin Adams, in the MAA dvd "The Great π/e Debate: Which is the better number?", moderated by Edward Burger.  Among his honors is the 2004 Haimo Award for Distinguished Teaching by the Mathematical Association of America. 

 

The Coordinator of PCMI's Undergraduate Faculty Program is William Barker, Bowdoin College.