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IAS/Park City Mathematics Institute

Ordinary and Extraordinary Differential Equations

JOHN C. POLKING, Rice University
PAUL BLANCHARD, Boston University
DANIEL L. GOROFF, Harvard University

Co-sponsored by Chautauqua Programs

For college teachers of: mathematics, physics, or related fields who have strong interest in undergraduate mathematics education and wish to increase both their content knowledge and teaching skills.

Prerequisites: five years of undergraduate mathematical teaching experience.  This program is generally not for graduate students or new PhD's.

Undergraduate faculty concerned with recharging college teaching come to PCMI from various types of institutions across the country to pursue the following activities:

  • Learning mathematics together: Participants will choose parts of the PCMI Graduate Summer School, Research Program, or Undergraduate Program to attend (see the sections on the Research Program and Graduate Summer School for a listing of topics, or consult the PCMI Research Programs brochure for more details).
  • Curriculum development: The content focus will be on the mathematics of grades 13 and 14. For 2001, this strand will concentrate on teaching and learning about Differential Equations. Courses, activities, and projects will examine current trends in college courses on this subject, including special attention to technology, modeling, visualization, numerical methods, and waves. The goal is to model the process of collectively producing useful lesson plans by holding a regular series of workshops where practice classes can be presented, critiqued, and improved. The products of this work should be of interest both to the general mathematical community and to national groups currently re-examining the undergraduate mathematics curriculum. In the spirit of PCMI, participation in these workshops by members of other programs, including students, AP teachers, and research professors, is especially encouraged.
  • Public perception of mathematics: Mathematicians must be ambassadors for mathematics. By thinking carefully about how to bring the case for mathematics before the general public, and by acting on these thoughts, members of the mathematical community can enhance the claim of mathematics for general support. In order to draw attention to the pressing need for more public support of mathematics, the Undergraduate Faculty Program, in conjunction with other interested groups at the Summer Session, will review existing examples of promotional materials and work on creating new ones. Having a cross section of the mathematical community present at PCMI provides a unique opportunity for members of the Undergraduate Faculty Program to put into a broader context their efforts to affect the public perception and support of mathematics.
  • Involvement with other PCMI programs: There will be ample opportunity for interaction both with other groups at PCMI who use Differential Equations to study Field Theory, the mathematical research theme this summer, and also with the high school teacher and educational research groups who are concerned with more pedagogical issues.  Undergraduate Faculty may spend a few hours each week, preferably in subgroups of two or three, as resource advisors to the various Working Groups of the High School Teacher Program (see the section on the High School Teacher Program for a listing of these working groups).

Each weekday, the Institute will run activities that include: parallel classes at the high school teacher, undergraduate, and graduate student levels; research seminars for specialists; colloquia accessible to all; discussion groups about policy issues of interest to mathematicians; joint luncheons; demonstrations in the computer laboratory; etc.

College faculty with a strong interest in undergraduate education are encouraged to apply to PCMI's Undergraduate Faculty Program. Those interested in Differential Equations, especially as they appear in mathematical physics generally and in field theory in particular, will be able to learn more about this topic. Preference will be given to faculty with plans for developing and sharing ideas related to Differential Equations that can enhance undergraduate education back at their home institutions and beyond.

John Polking is Professor of Mathematics at Rice University. Paul Blanchard is Professor of Mathematics at Boston University. Daniel Goroff is Professor of the Practice of Mathematics at Harvard University and Associate Director of the Derek Bok Center for Teaching and Learning. Professors Polking and Goroff are members of the PCMI Steering Committee.

Application Guidelines and Application Forms

PCMI Summer Session Page

PCMI Home Page

questions or concerns should be directed to C. Giesbrecht