Instructor: Robert L. Bryant
Visit my home page for contact information. The information from Duke's On-Line Course Synopsis is reproduced below. For more detailed information, visit the home page for the course.
A proper course title could be "Symmetry, Geometry, and Optimization". We will look at some classical problems involving soap bubbles and films, curves of shortest descent (Brachistochrone problems), shortest paths on curved surfaces, and the motion and shape of elastic rods and strings. All of these will be used as motivation for introducing the ideas of the calculus of variations and studying how they interact with geometric notions, such as symmetry, both in problems and solutions. If time permits, we may study some higher dimensional problems, such as Poincare's famous analysis of the three-body problem in celestial mechanics.
There will not be a textbook. Instead, I will hand out lecture notes.
Weekly homework assignments will be made and each student will be expected to present a number of these homework assignments in class.
There will be no inclass examinations (or final exam).
Each student will be required to write one term paper of approximately 15-20 pages that explains a problem of the type we will be developing and discussing in the course, together with its solution. The problem is to be selected in consultation with the the instructor.
A student's grade in the course will be based on the in-class presentations of homework assignments and the term paper, including a presentation of the term paper at the end of the semester.