Beginning with Winter Quarter 2005, a new program in Mathematical Modeling will be offered at the Paris Center of the University of Chicago. This program is designed to meet the needs of undergraduates in mathematics and the physical sciences who desire a comprehensive and intensive introduction to methods for dealing with continuous systems of the type commonly arising in analysis of the physical world, while at the same time experiencing the benefits of immersion in a foreign culture. The program may also be suitable for some concentrators in biological or social sciences. It is anticipated that the Paris Math quarter would fit most naturally into the academic schedules of Third Years, but applications from qualified Second and Fourth Years will also be considered.
This course deliberately defies categorization as either "pure," "applied" or "computational." mathematics. Students will be given a comprehensive treatment of the formal theory of ordinary differential equations, as well as a wide variety of methods for obtaining exact and approximate solutions to hard problems. In addition, the program will cover numerical methods, object-oriented programming for scientific simulation, and topics in chaos and nonlinear phenomena. The minimal prerequisites are Math 15100-15200 or 16100-16200, plus Math 20000 or Math 22000. No prior computer programming experience is assumed. This program will offer 9 hours per week of lecture, plus lab and recitation sections. The course will be taught by a team of University of Chicago physical sciences faculty, with the assistance of a lecturer from one of the many excellent institutions of higher learning in Paris.
Lectures will be in English, To further enrich their time abroad, participants in the program will also be enrolled in a course in the French language at the appropriate level for their abilities. The academic program will be supplemented by a program of cultural events, dégustations de vin, gastronomical experiences, field trips and laboratory visits.
The reasons for coming to Paris to study mathematics are more subtle, and perhaps less obvious, than the reasons for coming to Paris to study French, architecture, literature, political science or art history. On reflection they are, however, no less compelling. Almost anybody can benefit from the experience in living immersed in a foreign culture, from learning French in a place where it is actually spoken on the streets and in the shops, and from the cultural opportunities of Paris. In one sense, the Paris Math program simply makes it possible for physical science majors to enjoy this opportunity while at the same time advancing in their chosen specialty -- and doing so as part of an intensive applied and computational mathematics program of a sort that is not currently available on the Hyde Park campus. Science, as it is conducted today, is a very international enterprise, and most students pursuing careers in research will benefit from having some experience at coping with a culture and language that is not their own. Participants in the program will also benefit from comeraderie with a select group of like-minded students, and it is hoped that they will learn nearly as much through discussions with fellow students as from the formal course material. The program will offer students the opportunity to get to know their professors (and vice-versa) in an environment free from some of the normal distractions of academic life. (Students familiar with the Ross Program will know what we mean when we say that we'd like to do the same for Applied and Computational math that the Ross Program does for Number Theory). Beyond that, it should be recognized that France has a great tradition in mathematics and physical sciences every bit on a par with its tradition in philosophy, sculpture, literature or painting. One need only recall the names of Fourier,Laplace, Poincaré, Galois, Carnot and innumerable others, many of whose names in fact live on in the names of Paris streets as well as in textbooks. This tradition continues in the extraordinary concentration of laboratories and institutions of higher learning in Paris. Public lectures on technical and general topics in mathematics and science are offered regularly at the College de France. Students in the Paris Math program will have the opportunity to learn about some of the cutting edge research happening in Paris, and perhaps will form ties that someday will lead to longer visits, research collaborations, graduate study, or postdoctoral study.
A complete syllabus may be found here.
Part 1a Lecture Notes (Updated to include Green's function notes (though not proofread!))
Olga's ODE review
Problem Sets: Week 1 Week2 Week 3