Syllabus for Math-8600: Topics in
Applied Mathematics
From Statistical Mechanics to
Information and Pattern Theory
Spring, 2004, 1:25 -2:15pm, MWF, at Vincent Hall 6.
Fall, 2003, 1:30-2:20pm,
MWF, at Vincent Hall 20, by Jackie Shen.
Partially Supported by
Applied Math.
Program, Division of Math. Sciences of NSF.
- Mission
Statement: a one-page friendly statement explaining my
vision, motivation, and philosophy of opening this new course.
- Technical Scope:
- Learn
essential ingredients of Statistical Mechanics, especially those
significant in modern applied mathematics:, including entropy and free energies;
Gibbs ensembles and Gibbs
variational formulation of Statistical Mechanics; Monte-Carlo simulation;
simulated annealing,
mean-field theory and renormalization
group; phase transitions.
- Learn essential
ingredients of modern Information
Theory (as started by Shannon) and Pattern Theory (as formalized
and developed by Ulf Grenander)
- Explore the deeper and
intrinsic connections between Statistical
Mechanics and Information
and Pattery Theory, especially in terms of Mathematical Image
and Vision Analysis (Miva). Prepare graduate students for a well
trained entrance into Miva and this information era.
- Requirement: most
undergraduate core courses, plus, perhaps more crucially, your redhot Passion in
learning this exciting topic.
- Course Load:
- Attending as many lectures as you can.
- A final project with 5-10 pages of (professional)
written-up, and a 8-10 minutes of
friendly presentation to your fellow classmates.
- No exams or official homework. But mind-training problems
will be issued from time to time.
- Lecture Style:
- Lecturing on core textbooks of both Statistical Mechanics and Information and Pattery Theory.
- Reading and discussing research papers that are pertinent
to the mission and goal of this course.
- Reference Materials:
- Introduction to Modern
Statistical Mechanics, by David Chandler
(UC Berkeley), Oxford Univ Press, 1987.
- Statistical Physics, by Leo
Kadanoff (University of Chicago), World Scientific, 1999.
- Elements of Information Theory,
by Thomas Cover and Joy
Thomas (Stanford University), John Wiley & Sons, Inc., 1991.
- Elements of Pattern Theory,
by Ulf Grenander
(Brown University), Johns Hopkins Univ. Press, 1996.
- Research papers by Shannon (1948), Geman and Geman (brothers) (1984), Zhu and
Mumford (1997), Coifman and Wickerhauser (1992), Mumford (ICM 2002), etc.
- Plus numerous my own thoughts and approaches.
- How many holidays for
escaping in this academic year: The Academic
Calendar of 2003-2004.
First
created on September 4, 2003; Last modified on January 19, 2004.