Math 523  Advanced ProbabilitySpring 2009Instructors: Yuval Peres and Eyal Lubetzky Email: eyal [at] math [dot] washington [dot] edu Office: Padelford C529 Office hours: by appointment
Meeting Times and Locations
Mon,Fri 11:0012:20 at LOW 106.
Course description
The applications of probability to many areas in Mathematics and in other fields have multiplied dramatically in recent years. Rich interactions with classical analysis have been found in the study of random fractals; researchers in Combinatorics, Theoretical CS, machine learning, highdimensional geometry (and, of course, Statistics) increasingly need sophisticated probabilistic tools. The aim of this course is to provide such tools, while also preparing the students for more advanced courses in Probability.
Topics
The main focus will be on martingales and their applications in Discrete Mathematics and Computer Science. These include: concentration inequalities, optional stopping, maximal inequalities, L^{2} martingales, and much more.
Grading
Homework (35%), Takehome exam (35%) [done individually, but with open books], Presentations (30%).
Students can opt to be graded solely on the HW and takehome exam, 50% each. Group discussions on the material and HW are encouraged, yet writing up the HW must be done individually.
Assignments
Lectures
Topics for presentations


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Last modified: 6/5/2009 