Office: Travelstead Room B21, phone: 277-5446 The best way to reach me is
generally via email. I usually check email once a day around noon.
Office Hours: TBA or by appointment.
Note: I will always be available in my office during office hours. At other times, if my door is open, feel free to come
in. If the door is closed, I'm probably at work on a paper, grant or research problem. Please come by another time or make an appointment via email.
Class Info
The class meets 11-12:15 T/TH in MECH Room 400.
Course Description
This course will cover mathematical topics in Geometric and Probabilistic methods in Computer Science, with an eye towards modern applications (e.g. machine learning, big data, distributed computing).
The methodology will be rigorous i.e. theorems and proofs.
Text Book
See Syllabus for details
Class E-mail List
I have set up a google group to manage email for this class.
Directions for joining this group are here. This
link also contains an archive of emails.
Office Hours
Tuesdays and Thursdays 3:30-4:45pm or by appointment. I'll also try to be available after class when necessary.
U. Maryland Notes, Pages 41-44 give a good connection between convex hulls,
and upper/lower envelopes, Lecture 8 gives good connection between envelopes and linear programming. Lecture 16 gives good connections between convex hulls
and Voronoi diagrams, and Delanauy triangulations
You can embed an arbitrary metric into Euclidean space with O(log n) distortion (via Bourgain's theorem, see also here). Then, you can use Johnson-Lidenstrauss to project onto R^d where d = O(log n).
MIT Algorithm's Projects This is a general description of how to find a good
CS theory project. The specific project ideas in this class are, of course, different from our own class - if you'd like specific ideas, please talk to me.
Convex Optimization by Boyd and Vandenberghe Particularly of interest: Section 2.3 "Operations that Preserve Convexity" ;
Chapter 4 and onward discuss optimization algorithms (albeit informally, without proofs of convergence time; NB that many problems discussed (i.e. quadratic programming)are NP-Hard).
See Vishnoi's notes above for a more formal treatment.