## Course Web Page

Contact Info for Instructor, office hours, assignments and general information is all on the course
web page.
## Course Description

This course will cover topics in Geometric and Probabilistic methods in Computer Science, with an eye towards interesting, modern applications of these tools.
### Text:

We will use several sources in this class, including the following:
### What you should know

You should have a basic familiarity with algorithms and data structures as from a class such as CS362, CS561 or equivalent. You should also have a certain mathematical maturity and familiarity with proof techniques similar to what would be covered in a advanced
undergraduate mathematics class. Students completing CS362, CS561, CS530 or CS500 should be well-prepared for the class. If you haven't taken any of these classes and are still interested, please come talk to me.
### Topics

Topics we cover will likely include some subset of the following:
- Classic Problems in Computational Geometry: Convex Hull, Voronoi diagrams, Duality
- Multiplicative Weights Update (MWU) Method
- Linear Programming and Applications (solving LP via MWU)
- Applications of MWU to Machine Learning (Adaboost)
- Vector Spaces and Applications, particularly to coding theory
- Convex Optimization and Gradient Descent
- Higher Dimensional Spaces and Dimension Reduction (Johnson-Lindenstraus and SVD projections)
- Randomization in closest point queries, with connections to PAC learning and VC dimensions
- Randomized distributed algorithms: Maximal Independent Set,
Byzantine consensus, Leader Election
- Geometric Methods for Error-correcting codes
- Geometric Methods for Robotics and motion planning

This class will be fairly student-driven so there is the possibility of covering other topics. Grading will be based on
participation and a class project, with some (likely ungraded)
homeworks to practice concepts in the class.
### Course Assessment

Approximate weighting: - Homeworks 40% (3)
- Class Project, 40%
- General Participation, 20%.