18.06 Linear Algebra or 18.700 Linear Algebra.


Description

The course will present a thorough introduction to the fundamental algorithmic techniques of Discrete Mathematics - Linear and Convex Programming, Flow & Matching Theory, Randomization, and Approximation. We will tackle a variety of optimization problems by applying these techniques to find efficient algorithms.

Topics include

• How fast can a maximum matching be found in a graph?
• Why is the maximum flow equal to the minimum cut?
• What is duality and how to make use of it?
• Is optimization reducible to random sampling?
• Is there a strongly polynomial-time algorithm for linear programming?
• How to find a short traveling salesman tour?
• How to find disjoint flow paths?

Format

In addition to 3 hours of lectures each week, students will have regular assignments, and two in-class exams. There will also be a course project which can be either theoretical (e.g. write a report, solve an open problem) or practical (e.g. evaluate an algorithm).


Project

For the course project you will:

1. Work on a problem and/or experimentally evaluate an algorithm;
2. Write a short report and present your findings to class.

Students can work individually or in pairs.
Projects should be set up by the day after session #5.


Grading