Summary: An introduction to entropy and its many roles in different branches of mathematics, especially information theory, probability, combinatorics and ergodic theory. The aim is to give a quick overview of many topics, emphasizing a few basic combinatorial problems that they have in common and which are responsible for the ubiquity of entropy.
Provisionally, the course will separate into three parts:
In order to cover a wide range of subjects, I will have to sacrifice a lot of generality, and sometimes omit technical details. To get the most out of the course, students will need to support the lectures with reading from the notes and a variety of other sources.
Lectures: Mondays, Wednesdays and Fridays, 2--2.50, in Math Sciences 5148.
Office Hours: Mondays 10.30--11.30 and Wednesdays 3--4. These times may change in some weeks if I have to travel. I can usually also accommodate requests for appointments at other times.
Communication: Email is preferred. I will try to answer emails within 24 hours, excluding weekends. I prefer the pronouns he/him/his.
Grading: Enrolled students will be assigned letter grades, based on class participation and a small number of homeworks. Merely attending most classes will guarantee a B. An A grade also requires work on some homework problems. Details of the latter TBA. Some homework questions will be deliberately quite challenging, and so a good but incomplete attempt at one of these will be enough to contribute to an A grade.
Lecture notes (quite rough, probably still plenty of mistakes --- please beware):
My notes draw on several other references. Here are links to some of the main references (should work within UCLA). (I may add to this list during the fall quarter.)
tim AT math DOT ucla DOT edu