(MATH-GA 3011.001)

** Instructor:** Prof. Richard Kleeman
(Office: 929 Warren Weaver)

There will be 11 lectures. The contents are described briefly below. Relatively complete lecture notes as pdf files are linked to below.

__Lecture 1__

Introduction. Overview of Applications. Basic axiomatic
derivation following Shannon. Introduction to the information content
of codes. Lecture Notes.

__Lecture 2__

Entropic functionals and their properties. Lecture Notes.

__Lecture 3__

Stochastic Processes. Lecture Notes.

__Lecture 4__

Data Compression. Lecture Notes.

__Lecture 5__

Differential Entropy. The limiting process and coarse graining. Invariance properties. Lecture Notes.

__Lecture 6__

Maximum entropy and statistical mechanics. Lecture Notes.

__Lecture 7__

Gaussian special case. Lecture Notes.

__Lecture 8__

Dynamical system statistical prediction. Introduction
and commonly used practical methodologies. Lecture Notes.

__Lecture 9__

Theoretical predictability concepts. Lyapunov exponents
and their relation to information theory and predictability. An
information theory framework for studying predictability. Lecture Notes.

__Lecture 10__

Application of information theoretical techniques to a variety of simple but physically relevant dynamical systems. Lecture Notes.

__Lecture 11__

Information transfer. Empirical and formal approaches. Application to weather prediction. Lecture Notes.