Information Theory II
- Lecturer:Nihat Ay
- Date: Tuesday, 11:00 - 12:30
- Room: MPI MiS A3 02
- Language: English
- Target audience: MSc students, PhD students, Postdocs
- Keywords: Partial Differential Equations, Applications of PDEs in science
- Prerequisites: Basic knowledge in probability and measure theory is required.
- Remarks: This course consists of six lectures, which will take place on April 4, 25, and May 2, 9, 16, 23. In the first lecture on April 4, I will provide a brief summary of the basic results of Information Theory I that will be required for the course.
This is a continuation of my Information Theory I course, which I offered in the winter term 2016/2017. I concluded with elementary results on the Kolmogorov-Sinai entropy of dynamical systems and proved the Shannon-McMillan-Breiman theorem for information sources. This theorem will serve as a prerequisite for the second part of my course, Information Theory II, in which I will concentrate on information channels. I will introduce the transmission rate and the capacity of information channels. The central theorems of this part will be Shannon's celebrated coding theorems. I will develop Feinstein's fundamental lemma, which constitutes, together with the Shannon-McMillan-Breiman theorem, the main tool for the proofs of Shannon's coding theorems.
- A. I. Khintchine. Mathematical Foundations of Information Theory. Dover, New York, 1958.
- Y. Kakihara. Abstract Methods in Information Theory. World Scientific, Singapore, 1999.
- P. Walters. An Introduction to Ergodic Theory. Springer, 1982.
- T. M. Cover, J. A. Thomas. Elements of Information Theory. Wiley, 2006.
Please use the entry doors Kreuzstr. 7a (rooms A3 01, A3 02) and Kreustr. 7c (rooms G3 10, G2 01), both in the inner court yard, and go to the 3rd. floor (see the map). To reach the Leibniz-Saal (E1 05) use the main entry Inselstr. 22 and go to the 1st. floor.
Please note: The doors will be opened 15 minutes before the lecture starts and closed after beginning of the lecture!
Regular Lectures (Summer 2017)
- Basic Notions in (Geometric) Group Theory
- Karim Adiprasito
- Monday, 11:00 - 13:00, University A-314
- Information Theory II
- Nihat Ay
- Tuesday, 11:00 - 12:30, MPI MiS A3 02
- The variational approach to stochastic PDE
- Benjamin Gess
- Wednesday, 11:00 - 12:30, MPI MiS A3 01
- Mathematical methods in the neurosciences
- Jürgen Jost
- Friday, 13:30 - 15:00, MPI MiS A3 01
- Moduli spaces, stability conditions and birational geometry
- Christian Lehn
- Friday, 10:00 - 12:00, MPI MiS G3 10
- Tropical Probability
- Rostislav Matveev
- Thursday, 11.00 - 12:30, MPI MiS A3 02
- Partial Differential Equations
- Felix Otto
- Wednesday, 9:15 - 11:00, MPI MiS A3 01
- Tropical Geometry
- Yue Ren
- Monday, 9:00 - 10:30, MPI MiS A3 02
- Interpolation Spaces
- Jonas Sauer
- Tuesday, 9:00 - 10:30, MPI MiS A3 01
- Navier-Stokes Equations
- László Székelyhidi:
- Thursday, 9:00 - 11:00 and Friday, 9:00 - 11:00, University SG 3-11
- IMPRS-Ringvorlesung: Geometry and Dynamical Systems
- Tanja Eisner, Hans-Bert-Rademacher, Matthias Schwarz
- Tuesday, 13:15 - 14:45, MPI MiS E1 05 (Leibniz-Saal)
- Seminar on Ergodic theory of group actions
- Tanja Eisner, Tobias Finis, Artem Sapozhnikov
- Tuesday, 09:15 - 11:45, University SG 3-11