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Introduction to dynamical systems II


Tuesday, 25 February 2020 to Thursday, 30 April 2020
Total hours: 20
Hours of lectures: 10
Hours of supplementary teaching: 10

Examination procedure

  • oral exam


Information theory, codes, data compression and prediction.

Probability, entropy, inference. Maximum likelyhood method.

St. Petersburg paradox. Utility function. Kelly criterion. Horse races. Universal portfolios.

Pseudorandom number generators. Monte Carlo method.

Graphs. Random walks on graphs. Perron-Frobenius Theorem. Google's sage rank algorithm.

Iterated function systems (IFS)


Educational goals:

To introduce the fundamental notions of information theory and of dynamical systems theory and applications

Bibliographical references

Cover-Thomas: Elements of Information Theory

Mackay: Information theory, Inference and Learning Algorithms

Sternberg: Dynamical Systems

Falconer: Fractal Geometry: Mathematical Foundations and Applications

Shannon, Claude E. (July 1948). "A Mathematical Theory of Communication".

Bell System Technical Journal. 27 (3): 379–423.

Shannon, C. E. (1951), Prediction and Entropy of Printed English. Bell
System Technical Journal, 30: 50-64.

Kelly, J. L. (1956). "A New Interpretation of Information Rate" Bell
System Technical Journal. 35 (4): 917–926

MacLean, Thorp, Ziemba (2011) "The Kelly Capital Growth Investment
Criterion: Theory and Practice" World Scientific