This is an internal seminar of the Formela laboratory which aims at building a solid background in specific areas relevant to our current research. The material is presented both by senior Formela members and the participating students (undergraduate students are welcome). The emphasis is put on deep understanding of the presented material, which is verified by frequent questions and enforced by merciless feedback. The concrete topics may differ in each term, but usually we follow some book or a collection of papers.

- Topic 1:
*Continuous-time Markov chains* - Source: J.R. Norris: Markov Chains. Cambridge Series in Statistical and Probabilistic Mathematics, 1997.
- Time and Place: TBA, C417.

- Topic 2:
*Deep learning* - Source: TBA
- Time and Place: TBA, C417.

- Topic 3:
*Algorithmic Model Theory: automata, logic, and graphs* - Source: TBA
- Time and Place: TBA, C417.

- Topic 4:
*FO logic and model checking on graphs* - Source: relevant research papers
- Time and Place: Thursday 8-10, C417.

- Topic 1:
*Continuous-time Markov chains* - Source: J.R. Norris: Markov Chains. Cambridge Series in Statistical and Probabilistic Mathematics, 1997.
- Time and Place: Tuesday 12:00-13:40, C417.

- Topic 2:
*Deep learning* - Source: I. Goodfellow, Y. Bengio, A. Courville: Deep Learning. MIT Press, 2016. http://www.deeplearningbook.org/
- Time and Place: Wednesday 8:10-9:50, C417.

- Topic 3:
*Combinatorial geometry and geometric graphs* - Source: TBA
- Time and Place: Friday 12:00-13:50, C417.

- Topic 4:
*Mixing in Markov Chains* - Source: Speed of mixing in DTMC, eigenvectors and eigenvalues.
- Time and Place: Tuesday 9:30-11:20, C417.

- Topic 1:
*Measure theory* - Source: Jeffrey S. Rosenthal: First Look at Rigorous Probability Theory. World Scientific Publishing Company, 2006.
- Time and Place: Monday 10:00-11:40, C417.

- Topic 2:
*Graph Crossing Numbers - a structural view* - Research-oriented working seminar, starting from the basics of topological and structural graph theory, and studying in depth the rich structure of crossing-critical graphs (with many open fundamental questions).
- Time and Place: C417, currently Tuesday 12-14, C417.

- Topic 3:
*Algorithmic Model Theory: automata, logic, and graphs* - Source: TBA
- Time and Place: C417, time based on mutual agreement

- Topic 4:
*Fundamentals of Artificial Intelligence: Markov Decision Processes with Perfect and Partial Information* - Source: TBA
- Time and Place: TBA

- Topic 1:
*Measure theory* - Source: Jeffrey S. Rosenthal: First Look at Rigorous Probability Theory. World Scientific Publishing Company, 2006.
- Time and Place: Monday 10:00-11:40, C417.

- Topic 2:
*Graph Minors, Sparsity, and Beyond* - Source: TBA
- Time and Place: TBA

- Topic 3:
*Fundamentals of Artificial Intelligence: Markov Decision Processes with Perfect and Partial Information* - Source: TBA
- Time and Place: TBA

- Topic 1:
*Measure theory* - Source: Jeffrey S. Rosenthal: First Look at Rigorous Probability Theory. World Scientific Publishing Company, 2006.
- Time and Place: Wednesday 14:00-15:40, C417.

- Topic 2:
*Graph Minors, Sparsity, and Beyond* - Source: Jaroslav Nešetřil, Patrice Ossona de Mendez: Sparsity. Springer, 2012. http://link.springer.com/book/10.1007%2F978-3-642-27875-4.
- Time and Place: Friday 10:00-11:40, C417.

- Topic 3:
*Infinite state games* - Source: collection of papers
- Time and Place: Monday 10:00-11:40, C417.

- Topic 1:
*Probabilistic Graphical Models: Principles and Techniques* - Source: D. Koller and N. Friedman. The MIT Press, 2009.
- Time and Place: Monday, 13:00-14:40, C417.

- Topic 2:
*Queues and Queueing Networks* - Source: G. Giambene. Queueing Theory and Telecomunications: Networks and Applications. Springer, 2005. and L. Lipsky. Queueing Theory: A Linear Algebraic Approach. Springer, 2009.
- Time and Place: Monday, 15:00-16:40, C417.

- Topic 3:
*Patrolling Games* - working seminar based on a number of articles and current research results
- Time and Place: Wednesday, 8:00-9:40, C417.

The following courses supervised by Formela members are open to all undergraduate students, but they focus on rather specific topics. The number of enrolled students is usually small and the tuition is interactive. The students are expected to develop solutions to the presented problems and give short talks. The emphasis is on attractiveness and beauty of the presented material.

The aim of this seminar is to introduce interested students into the beauties of mathematics and of clean mathematical proofs. It is based on the famous textbook “Proofs from THE BOOK” (Aigner-Ziegler). This will teach students mathematical thinking - to understand math definitions, statements, and proofs in their full depth, and to make their own new proofs in all areas of mathematics and theoretical computer science. Particular topics cover: Number theory; Combinatorics; Combinatorial geometry; Graph theory.

Detailed course information: official IV119, informal

The course concentrates on selected topics in applied probability theory and game theory motivated by concrete practical problems. For each problem, a minimal amount of mathematical theory sufficient for solving the problem is presented. Then, the students are asked to solve the initial problem by using appropriate software tools. A special attention is devoted to the following areas:

- Markov decision processes and stochastic games.
- Modelling and analysis of basic board games, the existence and computation of equilibrium values and optimal strategies.
- The existence, properties, and computation of stationary distributions in Markov chains. PageRank and similar applications.
- Multiplayer games. Nash equlibria. Internet auctions.

Detailed course information: IV075 Seminar on Stochastic Methods in Computer Science

Some other relevant/recommended courses are listed below.