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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

NI-KTH Combinatorial Theories of Games Extent of teaching: 2P+1C
Instructor: Valla T. Completion: Z,ZK
Department: 18101 Credits: 4 Semester: L

Annotation:
Traditional game theory is a branch of mathematics, which has broad applications in economy, biology, politics and computer science. This theory studies the behaviour of agents (players) of a certain competitive process by designinng a mathematical model and investigating the strategies. The traditional task of classical game theory is to find the equilibria, which are the states of the game where no player wants to deviate from his strategy. Historically, the second big development in game theory of two-player full-information combinatorial games, was by Conway, Berlekamp and Guy. They developed a theory, originally used for solving end-games in Go, into a full fledged field. The idea is to evaluate games such that otherwise incompatible games can be added, that is, played simultaneously. This led to the algrebraic approach to study combinatorial games. The third most important step is the work of Beck, who established the theory of positional games (like tic-tac-toe and hex). In analysis of these game, one cannot escape the brute-force traversal of the game tree, which is no efficient. Beck introduced the "false probabilistic method", which aims to tackhle this problem. In this course we build the foundation of the theory of combinatorial and positional games. We focus on theoretical analysis of games and building the theory, not on the programming aspects of game solving algorithms. The course requires independent work, ability to mathematically analyse, think and proof. The course is also suitable for bachelors student in the third year, who attended introduction to graph theory, as well as for PhD students looking for research topics.

Lecture syllabus:
1) introduction to combinatorial games
2) formal definition of combinatorial games, game classes, strategy theorem
3) comparing games, game algebra (addition, negation, isomorphism)
4) no-number games, adding numbers
5) simplicity rule, dominating and reversible moves
6) infisitemal games, thermographs
7) strong and weak positinal games, strategy stealing, general tic-tac-toe
8) Hall theorem, pairing draw, resource counting
9) Erdös-Selfridge theorem, applications
10) ramsey games, other game versions

Seminar syllabus:
Tutorials designed for deeper understanding the theory presented in the course and for analysis of simpler games.

Literature:
Berlekamp, Conway, Guy: Winning Ways
J. Beck: Combinatorial Games, Tic-Tac-Toe Theory
Conway: On Numbers and Games Albert, Nowakowski, Wolfe: Lessons in Play Nisan, Roughgarden, Tardos, Vazirani: Algorithmic Game Theory

Requirements:
* do not fear the mathematics :) * basics in graph theory, combinatorics and algebra

The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
NI-PB.2020 Computer Security V Není
NI-ZI.2020 Knowledge Engineering V Není
NI-SPOL.2020 Unspecified Branch/Specialisation of Study V Není
NI-TI.2020 Computer Science V Není
NI-TI.2023 Computer Science V Není
NI-NPVS.2020 Design and Programming of Embedded Systems V Není
NI-PSS.2020 Computer Systems and Networks V Není
NI-MI.2020 Managerial Informatics V Není
NI-SI.2020 Software Engineering (in Czech) V Není
NI-SP.2020 System Programming V Není
NI-WI.2020 Web Engineering V Není
NI-SP.2023 System Programming V Není


Page updated 28. 3. 2024, semester: Z/2023-4, L/2019-20, L/2022-3, Z/2019-20, Z/2022-3, L/2020-1, L/2023-4, Z/2020-1, Z,L/2021-2, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška