Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Positional Games (17.D0M33)

Native organizations units: No data

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Godina: 2, Winter)

General information:

Category	Scientific-professional
Scientific or art field	Teorijska i primenjena matematika
Interdisciplinary	Yes
ECTS	10

Educational goal:

The educational objective of the course is to introduce the basic concepts of combinatorial game theory with special accent on positional game theory. The suggested topics may be of interest from both theoretical and practical aspect. Combinatorial games have many real world applications, such as network algorithms, artificial intelligence, scheduling, etc. On the other hand, many results from classical mathematics and theoretical computer science lean on combinatorial game theory.

Educational outcome:

Understanding the concept of a combinatorial game, having deeper insight in positional game theory, knowing the set of tools available, and knowing how to apply them.

Course content:

1. Introduction Types of combinatorial games. Strategy. Game tree. Total min-max search. Strategy stealing. Probabilistic approach. 2. Some combinatorial games Operations on the space of games. Equivalence of games. Nim-like games. Hackenbush. Potentials. Solitaire Army 3. Positional games Definition. Tic-tac-toe, generalization to n dimensions. Hales-Jewitt Theorem. Pairing strategy. Strong and weak games. Maker-Breaker games. Biased positional games. 4. Games on graphs¸Clique game. Hamiltonian cycle game. Perfect matching game. Ramsey games. Probabilistic methods. Part of the course is organized in the form of independent study and research work in the field of mathematics. The study and research work involves active study of primary scientific sources, organization and conduction of experiments and statistical data analysis, numerical simulations, and possibly writing a paper in the filed of mathematics.

Teaching methods:

Lectures. Consultations. The lectures are organized in combined form. The presentation of the theoretical part during the lecture classes is followed by the characteristic examples which contribute to better understanding of the subject matter. In addition to lectures there are regular consultations. Through research and study work the student will, on the bases of scientific journals and other relevant literature that has been studied independently, develop further understanding of the material covered in lectures. Working with the course teacher the student develops the ability to independently work on a scientific paper.

Literature:

Authors	Title	Year	Publisher	Language
J. Beck<\eng>	Tic-tac-toe theory<\eng>	2006	Cambridge University Press	English
E.R. Berlekamp, J.H. Conway, R.K. Guy<\eng>	Winning Ways<\eng>	1982	Academic Press, London<\eng>	English