Faculty of Science

Objectives

To provide students with basics notions and concepts of counting and linear programming.

Contents

Game theory: Nim sums and kayles for games, simple matrix games; Convexity and concavity of subsets of Rn and localisation of extrema, n×2 matrix games and optimal play strategies; Linear programming: Farka’s Lemma, the minimax theorem, Danzig’s Algorithm, Dual problems, the simplex method; Graph theory and Combinatorics: Physical properties of graphs, trees and their enumeration, maximal flow on graphs, partitions, enumeration of necklaces.