Discrete Mathematics

Logic, proofs and basic number theory:<br> Logic: negation, conjunction, disjunction, implication, bi-implication (equivalence), de Morgan's law, quantifiers, divisibility, modular arithmetic, fundamental theorem of arithmetic, proof by induction. Combinatorics and recurrence relations:<br> Basic combinatorics: permutations, combinations, variations. Inclusion/exclusion principle. The aspects of recurrence relations: arithmetic and geometric sequences, linear nonhomogeneous recurrence relations with constant coefficients, simultaneous recurrence relations. Graph theory and Graph algorithms:<br> Definitions and properties of different types of graphs: simple, undirected/directed, tree, planar, eulerian and hamiltonian graph, spanning tree, TSP (Travelling salesman problem) etc. DFS (Depth First Search) and BFS (Breadth First Search), Dijkstra’s, Prim’s and Kruskal’s algorithms. Modeling: Project where the student implements and tests simple graph algorithms in a programming language of their choice, e.g. Python.