|Category||Obligatory by selection|
|Class Hours - Lab Hours||4 - 0|
|Lecturers||Dimitris Fotakis, Theodora Souliou (T & R Associates)|
|Links||Helios, Course's Website|
Sets, countable and uncountable sets, diagonalization principle. Elements of propositional logic and first-order logic. Relations and functions, order relations, equivalence relations, transitive closure. Pigeonhole principle. Mathematical induction. Graphs, subgraphs, isomorphism, chromatic number, walks and paths, shortest paths, Euler cycles and trails, Hamilton cycles and paths. Trees, characterization, spanning trees. Planar graphs, Euler’s formula, Kuratowski’s theorem. Graph connectivity, bridges and cut sets, cut points and separators. Counting, permutations, combinations, permutations and combinations with repetition, binomial coefficients. Elements of discrete probability. Generating functions, exponential generating functions, applications to counting. Elements of number theory.