Learning Outcomes
1. Learning of various combinatorial enumeration methods for discrete structures.
2. Acquintance with mathematical proof techniques.
3. Knowledge of various topics from propositional logic such as formal proofs.
4. Knowledge of various topics from first order logics such as consistency and completeness.
5. Thorough understanding of basic graph theory concepts and definitions.
6. Acquintance with constructive and algorithmic proof techniques in graph theory.
7. Knowledge of various topics in trees and distances in graphs.
8. Knowledge of planarity, Hamilton and Euler graphs, higher connectivity and coloring in graphs.
9. Knowledge of various topics in matroid theory such as axiom systems, matroid classes, minors and duality.
Course Content (Syllabus)
Rules of addition and multiplication, generating functions, Polya theory, formal propositional language, tautologies, propositional logic, first order language, first order logic, consistency and completeness, basic concepts and definitions in graph theory, matrices of graphs, paths and cycles, connectivity, classes of graphs, graph sequences, constructive and algorithmic proofs, directed graphs, trees, binary trees, characterizations of trees, rooted trees, distances in graphs, spanning trees, enumerations of trees, Hamilton and Euler graphs, graph coloring, abstract independence, axiomatic systems of matroids, graphic matroids, representable matroids, decomposition theorems and recognition algorithms.