Topics in Combinatorics
More advanced concepts, methods and results of combinatorics and graph theory. Main topics: (linear) algebraic, probabilistic methods in discrete mathematics; relation of graphs and hypergraphs; special constructions of graphs and hypergraphs; extremal set families; Ramsey type problems in different structures; Regularity Lemma.
By the end of the course, students are enabled to do independent study and research in fields touching on the topics of the course. In addition, they develop some special expertise in the topics covered, which they can use efficiently in other mathematical fields, and in applications, as well. They also learn how the topic of the course is interconnected to various other fields in mathematics, and in science, in general.
Regular homework, and presentation or final
s: linear algebra