The course covers basic and advanced techniques in Discrete Mathematics that are necessary for the study and analysis of computer models and systems. Proof methods with an emphasis on induction and existence proofs (Pigeonhold principle, Diagonalization). Applications to Fibonacci Sequences and Number Theory. Elements of Ramsey Theory. Countanble and uncountable sets. Graph theory: trees, connectivity, planarity, bipartite matching. Equivalence and partial order relations. Theorems of Sperner and Dilworth. Tools from Probability Theory.
Basic textbook in Greek: Μ. Κολουντζάκης, Χ. Παπαχριστόδουλος. Διακριτά Μαθηματικά, ΣΕΑΒ/Κάλλιπος, 2015. Also the greek translation of C. L. Liu “Discrete Mathematics”.
Additionally the students have access to
1) Lecture notes by Emiris and Koutsoupias
2) transparencies by S. Kolliopoulos
3) recommended literature in English (Lazlo Lovasz, Jozsef Pelikan, Katalin Vesztergombi. Discrete Mathematics: elementary and beyond. Springer, 2003. Eric Lehman, Tom Leighton, Albert Meyer. Mathematics for Computer Science, MIT, 2015. Jiri Matousek, Jaroslav Nesetril. Invitation to Discrete Mathematics, 2nd edition. Oxford University Press, 2008.)