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Διακριτά Μαθηματικά Ι

 Title: Διακριτά Μαθηματικά Ι Lesson Code: 321-1501 Semester: 1 ECTS: 5 Theory Hours: 3 Lab Hours: 2 Faculty: Tzouramanis Theodoros

Content outline

Sets, set operations, principle of inclusion – exclusion. Logic and mathematical reasoning, propositions, propositional calculus, predicate calculus, inference rules. Proof techniques, mathematical induction, diagonalization. Formal languages. Relations and functions, binary relations, properties of binary relations, equivalence relations, partial and total orders. Graph theory. Basic definitions and terminology, Eulerian graphs, Hamiltonian graphs. Trees, spanning trees, rooted trees, binary search trees, breadth-first search, depth-first search. Minimum spanning trees, greedy algorithms, Kruskal’s algorithm, Prim’s algorithm. Shortest paths, Dijkstra’s algorithm. Planar graphs, Euler’s formula, Kuratowski’s theorem. Bipartite graphs. Chromatic number. Matchings, perfect, maximum, and maximal matching, augmenting paths, Berge’s theorem, Hall’s theorem. König’s theorem. Vertex and edge connectivity, Menger’s theorem, max-flow-min-cut theorem.

Learning outcomes

The widening of the field of mathematics for the student by examining a series of concepts and issues, which represent the foundation of Computer Science and are not included in the General Applied Mathematical courses. Aiming at developing and deepening students’ perception of related disciplines, such as the Foundations of Computer Science, the Theory of Algorithms, Data Structures, Formal Languages Theory, Graph Theory, the Theory of Computation, etc.

Prerequisites

Not required.

Basic Textbooks

1. Liu C.L.: Στοιχεία Διακριτών Μαθηματικών Πανεπιστημιακές Εκδόσεις Κρήτης, 2009, ISBN: 978-960-524-072-1 (in Greek).
2. Epp S.S.: 'Διακριτά Μαθηματικά με Εφαρμογές', Εκδόσεις Κλειδάριθμος, 2011, ISBN : 978-960-461-325-0 (in Greek).

1. Rosen K.H.: Διακριτά Μαθηματικά και Εφαρμογές τους, Εκδόσεις Τζιόλα, 5η έκδοση, 2008, ISBN : 978-960-418-144-5 (in Greek).

Learning Activities and Teaching Methods

Personal assignments and pair or group assignments, lab practice, regular short assessments in the form of a quiz test, final examination.

Classroom teaching, group activities, etc.

Language of Instruction
Greek, English (for Erasmus students)

Μode of delivery

Face-to-face.

 Lectures Διάλεξη 1 & 2 : Σύνολα (Κεφ 1, εκτός § 1.8) Διάλεξη 3: Προτάσεις (§ 1.8) Διάλεξη 4: Αποδεικτικές Διαδικασίες Διάλεξη 9 : Διμελείς σχέσεις και ιδιότητες Διάλεξη 10 & 11 : Σχέσεις μερικής διάταξης, ολικής διάταξης και ισοδυναμίας Διάλεξη 11 : Βασική ορολογία : Μονοπάτια και κύκλοι Διάλεξη 12: Κύκλοι Euler & Kύκλοι Hamilton Διάλεξη 13: Εύρεση μήκους μικρότερου μονοπατιού Διάλεξη 14 : Παράσταση γραφημάτων Διάλεξη 15: Δένδρα Διάλεξη 16: Συνδετικά Δένδρα

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