Discrete Mathematics

Course Code: Ν2-2030
Weekly Duty: 5 (3Th + 2E)
ECTS: 7
Typical Semester: 2nd
Course Category: General Infrastructure Course
Prerequisites:  

Learning Outcomes

As part of the course the student will learn and become familiar with the basic concepts of discrete mathematics. In particular, the course will teach students how to work with discrete structures, which are the abstract mathematical structures used to represent discrete objects and relationships between these objects. Also, the student will learn and understand mathematical reasoning in order to read, comprehend, and construct mathematical arguments.

The main objective of this course is the development of mathematical maturity of the student so that they can meet the course requirements in the disciplines where Discrete Mathematics find applications. Examples include Design and Analysis of Algorithms, Complexity Theory, Data Structures, Databases, Programming Languages, Parallel Computing, Distributed Systems, Artificial Intelligence, and Graphics.

Course Content
  • Propositional Logic. Predicates and Quantifiers.
  • Sets, Relations and Functions Σύνολα.
  • Equivalence Relations and Partitions, Countable and Uncountable Sets.
  • Diagonalization Principle, Mathematical Induction.
  • Discrete Numeric Functions. Recurrence Relations.
  • Introduction to Combinatorics. The Principle of Inclusion-Exclusion. Εισαγωγή στην Συνδυαστική. Αρχή του Εγκλεισμού-Αποκλεισμού.
  • Introduction to Graph Theory. Trees. Euler Paths/Circuits. Hamilton Paths.

Literature
  1. Susanna S. Epp, «Διακριτά Μαθηματικά και Εφαρμογές» Εκδόσεις Κλειδάριθμος, 2004.
  2. C. L. Liu, “Στοιχεία Διακριτών Μαθηματικών», Πανεπιστημιακές Εκδόσεις Κρήτης, 2003.
  3. Γρ. Πάντζιου, “Στοιχεία Λογικής και Θεωρίας Συνόλων”, Διδακτικές Σημειώσεις, Τ.Ε.Ι. Αθήνας, 1998.
  4. Kenneth H. Rosen. Discrete Mathematics and its Applications (sixth edition). McGraw Hill, 2008.
  5. Γ. Βουτσαδάκης, Λ. Κυρούσης, Χ. Μπούρας, Π. Σπυράκης. «Διακριτά Μαθηματικά: προβλήματα και λύσεις». Εκδόσεις Gutenberg, 2000.
  6. Ralph P. Grimaldi, “Discrete and Combinatorial Mathematics”. Addison-Wesley, 1989.
  7. K.A. Ross, C.R.B Wright, “Discrete Mathematics”. Prentice Hall, 1995.

Internationalisation I18n