# Discrete Mathematics

#### Module ID

Υ201

#### Semester

2

#### Hours/Week - ECTS

5 – 5

### Learning Outcomes

The course is the basic introduction to the concepts of distinct mathematical objects and the relationships between them. The course material aims to introduce students to the basic concepts of mathematical structures that are fundamentally distinct. Objects studied in discrete mathematics – such as integers, graphs, propositions of logic, recursive relations – are the basis for the study and description of objects and problems in computer science and in particular in algorithms, programming languages, cryptography, automated proof of theorems, and software development.

After the successful completion of the course students:

- will have understood the basic concepts of discrete mathematics,
- will be familiar with the methods and techniques of Logic, Proof, Numbering, Relationships, and Graphs, and will be able to apply them to solve algorithmic problems,
- will have learned to develop mathematical reasoning,
- will have learned to draw mathematical conclusions.

### Indicative Module Content

- Introduction to set theory, set operations, finite and infinite sets.
- Introduction to logic and proofs, mathematical induction, propositional calculus.
- Relationships and functions, properties of binary relations, equivalence relations, order and partial order.
- Typical languages, grammars, finite state machines, language recognition.
- Introduction to graph theory, levels, weighted and directed graphs, paths, circuits.
- Euler paths and circuits, Hamilton paths and circuits, the problem of the traveling salesman.
- Trees, overlapping trees, binary trees, tree and graph algorithms.
- Boolean algebra, circuit minimization.