Discrete Mathematics
| Title | Διακριτά Μαθηματικά / Discrete Mathematics |
| Code | 023 |
| Faculty | Engineering |
| School | Electrical and Computer Engineering |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Coordinator | Leonidas Pitsoulis |
| Common | No |
| Status | Active |
| Course ID | 600000971 |
Programme of Study: Electrical and Computer Engineering
Registered students: 122
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| CORE | Elective Courses | 4 | 2 | 6 |
| Academic Year | 2021 – 2022 |
| Class Period | Spring |
| Faculty Instructors |
|
| Weekly Hours | 4 |
| Class ID | 600198692
|
Class Schedule
| Building | Πολυτεχνείο - πτέρυγα Γ (ΤΗΜΜΥ & Τοπογράφων Μηχ.) |
| Floor | Όροφος 1 |
| Hall | Α3 (2) |
| Calendar | Δευτέρα 09:00 έως 11:00 |
| Building | Πολυτεχνείο - πτέρυγα Γ (ΤΗΜΜΥ & Τοπογράφων Μηχ.) |
| Floor | Όροφος 1 |
| Hall | Α1 (8) |
| Calendar | Πέμπτη 13:00 έως 15:00 |
Course Type 2016-2020
- Background
Course Type 2011-2015
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600198692
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
1. Linear Algebra
2. Calculus I
3. Set Theory
4. Elementary Algorithms
Learning Outcomes
1. Learning of various combinatorial enumeration methods for discrete structures.
2. Acquintance with mathematical proof techniques.
3. Knowledge of various topics from propositional logic such as formal proofs.
4. Knowledge of various topics from first order logics such as consistency and completeness.
5. Thorough understanding of basic graph theory concepts and definitions.
6. Acquintance with constructive and algorithmic proof techniques in graph theory.
7. Knowledge of various topics in trees and distances in graphs.
8. Knowledge of planarity, Hamilton and Euler graphs, higher connectivity and coloring in graphs.
9. Knowledge of various topics in matroid theory such as axiom systems, matroid classes, minors and duality.
General Competences
- Work autonomously
- Advance free, creative and causative thinking
Course Content (Syllabus)
Rules of addition and multiplication, generating functions, Polya theory, formal propositional language, tautologies, propositional logic, first order language, first order logic, consistency and completeness, basic concepts and definitions in graph theory, matrices of graphs, paths and cycles, connectivity, classes of graphs, graph sequences, constructive and algorithmic proofs, directed graphs, trees, binary trees, characterizations of trees, rooted trees, distances in graphs, spanning trees, enumerations of trees, Hamilton and Euler graphs, graph coloring, abstract independence, axiomatic systems of matroids, graphic matroids, representable matroids, decomposition theorems and recognition algorithms.
Educational Material Types
- Notes
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Communication with Students
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 120 | 4 | ✓ | ||
| Project | 30 | 1 | ✓ | ||
| Exams | 30 | 1 | ✓ | ||
| Total | 180 | 6 |
Student Assessment
Description
1. Written Examination of 180 minutes (max)
2. Assessment of optional open problems and projects during the course
Student Assessment methods
- Written Assignment (Formative)
- Written Exam with Problem Solving (Formative)
Bibliography
Course Bibliography (Eudoxus)
1. Στοιχεία Διακριτών Μαθηματικών, Liu C.L., Πανεπιστημιακές εκδόσεις Κρήτης, 2010.
2. Discrete Mathematics, Biggs N. Oxford University Press, 2003.
3. Discrete Mathematics, Aigner M., American Mathematical Society, 2007.
Last Update
23-12-2015
