Discrete Mathematics 1
Data is displayed for the academic year: 2024./2025.
Lectures
Laboratory exercises
Course Description
Homogeneous linear recursive relations. Non-homogeneous recursive relations. Basic notions from graph theory. Connectivity. Optimization algorithms on graphs. Trees. Planarity. Graph colourings. Directed graphs. Graph matchings.
Prerequisites
Basics of linear algebra, Enumerative combinatorics
Study Programmes
University undergraduate
[FER3-EN] Computing - study
(3. semester)
Learning Outcomes
- To solve homogeneous and non-homogeneous linear recursion.
- Apply the recursive way of thinking on the appropriate combinatorial problems.
- Describe and manipulate with basic notions from graph theory.
- Describe and solve appropriate engineering problems in terms of graph theory.
- Solve problems algorithmically using computers.
Forms of Teaching
Lectures
4 hours of lectures a week. The lecturer is going to follow the lecture materials.
Independent assignmentsDuring the semester 3 software excercises will be given to be solved by the students individually and to be shown in the framework of laboratory excercises.
Grading Method
Continuous Assessment | Exam | |||||
---|---|---|---|---|---|---|
Type | Threshold | Percent of Grade | Threshold | Percent of Grade | ||
Laboratory Exercises | 0 % | 15 % | 0 % | 15 % | ||
Homeworks | 0 % | 5 % | 0 % | 5 % | ||
Mid Term Exam: Written | 0 % | 40 % | 0 % | |||
Final Exam: Written | 0 % | 40 % | ||||
Exam: Written | 0 % | 80 % |
Week by Week Schedule
- Fibonacci's sequence, Homogeneous recursive relations
- Homogeneous recursive relations
- Non-homogeneous recursive relations
- Notion of a graph; Main definitions and examples; Graph isomorphism
- Connectivity; Paths; Eulerian and hamiltonian graphs, Optimization algorithms; Shortest path problem; Chinese postman problem; Travelling salesman problem
- Different characterizations of trees
- Labelled trees; Prüfer code, Minimum spanning tree; Algorithms
- Midterm exam
- Kuratowski's theorem, Euler's formula
- Dual graphs, Planarity testing algorithms
- Vertex colourings; Brooks' theorem, Edge colourings
- Face colourings of planar graphs; Four colour theorem
- Notion of a digraph; Connectivity and strong connectivity, Critical path problem; Algorithms, Tournaments
- Marriage problem, Hall's theorem, Transversals, Application to latin squares
- Final exam
Literature
(.), D. Kovačević, D. Žubrinić, Uvod u diskretnu matematiku, Element, Zagreb, 2014.,
(.), A. Nakić, M.-O. Pavčević, Uvod u teoriju grafova, Element, Zagreb, 2014.,
(.), J.M. Aldous, R.J. Wilson, Graphs and Applications - An Introductory Approach, Springer, 2004.,
(.), G. Chartrand, L. Lesniak, Graphs and Digraphs, CRC Press, 2005.,
General
ID 209648
Winter semester
6 ECTS
L1 English Level
L1 e-Learning
60 Lectures
0 Seminar
0 Exercises
6 Laboratory exercises
0 Project laboratory
0 Physical education excercises
Grading System
85 Excellent
70 Very Good
55 Good
45 Sufficient