Discrete Mathematics 1

Learning Outcomes

  1. To solve homogeneous and non-homogeneous linear recursion.
  2. Apply the recursive way of thinking on the appropriate combinatorial problems.
  3. Describe and manipulate with basic notions from graph theory.
  4. Describe and solve appropriate engineering problems in terms of graph theory.
  5. 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 assignments

During 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

  1. Fibonacci's sequence, Homogeneous recursive relations
  2. Homogeneous recursive relations
  3. Non-homogeneous recursive relations
  4. Notion of a graph. Main definitions and examples. Graph isomorphism
  5. Connectivity. Paths. Eulerian and hamiltonian graphs, Optimization algorithms. Shortest path problem. Chinese postman problem. Travelling salesman problem
  6. Different characterizations of trees
  7. Labelled trees. Prüfer code, Minimum spanning tree. Algorithms
  8. Midterm exam
  9. Kuratowski's theorem, Euler's formula
  10. Dual graphs, Planarity testing algorithms
  11. Vertex colourings. Brooks' theorem, Edge colourings
  12. Face colourings of planar graphs. Four colour theorem
  13. Notion of a digraph. Connectivity and strong connectivity, Critical path problem. Algorithms, Tournaments
  14. Marriage problem, Hall's theorem, Transversals, Application to latin squares
  15. Final exam

Study Programmes

University undergraduate
Computing (study)
(3. semester)

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.,

Laboratory exercises

General

ID 183396
  Winter semester
6 ECTS
L1 English Level
L1 e-Learning
60 Lectures
0 Exercises
6 Laboratory exercises
0 Project laboratory

Grading System

85 Excellent
70 Very Good
55 Good
45 Acceptable