Subject

Discrete mathematics

Course Title

Discrete mathematics
Discrete mathematics

Code

F23L2S011

Study Programme

Computer engineering

Organizer of the study programme (unit, institute, department or division)

Faculty of Computer Science and Engineering

Degree level (first, second, third cycle)

First Cycle

Academic year / semester

2 / Summer

Number of ECTS credits

Teacher

Dejan Spasov, Emil Stankov, Metodija Janceski, Natasha Ilievska, Vesna Dimitrievska Ristovska

Prerequisites for enrolling in the course

—

10.

Objectives of the course programme (competences)

The course provides an introduction to the fundamental mathematical concepts necessary for advanced courses in information technology, computer engineering, and software engineering.

11.

Course content

Lectures:
1. Sentences, operations on sentences, sentential forms, and logical laws
2. Expression functions, predicate calculus, translation of sentences into expression formulas and functions.
3. Locking methods and application
4. Methods of Proof
5. Sets
6. Functions
7. Relations, Ordering, and Equivalence
8. Graphs: presentation and properties (connectedness, Eulerian and Hamiltonian path, shortest path).
9. Isomorphism, coloring, and planarity of graphs.
Timber: Basic concepts of timber and root wads
10. Application of Root Trees and Searching in Root Trees
Skeletal trees (lightest trees and search trees)
11. Combinatorics (permutations and combinations with and without repetition). Binomial formula
12. Principle of inclusion and exclusion, iteration and recursion

12.

Learning methods

Lectures using presentations, interactive lectures, exercises (using equipment and software packages), teamwork, case studies, guest lecturers, independent preparation and defense of a project assignment and a seminar paper.

13.

Total available time

6 ECTS x 30 hours = 180 hours

14.

Distribution of available time

45 + 45 + 0 + 0 + 90 = 180 hours

15.

Forms of teaching activities

15.1.	Lectures - theoretical instruction	45 hours
15.2.	Exercises (laboratory, auditory), seminars, teamwork	45 hours

16.

Other forms of activities

16.1.	Project assignments	0 hours
16.2.	Independent assignments	0 hours
16.3.	Home study	90 hours

17.

Assessment method

17.1.	Tests	0 points
17.2.	Seminar paper / project (presentation: written and oral)	0 points
17.3.	Activities and learning	0 points
17.4.	Final exam	100 points

18.

Grading criteria (points / grade)

up to 50 points	5 (five) (F)
from 51 to 60 points	6 (six) (E)
from 61 to 70 points	7 (seven) (D)
from 71 to 80 points	8 (eight) (C)
from 81 to 90 points	9 (nine) (B)
from 91 to 100 points	10 (ten) (A)

19.

Requirement for obtaining a signature and taking the final exam

Activities 15.2 and 16.1 have been completed.

20.

Language of instruction

Macedonian and English

21.

Method for monitoring the quality of teaching

internal evaluation and survey mechanism

22.

Literature

22.1.	Required literature 1. Kenneth H. Rosen \| Discrete Mathematics and Its Applications, Sixth Edition, International Edition, ISBN-13: 978-007-124474-9 \| The McGraw-Hill Companies \| 2007 2. Rowan Garnier and John Taylor \| Discrete Mathematics for New Technology Second Edition, ISBN 0 7503 0652 1 \| OP Publishing Ltd \| 2002
22.2.	Additional literature No. Author Title Publisher Year