Subject

Discrete mathematics

Course Title

Discrete mathematics
Discrete Mathematics

Code

F18L1W011

Study Programme

Application of Information Technologies, Software Engineering and Information Systems, Internet, Networks and Security, Computer Education, Computer Engineering, Software Engineering and Information Systems

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

—

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

(1) Sentences, operations on sentences, sentential formulas and logical laws (1) Sentential functions, predicate calculus, translation of sentences into sentential formulas and functions. (1) Methods of deriving conclusions and applications (1) Proof methods (1) Sets (1) Functions (1) Relations, ordering, and equivalence (1) Graphs: presentation and properties (connectedness, Eulerian and Hamiltonian paths, shortest path). (1) Isomorphism, coloring, and planarity of graphs.
Trees: Basic Concepts of Trees and Root Trees (1) Application of Root Trees and Searching in Root Trees.
Skeleton trees (lightest trees and search trees) (1) Combinatorics (permutations and combinations with and without repetition) Binomial formula (1) Inclusion–exclusion principle, iteration, and recursion

12.

Learning methods

Lectures using presentations, interactive lectures, exercises (using equipment and software packages), teamwork, case studies, guest lectures, 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 No. Author Title Publisher Year
22.2.	Additional literature No. Author Title Publisher Year