Discrete Mathematics

Course title

Code

F18L1W011

Study programme

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

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.

Course objectives (competences)

To introduce students to basic mathematical concepts as a foundation for the following courses in information technologies, computer and software engineering.

11.

Course content

(1) Propositions, operations with propositions, compound propositions and Laws of logic, (1) Propositional functions, predicate calculus and translating sentences into compound propositions and propositional functions, (1) Rules of inference and applications, (1) Proof methods, (1) Sets, (1) Functions, (1) Relations: equivalence relations and partial ordering, (1) Graphs: representation and properties (connectivity, Euler and Hamilton paths, shortest path (1) Isomorphism , graph coloring and planar graphs. Trees: basic terminology and rooted trees, (1) Applications of rooted trees, Spanning trees (minimum spanning trees and search trees), (1) Combinatorics (permutations and combinations), binomial formula, (1) Inclusion-exclusion principle, iterations 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 the available time

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

15.

Forms of teaching activities

15.1.	Lectures – theoretical teaching	45 hours
15.2.	Exercises (laboratory, auditory), seminars, team work	45 hours

16.

Other forms of activities

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

17.

Grading

17.1.	Tests	0 points
17.2.	Seminar paper / project (presentation: written and oral)	0 points
17.3.	Activity and participation	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.

Requirements for signature and taking the final exam

Activities 15.2 and 16.1 have been completed.

20.

Language of instruction

Macedonian and English

21.

Method of monitoring teaching quality

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