Discrete Мathematics

Објавено: June 28, 2022
1. Course Title Discrete Mathematics
2. Code 4ФЕИТ08З003
3. Study program КТИ
4. Organizer of the study program (unit, institute, department) Faculty of Electrical Engineering and Information Technologies
5. Degree (first, second, third cycle) First cycle
6. Academic year/semester II/3 7. Number of ECTS credits 6
8. Lecturer D-r Sonja Gegovska – Zajkova
9. Course Prerequisites
 Passed: Mathematics 1
10. Course Goals (acquired competencies): Upon completion of the course, the student will be able to: reason mathematically about basic data types and structures, such as sets, relations, mappings, graphs, used in computer algorithms and systems; evaluate elementary mathematical arguments and identify fallacious reasoning; model and analyze computational processes using analytic and combinatorial methods; prove elementary properties of modular arithmetic and explain their applications in cryptography and hashing algorithms; solve problems using recursive methods, apply graph models of data structures; think critically and express clearly and precisely.
11. Course Syllabus: Logic: propositional and predicate logic, logical equivalences, inference rules, methods of proofs. Sets, relations and their applications. Differential and difference equations. Combinatorics, generating functions, counting problems. Number theory, modular arithmetic, linear congruences, systems linear congruences and their application. Elements of graph theory.
12. Learning methods: Blended teaching method: lecturing, tutorials supported by presentations and visualization of concepts, active participation of students through tests and assignments, all supported by learning management system.
13. Total number of course hours 3 + 3 + 0 + 0
14. Distribution of course hours 180
15. Forms of teaching 15.1. Lectures-theoretical teaching 45
15.2. Exercises (laboratory, practice classes), seminars, teamwork 45
16. Other course activities 16.1. Projects, seminar papers 0
16.2. Individual tasks 30
16.3. Homework and self-learning 60
17. Grading 17.1. Exams 20
17.2. Seminar work/project (presentation: written and oral) 0
17.3. Activity and participation 10
17.4. Final exam 70
18. Grading criteria (points) up to 50 points 5 (five) (F)
from 51to 60 points 6 (six) (E)
from 61to 70 points 7 (seven) (D)
from 71to 80 points 8 (eight) (C)
from 81to 90 points 9 (nine) (B)
from 91to 100 points 10 (ten) (A)
19. Conditions for acquiring teacher’s signature and for taking final exam Аttend classes regularly and take tests.
20. Forms of assessment During the semester, two partial written exams are provided (in the 8th and 15th week of the semester, lasting up to 90 minutes) and tests that could be conducted during the classes. In the exam sessions, a student can take a written exam i (duration up to 135 minutes).
For students who have passed the partial exams/written exam, a final oral exam can be conducted (duration 60 minutes). The points from the partial exams/written exam, as well as the points from the tests and the final oral exam are included in the final grade.
21. Language Macedonian and English
22. Method of monitoring of teaching quality Self-evaluation and surveys
23. Literature
23.1. Required Literature
No. Author Title Publisher Year
1 Sonja Gegovska-Zajkova, Vesna Andova, Sanja Atanasova Discrete Mathematics 1 FEIT 2019
23.2. Additional Literature
No. Author Title Publisher Year
1 Sonja Gegovska-Zajkova, Vesna Andova, Sanja Atanasova Solved Problems in Discrete Mathematics FEIT 2019
2 Kenneth H. Rosen Discrete Mathematics and its Applications WCB/Mc Graw-Hill, 8th edition 2018