Discrete Mathematics 2

Објавено: October 23, 2019
  1.    Course Title Discrete mathematics 2
  2.    Code 3ФЕИТ08З004
  3.    Study program KTI
  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 III/5   7.    Number of ECTS credits 6.00
  8.    Lecturer Dr Aneta Buchkovska, Dr Biljana Jolevska-Tuneska, Dr Biljana Nachevska-Nastovska, Dr Katerina Hadji-Velkova Saneva, Dr Sanja Atanasova, Dr Sonja Gegovska-Zajkova, Dr Vesna  Andova
  9.    Course Prerequisites Taken course: Discrete Mathematics 1

10.    Course Goals (acquired competencies):  After finishing this course, the student should adopt the basic concepts of combinatorics, number theory and classical graph theory.  The student should develop an ability for analytic thinking, critical observations, and learning ability.

11.    Course Syllabus: Combinatorics, generating functions. Number theory. Basics of cryptography. Graphs. Graphs isomorphisms. Subgraphs and spanning subgraphs. Connectivity. Euler and Hamilton graphs. Tournaments. Plane graphs. Graph coloring. Discharging method. Matching.  Spectral graph theory and application. Laplace specter. Google page rank. Transporting networks, cuts and flows.  Ford–Fulkerson algorithm. Random graphs, Reny-Erdos model,  Случ Watts–Strogatz model.  Probability method. Large graphs and electrical networks.
12.    Learning methods:  Lectures, exercises and individual work
13.    Total number of course hours 3 + 2 + 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 30
16.    Other course activities 16.1. Projects, seminar papers 10
16.2. Individual tasks 20
16.3. Homework and self-learning 75
17.    Grading 17.1. Exams 30
17.2. Seminar work/project (presentation: written and oral) 20
17.3. Activity and participation 0
17.4. Final exam 50
18.    Grading criteria (points) up to 49 points     5 (five) (F)
from 50 to 59 points     6 (six) (E)
from 60 to 69 points     7 (seven) (D)
from 70 to 79 points     8 (eight) (C)
from 80 to 89 points     9 (nine) (B)
from 90 to 100 points   10 (ten) (A)
19.    Conditions for acquiring teacher’s signature and for taking final exam none
20.    Forms of assessment During the semester, two partial written exams (at most 90 minutes each) are provided, at the middle and at the end of the semester, tests that are conducted during the classes and a project assignment. The student should prepare a project assignment and submit it by the end of the semester.  For students who have passed the partial exams and tests, a final oral exam may be conducted (maximum duration 60 min). The scores from the partial exams, tests, project assignment and the final oral exam are included in the final grade. A written exam (maximum duration 135 min) is taken in the scheduled exam sessions. For students who have passed the written exam, a final oral exam  can be conducted. The scores from the written exam and the final oral exam are included in the final grade
21.    Language Macedonian and English
22.    Method of monitoring of teaching quality Еvaluation and questionnaires
23.    Literature
23.1. Required Literature
No. Author Title Publisher Year
1 D.West Introduction to Graph theory Prentice Hall 2001
2 A. Bondy, U.S.R. Murty Graph theory Springer 2001
3 J.H. van Lint, M.S. Wilson A course in combinatorics Cambridge Univ. Press 2001
23.2. Additional Literature
No. Author Title Publisher Year
1 N. Biggs  Algebraic graph theory  Cambridge Univ. Press  1996