Subject

Modern Simulation and Modelling

Course Title

Modern Simulation and Modelling
Modern simulations and modeling

Code

m23_w_044

Study Programme

—

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

Faculty of Computer Science and Engineering

Degree level (first, second, third cycle)

Second cycle

Academic year / semester

9 / Winter

Number of ECTS credits

Teacher

Biljana Toytovska Ribarski, Maria Mihova

Prerequisites for enrolling in the course

—

10.

Objectives of the course programme (competences)

The goal of the course is to familiarize students with the way mathematical models are built to describe various processes and structures. Well-known models based on probability, statistics, and graph theory will be examined—neural networks, predator-prey models, mathematical models of stock market trading, complex networks, etc.

11.

Course content

Generation of random numbers. Stochastic processes. Brownian motion, modeling with stochastic differential equations. Numerical algorithms for simulating stochastic processes. Graph theory, random graphs. Application:
- Stochastic neural networks;
Predator-prey model
Complex networks studied through graph theory (e.g., the Internet, epidemic spreading, computer virus spreading, the global airport network, social networks, etc.)
Models of financial instruments, interest rates (mathematics of the stock market)
...

12.

Learning methods

Lectures, exercises, projects, seminar papers, independent problem solving

13.

Total available time

6 ECTS x 30 hours = 180 hours

14.

Distribution of available time

30 + 30 + 45 + 45 + 30 = 180 hours

15.

Forms of teaching activities

15.1.	Lectures - theoretical instruction	30 hours
15.2.	Exercises (laboratory, auditory), seminars, teamwork	30 hours

16.

Other forms of activities

16.1.	Project assignments	45 hours
16.2.	Independent assignments	45 hours
16.3.	Home study	30 hours

17.

Assessment method

17.1.	Tests	60 points
17.2.	Seminar paper / project (presentation: written and oral)	45 points
17.3.	Activities and learning	10 points
17.4.	Final exam	0 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

completed activities 15.1 and 15.2

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. Sheldon M. Ross \| Introduction to probability models \| Academic Press, Elsevier \| 2014 2. Bernt Oksendal \| Stochastic differential equations \| Springer \| 2010 3. Albert-Laszlo Barabasi \| Network Science \| Cambridge University Press \| 2016 4. Sergey N. Dorogovtsev \| Lectures on Complex Networks \| Oxford University Press \| 2010
22.2.	Additional literature No. Author Title Publisher Year