Mathematics 3

1.

Subject title

Mathematics 3

Математика 3

2.

Code

F23L3W001

3.

Study program

Примена на информациски технологии, Компјутерски науки, Компјутерско инженерство, Интернет, мрежи и безбедност, Софтверско инженерство и информациски системи, Software engineering and information systems, Примена на информациски технологии, Компјутерски науки, Компјутерско инженерство, Интернет, мрежи и безбедност, Информатичка едукација, Софтверско инженерство и информациски системи, Software engineering and information systems, Стручни студии за програмирање, Стручни студии за програмирање,

4.

Organizer of the study program (unit, institute, department, division)

Faculty of Information Sciences and Computer Engineering

5.

Study cycle (first, second, third)

Прв циклус

6.

Academic year / semester

2 / Зимски

7. Number of ECTS credits

6.0

8.

Instructor

проф. д-р Александра Поповска Митровиќ проф. д-р Билјана Тојтовска Рибарски доц. д-р Илинка Иваноска проф. д-р Марија Михова ворн. проф. д-р Методија Јанчески проф. д-р Наташа Илиевска проф. д-р Верица Бакева

9.

Prerequisites for enrollment

10.

Subject goals and competencies:

To introduce the basic concepts of probability and statistical analysis with a discussion of applications in computer science. To enable students to successfully follow vocational courses in which elements of probability theory and statistics are applied.

11.

Subject content:

1. Elements of combinatorics. 2. Experiments and events: set of elementary events, random events, operations with events Definition and properties of probability. Classical definition of probability. 3. Conditional probability. Independence. Total Probability Formula. Bayesian formulas. 4. Discrete random variables: definition, examples, distribution law and function. Known distributions of discrete type (Benoulli, binomial, uniform, Poisson) 5. Random variables of absolutely continuous type: definition, function and distribution density. Known distributions of absolutely continuous type (uniform, exponential, gamma, normal) Independence of random variables definitions and examples 6. Quantitative features: mathematical expectation and dispersion and their properties. Covariance and correlation coefficient between two random variables. 7. Central limit theorem. More significant distributions in statistics. 8. Elements of statistics: population and sample, types of data, parameters and statistics. 9. Descriptive statistics (mean, dispersion, standard deviation, median, ordered statistics, rank, quantiles, median). 10. Confidence intervals for mathematical expectation, dispersion, probability of an event. 11. Hypothesis testing: first and second type error, test power, test statistic, critical domain. One-sign tests: mathematical expectation value tests, event probability value test, variance value test. 12. Two-sign tests: test for equality of variances, test for equality of mathematical expectations. Nonparametric tests of independence of two categorical features.

12.

Learning methods:

Предавања со користење на презентации, интерактивни предавања, вежби (користење на опрема и софтверски

13.

Total available time fund

6.0 ECTS x 30 hours = 180 hours

14.

Time distribution

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

15.

Forms of teaching activities

15.1.

Lectures - theoretical teaching

45 hours

15.2.

Exercises (laboratory, classroom), seminars, team work

45 hours

16.

Other forms of activities

16.1.

Project tasks

0 hours

16.2.

Independent tasks

45 hours

16.3.

Homework

45 hours

17.

Grading method

17.1.

Tests

points

17.2.

Seminar work / project (presentation: written and oral)

0 points

17.3.

Activities and learning

points

17.4.

Final exam

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.

Condition for signature and taking final exam

20.

Language of instruction

Македонски и англиски

21.

Quality assurance method

механизам на интерна евалуација и анкети

22.

Literature

22.1.

Mandatory literature

22.2.

Additional literature