Linear algebra and Applications

1.

Subject title

Linear algebra and Applications

Линеарна алгебра и примени

2.

Code

F23L3W035

3.

Study program

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

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 Марија Михова проф. д-р Весна Димитриевска Ристовска

9.

Prerequisites for enrollment

Дискретна математика или Дискретни структури 2 или Математика 2 или Избрани теми од математика

10.

Subject goals and competencies:

Familiarity with the concepts and methods of linear algebra and how to use them for thinking and solving problems arising from computer science

11.

Subject content:

Linear Geometry: Vectors in R2 and R3, dot product of vectors, angle between two vectors, cross product of vectors, equation of line and plane and applications. Matrices: Definition and matrix operations and properties. Special types of matrices, transpose matrix, symmetric matrices, diagonal matrix, inverse matrix. Systems of linear equations. Gaussian method for solving systems of linear equations. Multiple solutions of systems of linear equations. Geometric interpretation of a solution of a system of linear equations. Elimination using matrices: Elementary matrices, elimination matrices and permutation matrices. LU factorization and application to solving systems of linear equations. Reduced staggered matrix form. Real vector spaces: Definition of vector space, vector subspaces. Linear independence, basis and dimension of a vector space. Vector spaces and homogeneous systems, matrix rank and applications. Coordinates and change of bases. Application. Orthogonal bases in Rn and orthogonal complement. Linear transformations, definition and examples. Kernel and rank of linear transformation. Linear transformation matrix. Orthogonal projections and application. Determinants and properties. Eigenvalues and eigenvectors. Diagonalization of a matrix. Diagonalization of symmetric matrix and application. SV matrix decomposition and application.

12.

Learning methods:

Предавања со користење на презентации, интерактивни предавања, вежби (користење на опрема и софтверски пакети), тимска работа, пример случаи, поканети гости предавачи, самостојна изработка и одбрана на проектна задача и семинарска работа.

13.

Total available time fund

6.0 ECTS x 30 hours = 180 hours

14.

Time distribution

30 + 45 + 15 + 0 + 90 = 180 hours

15.

Forms of teaching activities

15.1.

Lectures - theoretical teaching

30 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

15 hours

16.3.

Homework

90 hours

17.

Grading method

17.1.

Tests

0 points

17.2.

Seminar work / project (presentation: written and oral)

0 points

17.3.

Activities and learning

20 points

17.4.

Final exam

80 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

Реализирани актибвности 15.2 и 16.1

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