Linear algebra and applications

Course title

Code

F18L3W035

Study programme

Computer Science (4 years)

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

Faculty of Computer Science and Engineering

Degree level (first, second, third cycle)

First cycle

Academic year / semester

5 / Winter

Number of ECTS credits

Teacher

—

Prerequisites for enrolling in the course

Дискретна математика или Дискретни структури 2

10.

Course objectives (competences)

In this course you will learn the concepts and methods of linear algebra, and how to use them to think about problems arising in computer science.

11.

Course content

. Linear geometry: Vectors in R2 and R3, dot product, angel between two vectors, cross product in R3, lines and planes and applications. Linear equations and matrices: Matrix operations and properties, special types of matrices, transpose of a matrix symmetric matrices, diagonal matrices, inverse of a matrix. Solution of system of linear equations: Gaussian elimination, geometric interpretation of solution set. Elimination with matrices: elementary matrices, elimination and permutation matrices. LU – factorization. Reduced echelon form of a matrix. Real vector spaces: Definition of a vector spaces and subspaces, linear independence, basis and dimension of a vector space. Vector spaces and homogeneous systems, rank of a matrix and applications. Coordinates and change of basis. Applications. Orthogonal basis in Rn and orthogonal complement. Linear transformations, definition and examples. The kernel and range of a linear transformation, The matrix of a linear transformation. Orthogonal projection and applications. Determinants and properties. Eigenvalues and eigenvectors, diagonalization, diagonalization of symmetric matrices and applications. SV decomposition of matrices.

12.

Learning methods

Lectures using presentations, interactive lectures, exercises (using equipment and software packages), teamwork, case studies, guest lecturers, independent preparation and defense of a project assignment and a seminar paper.

13.

Total available time

6 ECTS x 30 hours = 180 hours

14.

Distribution of the available time

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

15.

Forms of teaching activities

15.1.	Lectures – theoretical teaching	30 hours
15.2.	Exercises (laboratory, auditory), seminars, team work	45 hours

16.

Other forms of activities

16.1.	Project assignments	0 hours
16.2.	Individual assignments	15 hours
16.3.	Home study	90 hours

17.

Grading

17.1.	Tests	0 points
17.2.	Seminar paper / project (presentation: written and oral)	0 points
17.3.	Activity and participation	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.

Requirements for signature and taking the final exam

Activities 15.2 and 16.1 have been completed.

20.

Language of instruction

Macedonian and English

21.

Method of monitoring teaching quality

internal evaluation and survey mechanism

22.

Literature

22.1.	Required literature No. Author Title Publisher Year
22.2.	Additional literature No. Author Title Publisher Year