Subject

Linear Algebra and Applications

Course Title

Linear Algebra and Applications
Linear Algebra and Applications

Code

F23L3W035

Study Programme

Computer Science, Statistics and Data Analytics

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

Faculty of Computer Science and Engineering

Degree level (first, second, third cycle)

First Cycle

Academic year / semester

3 / Winter

Number of ECTS credits

Teacher

Maria Mihova, Vesna Dimitrievska Ristovska

Prerequisites for enrolling in the course

Discrete Mathematics or Discrete Structures 2 or Mathematics 2 or Selected Topics in Mathematics

10.

Objectives of the course programme (competences)

Familiarization with the concepts and methods of linear algebra and how to use them to think about and solve problems arising from computer science.

11.

Course content

Linear geometry: Vectors in R2 and R3, scalar product of vectors, angle between two vectors, vector product of vectors, equation of a line and a plane and applications. Matrices: Definition and operations with matrices and properties. Special types of matrices: transposed matrix, symmetric matrices, diagonal matrix, inverse matrix. Systems of linear equations. Gaussian elimination for solving systems of linear equations. Solutions of systems of linear equations. Geometric interpretation of the solution of a system of linear equations. Elimination using matrices: elementary matrices, elimination matrices, and permutation matrices. LU factorization and its application to solving systems of linear equations. Reduced echelon form of a matrix. Real Vector Spaces: Definition of a 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 basis. Applications. Orthogonal bases in Rn and orthogonal complement. Linear transformations, definition and examples. Kernel and rank of a linear transformation. Matrix of a linear transformation. Orthogonal projections and applications. Determinants and properties. Eigenvalues and eigenvectors. Diagonalization of a matrix. Diagonalization of symmetric matrices and applications. SV decomposition of matrices and applications.

12.

Learning methods

Lectures using presentations, interactive lectures, exercises (using equipment and software packages), team work, 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 available time

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

15.

Forms of teaching activities

15.1.	Lectures - theoretical instruction	30 hours
15.2.	Exercises (laboratory, auditory), seminars, teamwork	45 hours

16.

Other forms of activities

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

17.

Assessment method

17.1.	Tests	0 points
17.2.	Seminar paper / project (presentation: written and oral)	0 points
17.3.	Activities and learning	20 points
17.4.	Final exam	Eighty 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

Activities 15.2 and 16.1 have been completed.

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. David C. Lay \| Linear Algebra and its Applications \| Addison-Wesley \| 2012 2. Jim Hefferon \| Linear Algebra \| http://joshua.smcvt.edu/linearalgebra \| 2014 3. Bernard Kolman & David R. Hill \| Introductory Linear Algebra: An Applied First Course 8/E \| Pearson Education International \| 2005
22.2.	Additional literature No. Author Title Publisher Year