Master
2023/2024
Linear Algebra
Type:
Compulsory course (Master of Data Science)
Area of studies:
Applied Mathematics and Informatics
Delivered by:
Big Data and Information Retrieval School
Where:
Faculty of Computer Science
When:
1 year, 3 module
Mode of studies:
distance learning
Online hours:
52
Open to:
students of one campus
Instructors:
Nikita Medved
Master’s programme:
Master of Data Science
Language:
English
ECTS credits:
3
Contact hours:
10
Course Syllabus
Abstract
Linear algebra is a basic tool used along with mathematical analysis in all applied disciplines. The course develops abstract mathematical thinking on the one hand and introduces powerful tools used in machine learning, signal processing and other areas of computer science.
Learning Objectives
- Introducing students to the basics of linear algebra;
- Developing students' skills in structural mathematical thinking; .
- Developing students' skills in using linear algebra in applied problems, especially those arising in data analysis problems and in computer science;
- Raising the intellectual level and broadening the general cultural horizons of students;
- Preparing students to study further sections of mathematics and/or related disciplines
Expected Learning Outcomes
- Able to find the solution of a system of linear equations using Gaussian elimination
- Able to calculate LU and PLU decompositions
- Able to calculate and use full rank decompositions
- Able to use the linear regression model to make simple prognoses
- Able to use the Gram-Schmidt method for the orthogonalization
- Able to find the characteristic polynomials and the eigenvalues of a matrix
- Able to calculate and use SVD decomposition
- Able to implement the above methods in Python for machine learning solutions
- Perform basic operations with vectors and matrices.
- Be able to calculate determinants.
- Understand and be able to calculate vector and matrix norms.
- Be able to find the rank of a matrix.
- Understand the difference between vector and its coordinates.
- Understand the idea of a basis. Be able to find and use a basis of a vector space.
- Be able to find coordinates of a vector in another basis.
- Work with a matrix of a linear mapping.
- Be able to find the form of a linear mapping in another basis.
Course Contents
- 1. Systems of linear equations and linear classifier
- 2. Full rank decomposition and systems of linear equations
- 3. Dimensionality reduction
- 4. Linear operators and walks on graphs
- 5. Distances and operators in Euclidean space
- 6. Singular value decomposition (SVD) and Principal Component Analysis (PCA)
Assessment Elements
- Staff Graded Assignment 2Week 6 assignment
- Staff Graded Assignment 1Week 3 assignment
- WeeklyScoreWeekly quizzes
- FinalProject
Interim Assessment
- 2023/2024 3rd module0.3 * FinalProject + 0.2 * Staff Graded Assignment 1 + 0.2 * Staff Graded Assignment 2 + 0.3 * WeeklyScore
Bibliography
Recommended Core Bibliography
- Anthony, M., & Harvey, M. (2012). Linear Algebra : Concepts and Methods. Cambridge, UK: Cambridge eText. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=443759
- Williams, G. (2019). Linear Algebra with Applications (Vol. Ninth edition). Burlington, MA: Jones & Bartlett Learning. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1708709
Recommended Additional Bibliography
- Anton, H. (2014). Elementary Linear Algebra : Applications Version (Vol. 11th edition). Hoboken, NJ: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1639248