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Regular version of the site
Master 2023/2024

# Linear Algebra

Type: Compulsory course (Master of Data Science)
Area of studies: Applied Mathematics and Informatics
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 provides arithmetic and algebraic operations which can be applied to large arrays of data. These operations are in the core of the most methods of data analysis. In this course, we discuss the most important linear algebra concepts and algorithms. Then we use this theory to treat a serious data analysis case. Each topic of our course contains theory, numerical examples, and examples of programming using Python. In the final project, you will develop a python software for recognizing hand-written digits.

#### Learning Objectives

• The aim of the course is to provide the theoretical background of solutions to linear algebra problems which appear in data analysis and machine learning.

#### 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

#### 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

Week 6 assignment
Week 3 assignment
• WeeklyScore
Weekly quizzes
• FinalProject

#### Interim Assessment

• 2023/2024 3rd module
0.3 * FinalProject + 0.2 * Staff Graded Assignment 1 + 0.2 * Staff Graded Assignment 2 + 0.3 * WeeklyScore

#### 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