Linear Algebra

2024/2025

Academic Year

ENG

Instruction in English

Delivered at:

Big Data and Information Retrieval School

Course type:

Compulsory course

When:

1 year, 1, 3 module

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

• Matrix and vector operations
• Linear dependence, bases of vector spaces
• Linear mappings and operators
• Linear systems and matrices
• Eigenvalues and eigenvectors
• Matrix decompositions

Assessment Elements

• Quizzes
  There will be short synchronous or asynchronous quizzes. Each quiz will take 10-15 minutes from starting an attempt and will cover the material of the previous topics. Question types might be a multiple-choice or a short answer.
• Home Assignments
• Midterm
• Exam
  There will be a final work at the examination session of the module 1, at the end of October, synchronously with online proctoring at Smart LMS. The duration of the exam is 2 hours.

Interim Assessment

• 2024/2025 1st module
  0.4 * Exam + 0.2 * Home Assignments + 0.3 * Midterm + 0.1 * Quizzes

Bibliography

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

Authors

• Ахмедова Гюнай Интигам кызы
• KARPOV GLEB ALEKSANDROVICH