Math106BKK
Linear Algebra 1
Faculty
Andrey Kechin
Master of Science fellow
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
This course introduces the fundamental concepts of linear algebra, including vectors, matrices, systems of linear equations, determinants, eigenvalues, and eigenvectors. Emphasis is placed on both computational techniques and theoretical understanding, with real-world applications in science, engineering, and computer science.
Learning highlights
- This course introduces programming students to the core concepts of linear algebra, with a focus on practical applications in computing.
- Students will learn to work with vectors and matrices, perform basic operations, and solve systems of linear equations—essential tools for graphics, simulations, and machine learning.
- Key topics include vector spaces, matrix transformations, determinants, eigenvalues, and eigenvectors.
- The course emphasises algorithmic thinking, with hands-on coding exercises to implement linear algebra methods in Python.
- Students will explore how linear algebra powers 3D graphics, search engines, neural networks, and data processing pipelines.
- The course combines classical mathematical problems with real-world examples and projects.
Course outline
15 classes
Session 1
Vectors.
Vector operations.
Session 2
Vector norms.
Vector space.
Session 3
Dot product.
Geometrical means.
Ortogonality.
Session 4
Matrix.
Determinant.
The rank of a matrix.
Session 5
Cross product.
Mixed product.
Geometrical meaning.
Session 6
Systems of linear equations.
Gauss method.
Cramer method.
Session 7
Eigenvalues.
Eigenvectors.
Diagonal matrix.
Session 8
Midterm.
Session 9
Operations on matrices.
Inverse matrix.
Session 10
Transpose of matrices.
Pseudoinverse matrix.
Session 11
Orthogonal vectors and matrices.
Elementary orthogonal matrices.
Session 12
Practical applications.
Solving least squares problem.
Session 13
Applications.
Tangent distance.
Text mining.
Session 14
Review.
Session 15
Final Exam.
Prerequisites
Math logic and proving techniques.
Math notations.
Calculation skills.
Methodology
The methodology is based on mixing PBL (problem-based learning) and IVL (interactive and visual learning) technologies.
PBL is based on presenting real-world problems and guiding students to apply discrete math concepts like graph theory or combinatorics to solve them.
IVL technology considers using visualisation tools in lecture studies.
Each class can be divided into three parts: Lection part, Active learning (discussion, Q&A), Problem-solving part.
Students are encouraged to solve a task during the class that follows the homework.
The homework is discussed at the beginning of the following class.
The Exams is splitted into two parts: theory and practice. 1/3rd of the score is theory 2/3 is practice.
Grading
Andrew graduated from Siberian Federal University and obtained the Master of Science degree in Physics in 2021.
The scientific interests are in biophysics, medicine, and modelling of real biology features in-silico. The master article is devoted to the quantum modelling of an Endothelial Growth Factor Receptor`s ligand as a target for positron emission tomography. Andrew is an awardee of a students olympiad and an active member of a math book translation team.
See full profileApply for this course
Linear Algebra 1
by Andrey Kechin
Total hours
45 Hours
Dates
Dec 01 - Dec 19, 2025
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.