Math107BKK
Linear Algebra 1
Faculty
Mikhail Romanov
Senior Machine Learning Engineer, Yandex, Expert
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
Linear algebra is one of the core mathematical fields. Since the beginning of the 20th century, the demand in this area has grown tremendously with the rise of quantum mechanics. Since then, it has found numerous applications in the majority of the natural sciences (physics, chemistry, electronics, etc.) as well as in scientific computing (optimisation theory, theory of control, machine learning, computer vision, signal processing, etc.). To be short, computer science is 80% linear algebra.
This course is a must-know for areas such as machine learning, optimisation theory, theory of control, deep learning, and neural networks (these are the courses that may demand this course as a prerequisite).
Learning highlights
- To develop a good understanding of what linear transforms do and how to efficiently perform analysis of linear transforms.
- To learn two main algorithms of Linear Algebra: Gauss Elimination and Gram-Schmidt Orthonormalization.
- Learning how to utilise these algorithms in different scenarios.
Course outline
15 classes
Session 1
Vectors and vector operations.
Lengths and dot products.
Orthogonality.
Gramm-Schmidt Orthogonalization procedure.
Session 2
Seminar
Session 3
Matrices and matrix operations.
Matrix-matrix product and its properties.
Transforms. Invertible transforms. Matrix as a transform.
Session 4
Seminar
Session 5
Square systems of linear equations (SLE) in matrix form.
Solving SLEs Gauss Algorithm.
Matrix Inversion. Criterion of Matrix Invertibility.
Session 6
Seminar
Session 7
LU, PLU, PLDU decomposition and their calculation. QR decomposition
Session 8
Seminar
Session 9
Rectangular SLEs. Underdetermined SLEs. Partial and General Solutions. Null-Space of a Matrix.
PLU decomposition of Rectangular Matrices. QR decomposition of Rectangular Matrices.
Session 10
Seminar
Session 11
Determinant and its properties.
Efficient calculation of Determinant.
Determinant as transformation of Volume.
Session 12
Seminar
Session 13
Tensors. Einstein’s Rule.
Session 14
Oral Exam I
Session 15
Oral Exam II
Prerequisites
Proficiency in Python.
Some experience with VScode.
Basic experience with Git.
Willingness to work extensively on practical tasks.
Methodology
Our sessions consist of two parts: a lecture session with slides and theoretical materials and a seminar session with problem-solving (most likely they will be mixed and lectures and seminars will be intertwined). Seminar sessions will include problem solving and theorem proofs.
Homeworks will contain tests and coding tasks. Some of the coding tasks will require analysis first. The homework will be individual and automatically graded. You are encouraged to share your ideas with your group and strictly forced to ask for help from your group (and the teacher if it is necessary) if you need it. Thoughtless copying will be strictly prosecuted. We have tools to detect that, so beware.
In the end, we will have an oral exam. The oral exam will be a random check of some (most likely complicated) homework task with a full check of understanding of what you are doing in the solution together with philosophical discussion about the topics of the course.
Grading
Mikhail Romanov, PhD, is a deep learning researcher and engineer. His experience includes deep learning for production, scientific computing and research, accompanied by teaching mathematics and machine learning in general.
His academic experience includes teaching courses at MIPT, HSE, Harbour Space Universities and online platforms. As a researcher, he has conducted research at the Technical University of Denmark, Mail.ru, Samsung Research, Quantori, and Yandex. In his research, his main areas of interest are depth estimation, optical flow, optimisation of neural networks, multi-task learning, self-supervised learning, LLMs and diffusion models. He has published papers on tomography, deep learning, scientific computing, computer vision, generative AI, and diffusion models.
See full profileApply for this course
Linear Algebra 1
by Mikhail Romanov
Total hours
45 Hours
Dates
Jun 09 - Jun 27, 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.