Math203
Linear Algebra 2
Faculty
Andrey Gavrilyuk
Team Leader of the HSE Team
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
The Linear Algebra 2 course is a natural continuation of Linear Algebra 1, though it’s not “the second half”. The courses have different purposes; Linear Algebra 2 is a bridge between the theoretical elementary concepts of linear algebra (of Linear Algebra 1) on the one hand, and the advanced techniques needed in applications such as number theory, optimisation, integral and differential calculus, data analysis, and computational methods on the other hand.
Learning highlights
- The main objective of the course is to immerse students in a variety of advanced linear algebra techniques. It introduces areas with the same underlying basic structures (operator, matrix, etc.) hidden under different description languages in applications. Also, the course suggests exquisite intrinsic linear algebra techniques (matrix decomposition, low-dimensional linear algebra, etc.), which expand the possibilities of using this branch of mathematics.
Course outline
15 classes
Session 1
Recap. Matrix slicing and block operations
Session 2
Linear algebra and number theory: linear representation of GCD
Session 3
Linear algebra and number theory: surds
Session 4
Recurrence relations: general solution
Session 5
“Naïve” matrix algebra: like real numbers
Session 6
Low dimensional linear algebra: scalar, vector, and mixed products
Session 7
Scalar product. SV decomposition
Session 8
Elements of spectral theory: invariants and estimations
Session 9
Computations methods for finding eigenvalues
Session 10
Midterm
Session 11
Optimization, problems of linear programming
Session 12
Least squares method
Session 13
Differential operators and tangent linear spaces
Session 14
Recap, Q&A
Session 15
Final test
Prerequisites
Formal mathematical reading and writing (intermediate)
Inference theory (intermediate)
Matrix algebra (basic)
Linear operators (basic)
Polynomials (basic)
Spectral theory (basic)
Awards
- Winner of the 46th International Mathematical Olympiad (IMO),Merida, Mexico
Teacher, trainer, scholar and entrepreneur in education with almost 20 years of experience in 'big math'.
Taught the full range of students from 10 to 65 years old, from having zero background in math to the winners of respectful international competitions. Made his PhD thesis in collaboration in Russia, Canada and Switzerland and came back to Russia to launch his courses on mathematics for adults (after grad people).
See full profileApply for this course
Linear Algebra 2
by Andrey Gavrilyuk
Total hours
45 Hours
Dates
Nov 06 - Nov 24, 2023
Fee for single course
€1500
Fee for degree students
€750
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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.