Math107
Calculus 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
This course is the next step for students in order to master Calculus. It combines more sophisticated techniques of qualitative and quantitative study of functions, including value approximation, asymptotic methods, multivariate differentiation and integration, and selected optimization methods. Generally, it gives a broad overview of modern analytic methods formally and informally used in such applications as computing complexity of algorithms, evaluation of probabilities, back propagation and gradient descent methods of machine learning (without diving deeply into the applications).
Learning highlights
- The main goal of the course is to establish a solid understanding of the basic principles of analysis for further broadening and specialization for applications.
- The objectives are to get familiar with areas of inequalities and comparison, asymptotic estimates, differential equations, differential geometry, integration methods, and approximation methods.
Course outline
15 classes
Session 1
Inequalities: basic inequalities, basic methods, multivariate calculus ``by hand’
Session 2
Inequalities: axioms, rigor of a proof, revisiting ``basic facts’’.
Session 3
Inequalities: analytic methods.
Session 4
Approximation: approximation of numbers, Dirichlet’s theorem, Pell’s equation.
Session 5
Approximation: asymptotics in applications (geometry, number theory, etc.).
Session 6
Approximation of functions, uniform convergence.
Session 7
Approximation: complete systems of functions.
Session 8
Midterm.
Session 9
Vector analysis: complete differential, differential equations, equations from applications.
Session 10
Vector analysis: curves and surfaces in Euclidean space, elements of differential geometry.
Session 11
Vector analysis: change of variables, Jacobian, differential of a mapping.
Session 12
Optimization: LSM (least squares method).
Session 13
Optimization: gradient descent.
Session 14
Recap, Q&A, problem solving.
Session 15
Final test.
Methodology
The course is practice oriented; therefore, each class will be supplied with a list of relevant problems to be solved in class, discussions and further completion as a home task. Each topic will be accompanied with theoretical blocks, discussions and personal or group in-class solution presentation sessions. The remaining part of a day’s task becomes a task for self-preparation. Mini-group assignments will be implemented.
Grading
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
Calculus 2
by Andrey Gavrilyuk
Total hours
45 Hours
Dates
Feb 20 - Mar 10, 2023
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.