Dynamical Systems seminar is supported by RFBR project 20-01-00420-a and Laboratory Poncelet.

# Участник:Yury G. Kudryashov/Teaching Statement

Mathematics <…> starts with certain simple principles and proceeds by steps. You can start with nothing and learn. It’s practically designed for that.— Isaac Asimov,

Profession

While being an Assistant Professor at Higher School of Economics and Independent University of Moscow, I gave lectures to students with very different mathematical background, both in Russian and in English, both introductory and advanced courses.

I am ready to develop and deliver any mathematical introductory course, and advanced courses on most Calculus/Analysis/Differential Equations-related subjects. Also, I am ready to further improve my teaching skills and enlarge my area of expertise.

In the next sections I will describe some concrete problems I faced and how I solved them.

## High School #57

I started my teaching career when I was a 3rd year undergraduate student. Ivan Yashchenko and a team of undergraduate students gave a 4-year course on Pre-Calculus and Calculus at one of the best Moscow mathematical high-schools.

The main feature of our course was that all theorems were given to students as lists of problems. Students solved these problems, we read their solutions, and discussed them with authors. Each teacher was responsible for 3-4 students, so we worked with them individually.

## Pre-calculus for non-mathematicians

The first year I came to HSE I gave pre-calculus courses at Faculty of Political Science (practice lessons) and at Faculty of History (lectures). Many students were anxious about math or thought that they would never need it.

My first goal was to convince them that mathematics is useful and is not too hard to understand. For this end, I gave many examples related to the real life, or students' area of interest. Another goal was to explain to them that mathematics is not about applying some formulas, but about understanding the problem.

I think that I achieved these goals with most of the students.

## Math for linguists

The year I came to HSE, the Faculty of Philology was opened. Ilya Schurov and me developed the program of a two-year mathematical course for linguists. We talked to many professors of this faculty to understand what kind of mathematics do they need for their courses.

As a result, the course includes mathematical logic, combinatorics, probability theory, regular expressions and finite state automata, and calculus.

## Math for economists

I gave practice lessons on Calculus and Linear Algebra to 1st-year students of the joint NES/HSE “Bachelor in Economics” program (1 year), and lectures on Calculus of Multiple Variables to second-year students of the same program (1 semester × 3 times).

For the latter course, I also developed the program (mostly based on Stewart, part II). Students coming to this program have different background. Some of them are the winners of Russian Mathematical Olympiad, others don't know how to find a vector parallel to the plane 3x+2y+z=0.

So, my goal was to fill the gaps in the background of some students while not making it too boring for the top ten students. To achieve this goal, the main part was targeted at average and below-average students, and we gave some exercise sheets on advanced topics for the best students.

## Faculty of Mathematics

The main difference between this Faculty and others is that the mathematical background of the students is extremely high. It is a great pleasure for me to discuss mathematics with these students, but I should be always ready to discuss very advanced topics.

I delivered both lectures and practice lessons. In particular, I had a very interesting experience of delivering courses on subjects out of the scope of my research interests (Calculus of Variations, Game Theory, Programming in Python).

## Math in Moscow Program

“Math in Moscow” is a program for foreign students. Each semester several students come to Moscow, listen some courses (in English), get credits, and these credits are transferred to their home institutions.

The small size of the groups allowed me to work with students personally. For example, practice lessons proceeded like this: I gave students a list of problems, the students tried to solve them, and I came to each student to discuss his ideas.