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, I gave lectures to students with very different mathematical background. In the next sections I will describe some concrete problems I faced and how I solved them.

Pre-calculus for non-mathematicians

The first year I came to HSE I gave pre-calculus courses at Faculty at Politology (practice lessons) and at Faculty of History (lectures). Many students were anxious about math or thought that they will 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 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 goal with most of the students.

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 won Russian Mathematical Olympiad, others don't know how to find a vector parallel to 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.

Developing courses

Besides following already developed courses, I also developed some courses on my own.

For me, the most interesting experience was developing the program of the pre-calculus course for linguistics departement. Ilya Schurov and me talked to many professors who teach linguistics to understand what are mathematical prerequisites for their courses.

Also, I developed the course “Calculus of several variables” for the bachelors in Economics.