‘I Want the Students to Understand the Subject “From the Inside”’

Vladlen Timorin, Professor at the HSE master’s programme in mathematics, told us about his students and the course.

Vladlen Timorin, Professor at the HSE master’s programme in mathematics, told us about his students and the course.

— Tell us about the students on your course?

— The class was a mix of Russian and international students from our master’s programmes, and the students of “Math in Moscow” – a short-term student internship/exchange programme.

— What difficulties did you face as a lecturer teaching the Basic Representation Theory course to an international audience?

— Since all the participants had different backgrounds, I had to go into more detail on terminology and definitions, for those from related disciplines, too. Sometimes I needed to discuss the terminology with Russian-speaking participants and answer questions like, ‘Is it true that what you are talking about is called so and so in Russian?’ I encouraged these questions, since they are  not about  language, but about terminology. Unfortunately, I was short of time, so I couldn’t cover  much ground. But I hope that I managed to set the focus in the right way.

Generally, the participants were very lively. They eagerly answered questions and even came to the blackboard, but sometimes I had to translate the discussions with some students to the audience in different words to make sure everyone understood what was being said.

— What is an ideal student in your view? Are there any national specifics in students’ attitudes to learning?

— There’s something special about mathematics: you cannot separate learning mathematics from doing mathematics. That’s why an ideal student not only wants to gain mathematical knowledge, he wants to know immediately how the new knowledge is connected with the old, and what advantages it gives him for solving his old problems. Of course, an ideal student lives and breathes mathematics and thinks about it 24/7.

In real life, different students study in different ways. I believe that a teacher’s purpose is to stimulate independent, individual learning, rather than trying to ‘teach’. But the support will be the more effective the more a student trusts the teacher and follows his recommendations. This is where national specifics show up. Unfortunately they don’t show domestic students in a favourable light as they are used to rely only upon themselves. Domestic students are not used to discussing unsolved tasks with teachers, are not used to doing homework in time. I believe that working alongside  international students who usually try to get as much as they can from a teacher will be a fruitful experience for them.

— What are you trying to achieve on your course?

— I want  the students to understand the subject ‘from the inside’. The aim of the course is to make sure students can effectively use the methods of representation theory in problems which are not actually part of this theory. To do that, they need to have a deep understanding of not only the key theorems (even with all the details of proofs), but also the mechanisms responsible for these theorems.