The Most Important Thing at HSE’s Faculty of Mathematics is the People
Graduates of the Faculty of Mathematics at HSE, Andrey Ionov and Lera Starichkova, who have since enrolled in educational programmes at leading international universities, spoke about their love for mathematics, the level of the Bachelor programme at HSE, and admission to foreign PhD programmes.
Andrey Ionov, PhD programme in Mathematics, Massachusetts Institute of Technology (MIT)
My parents instilled in me a genuine interest in science. In addition to the occasional cartoon, I also watched a lot of documentaries, and on weekends my family and I went to museums. As I got older, I started going to meetings of various clubs and having additional lessons. I also participated in Olympiads in biology, history, mathematics, physics and chemistry. In the sixth grade, I started going to a maths club at the MSU Faculty of Mathematics and quickly discovered that I had much more common with its members than I did with my classmates. In the eighth grade, I enrolled at a high school specializing in mathematics and began to study mathematics and physics on a more frequent basis. At a summer school, a student teacher noticed my interest in more advanced areas of mathematics and advised me to attend classes at the Independent University of Moscow (NMU). As a result, by the time I graduated from school, I was already at second-year level.
Everywhere I studied, I had teachers who recognised my interest and encouraged me to develop it.
Lera Starichkova, Master's programme ‘Mathématiques et Applications’, University Paris-Sud
My involvement in Maths Olympiads began in the sixth grade. There were evening maths lessons at my high school and also a maths club for students. We began to participate in Olympiads and other competitions. I liked the process of solving logical problems and, in the eighth grade, I chose to pursue mathematics. I had many fantastic teachers for various subjects, but I still found mathematics easier to understand than other classes. Therefore, there was no question as to what I would study at university. I had heard many positive things about the Faculty of Mathematics at the Higher School of Economics, including from my own sister. I decided to enroll.
In my first year, I worked a lot: I was an assistant at the Faculty of Mathematics, the Faculty of Computer Science and the New Economic School. I led maths club meetings and I tutored. I also wanted to try my hand at applied mathematics, and so I chose the Master's programme ‘Mathématiques et Applications’, which consists of two independent years of study: Master 1 and Master 2. I chose the programmes ‘Voie Jacques Hadamard’ and ‘Analyse, Arithmétique, Géométrie’.
What Are the Advantages of HSE
Andrey Ionov: In my opinion, what HSE’s Faculty of Mathematics has going for it is the people, both employees and students. My interaction with them has played and still plays an important role in my mathematical development. Many of the teachers are world-class mathematicians who not only regularly give lectures, but are also always ready to help students. In addition, leading mathematicians from all over the world often visit as guest lecturers. A lot of students are actively engaged in mathematics. This makes it possible to discuss mathematical problems, understand them, and ask questions. Independent student seminars are frequently organized where you can share the results of your scientific work, discuss articles and so on. I believe that community is very important when it comes to maths and other fields of science, and the more active it is, the more successful the university is. Inthissense, HSEisaverystronginstitution.
In terms of other more ‘practical’ advantages, students are able to decide on their own curriculum. There is also a common room and scholarships available for those who need them. Students who work as interns at the laboratories are eligible and there is also financial support for participation in international schools and conferences.
Lera Starichkova: At the Higher School of Economics, we had a large workload. To solve mathematical problems, we had to do a lot of the work ourselves - search for the necessary theory, communicate with other students and ask the teachers for support if we needed it. Of course, the skills we developed as a result are extremely valuable, but the process itself takes a long time. Subsequently, in my fourth year, I was exhausted - more morally than physically.
By contrast, I found the first year of the master's programme at Orsay easier than my first year at HSE. Courses at Orsay have a larger number of contact hours- a general course consists of 5 hours of lectures and 6 hours of seminars per week, whereas at HSE there are only 1.5 hours of lectures and seminars. However, the amount of material given to students was even greater than at Orsay. For the first time, I thought about the level of the Bachelor's programme at the HSE. On the one hand, I had a great head start upon my arrival in France, but on the other hand, there was simply not enough time at HSE to explore individual topics in more detail. At Orsay, I had the opportunity to do just this.
What Mathematicians Find Interesting
Andrey Ionov: The main spheres of my scientific interests include algebraic geometry, representation theory and mathematical physics. I randomly heard the phrase ‘algebraic geometry’ while I was in high school, and I started asking teachers and friends about it. I understood the main concept, which I really liked – one can think about geometric objects (manifolds, bundles) as algebraic objects (rings, modules), and vice versa. I then realized that one of the most productive methods in mathematics of the last few decades is to think about objects of one area of mathematics in terms of another area, and to transfer methods and techniques. Also, I was excited by examples of how meaningful mathematics arises in physics, for example, in representation theory in quantum mechanics. I really like tasks inspired by physics and I started to enjoy representation theory after finishing my first year at HSE. Thanks to HSE, I have been able to develop my mathematical interests.
Lera Starichkova: In Moscow, I was working on dynamic systems with my supervisor, Yuly Ilyashenko. That is, the classification of bifurcations using graph theory. This year, I have been working on a project related to an article on number theory. I think that I was inspired by the ‘Number Theory’ course taught by Vadim Vologodsky at HSE. Generally, I like everything, it's all very interesting. The crossover between different scientific fields is fascinating. Initially, I was surprised, but now it seems so perfectly logical. At school, we always had to solve Olympiad problems in two ways, using two different approaches- this is practically it.
Of course, my main non-mathematical hobby since September has been the French language.
How to Get Into a Foreign University
Andrey Ionov: I was perfectly happy to continue my education at HSE, where I am currently studying, so I wasn’t worried about not getting into a foreign programme. For this reason, I applied only to the best universities. I had several important criteria, including a strong mathematical community and faculty, and courses that corresponded to my mathematical interests. I chose the Massachusetts Institute of Technology because it met all my requirements, and also because it is also located in the suburbs of Boston. This city is one of the main mathematical centers of the world and Harvard, Northwestern and the University of Boston are not far away and actively cooperate with MIT. Students of these universities often attend each other’s courses and seminars.
Preparation of the documents necessary for admission to a PhD programme at an American university should be done one year before the intended start. In Autumn, you have to sit several tests in mathematics and English (GRE, TOEFL), collect references from teachers who are familiar with your scientific work, and then, by mid-December, apply electronically via the university's website. References are very important and this aspect of the application should be taken seriously. Test results and written works also obviously count towards your application, such as articles, pre-prints and theses. To increase your chances of being accepted, tell a professor at the university about your application. Every year, they receive several hundred applications. Reminding them about yours increases the chances of your application being noticed.
Lera Starichkova: It was rather ambitious for me to apply for a French-language master's programme with absolutely no French skills whatsoever. The application for the programme could be submitted in English, and, in my interview with the professors, I said that I didn’t speak any French. They laughed and continued to talk to me about mathematics in English.
In mathematics, there are a lot of universal terms, which helps when it comes to studying. I was able to write down what was on the board, then translate it and go through all my notes to understand the lesson. Questions could also be asked in English. At the seminars, everything was clear, except for the odd joke and maths problems which involved a lot of text on the theory of probability.
Except for two students, all my classmates at Orsay are French and they don’t really like to speak English. This means I have plenty of opportunity to practice my French. Back in September, it was difficult to communicate and it was especially tricky to deal with all the documentation and the administration. Now, my classmates say that my French is not bad at all, and it will no doubt get better as time goes on.
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