Maths in the society / Study experience

East vs West: where do they train better mathematicians?

Maths always stays the same, no matter where you live, what language you speak or what you do. However, studying maths can be a completely different experience depending on the country or even university you’ve chosen. While doing my degree I’ve spent some time at four universities in two countries (unless you believe that Scotland and England count as separate ones): University of Warsaw, University of Edinburgh, University of Reading and Imperial College London. This experience showed me that Polish and British universities differ. A lot.

Having studied three years in Warsaw I came to Edinburgh, apprehensive that I won’t cope with demands of such a good university. Studying in the institution ranked as one of the best in the world must be extremely demanding, right? Well, not if you’ve gone through Faculty of Mathematics, Informatics and Mechanics in Warsaw.

The attitude of maths professors in Central and Eastern Europe is completely different than those in Western countries. In Poland students are expected to gain much deeper knowledge than in the UK. Even our semesters are longer: fifteen weeks per term gives us annually about two extra months compared to the time British students spend at the university. We use this time to dig into complicated proofs.

One thing that struck me in UK is that professors sometimes skip proofs and focus on applying the theorem in various exercises. I don’t think this ever happened in during my first years: a theorem not proven during the lecture cannot be used in the test, unless you’re brave enough to prove it yourself. This has taught me that mathematics isn’t an experimental field. Even if a rule works for hundred examples, in the hundred first it might fail. I remember graduates of a famous mathematical high school getting annoyed that they had to learn complicated methods of solving some types of problems even though they had learned much easier ways at school. Well, they had to wait for a long proof (as far as I remember, proving L’Hôpital’s rule took our professor more than ninety minutes). By the way, lectures and tutorials in Warsaw lasted that long (without breaks), so 50-minute slots in Edinburgh felt really short.

Tutorials also look completely different. I was used to a standard classroom filled with ten to forty students, where the number depended on the tutor’s reputation. We were meeting there once or twice a week to spend 90 minutes watching our professor solving some example problems on the blackboard. Alternatively some students were “volunteered by” the tutor to solve it in front of the whole class. As you can imagine, the quality of tutorials highly depended on its leader, thus in the beginning of each semester we used to beg, threaten and use various tricks to get to the group we wanted – but this is a topic for another post.

Then came the time for my first tutorial in Edinburgh. I walked into the classroom arranged in small tables, sat down and started to wait. And wait. Finally I asked a classmate if I’m in the right place and when the tutorial is supposed to start. He looked at me surprised and answered: “It has started fifteen minutes ago. We are supposed to solve this set of problems”. Tutors were just walking around, answering questions and giving hints in case someone had a problem. No blackboards, no formal tutoring, just independent study with peers. It made sense, especially considering that the exercises were rather standard ones, not the hard-core problems sometimes given at my first university.

Studying is fun but it always finishes with exam session. Again, they look different in Poland and the UK. First of all, in Warsaw we had at least one mid-term exam for each course, while in British institutions there were only finals. I became used to coming to an exam with snacks, drinks and all my stuff, sitting where I wanted to and writing down my name on my own paper. The atmosphere was quite relaxed. Honestly, no matter how hard we had studied, it was easy to fail, because in most courses we could forget about easy exercises. Getting non-solvable problems also happened.

How does it look in the UK? Everything is so formal! Our id’s were checked, we couldn’t bring anything but pens and pencils, had to encode our names etc. At first it made me feel very tense – but then I saw the problem sheet and smiled. British exams are constructed in such a way that an average student should become the average grade. If one studies hard, she won’t have troubles getting the highest note. After one of my exams students wrote a complaint that there wasn’t enough standard problems, just the “difficult” ones. The exam was quite hard but passing it wasn’t an issue, even though in my opinion it was the hardest course I took in Scotland. In contrast, in Warsaw failing half of the students is normal. Only about one third of freshers succeeded to graduate; these numbers are way higher at British universities.

Another difference that struck me is the attitude towards applied mathematics. Applied courses in Poland looked similarly to pure ones. Namely, first we had to master the theory and proofs, later we could think of applying them to an example that would illustrate the theoretical idea. Thus applications are viewed as examples confirming the theory rather than research goals themselves.

When I enrolled on applied postgraduate program in England, I was surprised by the approach. Here we first find an interesting “real world” problem and only then seek appropriate mathematical tools. Sometimes we even don’t worry about the proof that a method works – as long as it gives desired results, everyone is happy. Moreover, I was shocked to hear that many of my peers are interested in computational mathematics. I must admit that in Warsaw most of students (including myself) neglected this course completely. Hardly anyone considered it “real” mathematics, even the lecturer was a computer scientist rather than a mathematician. In England I learned to appreciate computational mathematics as a “proper” area of maths. What’s more, I even decided to focus my research on computational methods.

I could keep listing differences I noticed. I’m not writing about cultural issues, which also strongly influence studying experience in both countries. You might wonder how I’d compare these periods in my education. Is British system better than Polish or the other way around? I see benefits and drawbacks of both approaches, I’m also glad I could experience both. University of Warsaw gave me the strength to keep studying even when my results weren’t satisfactory or I heard from lecturers that I’m useless and should rather study history (why history?!). In Poland I also gained a strong theoretical background that I feel many British graduates lack. On the other hand, only in the UK I feel that my research is actually useful. Here applied maths goes hand in hand with other sciences, because we solve real problems. Moreover, studying here is just easier, one can be confident that hard work will provide good results.

To sum up, I would recommend changing universities and countries for at least one semester. It gives a great perspective on what we are doing. I’m aware that this sounds like a cliché, but this experience really broadened my horizons. Diversity enriches the scientific world, this is why so much amazing research is done in collaboration with scientists from different backgrounds. If we were all the same, the world would be so boring!

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