Math programs in Russia and post-Soviet states - how do they compare to US?

Question

I studied math in college and also took a few years of Russian. For a time, I was looking for a way of living in Russia post-graduation (well before the recent war) and I asked one of my professors, who spent about half the year in Russia, about entering a math graduate program there. She said I had no chance, as a high school graduate in Russia knew about as much math as someone with a math undergrad from my college, a well-regarded school in US, a but liberal arts college so not as intense of focus on major -- the math program was designed to be completable with only 12 courses for someone who hadn't taken any calculus in high school.

I never ended up going to grad school (in the US or Russia) but I have thought about this comment occasionally since then when I hear something about Russia and math. My assumption is that the professor doesn't even know what math looks like after calculus, and that she was pulling things out of somewhere, but I'm curious whether anyone knows more. My impression has been that in Russia there is/was a much greater emphasis on applied mathematics compared to 'pure' mathematics (not sure whether that's a loaded term, but hopefully you understand what I mean).

While studying for a few months in Russia, a friend I made showed me some sort of standardized high school mathematics exam, I think a college entrance exam. I can't remember any specifics but I think it used math that is taught in US schools but in significantly more difficult / complex ways than say, the SAT or even the SAT subject test (RIP). Based on that, my guess is that Russian high school students on average have a higher comprehension of the subject material, but that what the material is is not far off from the US. As for how a college math program in Russia compares to the US, I have no idea. I'd be interested in anything anyone with more experience or knowledge can share about the similarities and differences across high school, undergraduate, and potentially graduate programs.

Answer 1

As for how a college math program in Russia compares to the US, I have no idea.

I can speak only about how it was at Saint-Petersburg State University back in late 80's, early 90's when I was first a student and then a graduate student there as a pure math major.

The key differences are:

0. The education was not only free, but the students were paid quite decent stipends. There was a basic amount that you would get if you maintained a decent academic record, 25% raise to that if your record was really good, and 2.5 times the base if it was truly outstanding (Lenin stipend).

1. The syllabus for the first 3 years is rigidly structured. One should take certain courses in a certain order. Many courses are interdependent even when run concurrently and professors coordinate with each other to make sure that the proof in one course today could rely on a material from another course from yesterday. The electives appear only during the last two years when all basic are covered and you can choose which part of math you are more interested in.

2. Everything is done rigorously with full proofs (entirely self-contained) and done just once (in exceptional cases twice). No "gentle introductions", hand-waving, etc. first. You are thrown into the water from day one. The pace is rather fast. If you cannot catch up, you are out and that doesn't bother anyone (they are always ready to help you if you ask for help, but there is no babysitting, grade adjustments, or anything else like that)

3. There is a separate recitation section for every theory course. Usually the theory is presented in large lectures (100+ students in a room) and recitation groups are 20-25 students. Before you can take an exam, you should get a "zachjot" in the recitation section (pass/fail).

4. Exams are oral. You should answer a theory question, then show adequate knowledge of the entire course by answering several additional questions. That gave you 4 (an equivalent of B). If you want 5 (A), you should also solve a problem, for which they allow you an hour or an hour and a half. The problem is usually not extremely difficult, but requires some thinking, not merely an application of a ready theorem.

5. Starting from the 3rd year one should write a piece of original research every year (not necessarily a groundbreaking one, but still not a mere compendium of what is known). Mine was pretty good in year 3, in year 4 the results were rather weak, but still passable, and the final 5th year (when it becomes your "diplom", i.e., the work based on which you get the final certification) was stellar (so my later candidacy of science thesis was 80% based on it). I don't know how other people managed and how strictly the "original work" requirement was enforced, but formally it was there. Nobody would give you a master's degree for just rewriting a dozen pages from an old treatise with fewer than 3 mistakes per page, as I often see in the US.

That is the undergraduate education.

Graduate one was easier: you were supposed to

a) work on your thesis with your adviser,

b) take a few math courses of your choice (and a few compulsory one like "Scientific Communism", of course, but in 90's the teachers of that junk were quite confused themselves about what direction the next gust of the political wind will blow in, so they behaved less aggressively than usual; I got away with 3 (C) knowing next to nothing, and that was sufficient to be allowed to defend)

c) Teach a few recitation sections.

Then you ended with your defense, got the first (candidate of science) degree, and could look for an employment.

If you want to know more details, feel free to ask more specific questions. Note that the Saint-Petersburg University was considered one of the top 3 schools in Russia (the other two were Moscow and Novosibirsk). My friend and colleague from Rostov region always tells me that the metropolises were not real Russia at all and that in their university it all was rather different, but I can tell only what I saw with my eyes and only to the extent I remember it now.

What to consider an advantage and what to consider a disadvantage of such a system compared to the US one can be argued about forever. IMHO, every system can be made to work efficiently if you execute it exactly in the way it was intended and keep in mind that the main goals of an academic institutions is research and education.

Just my two cents, as usual :-)

Answer 2

Since you believe "the professor doesn't even know what math looks like after calculus" your professor is evidently not a mathematician, so her belief that "a high school graduate in Russia knew about as much math as someone with a math undergrad from my college" could reasonably be dismissed. For example, Russian high schools do not teach real analysis or abstract algebra, which are standard course requirements at universities for math majors. At the same time, her belief that the minimal requirements to get a math degree at your college are inadequate preparation for math grad school in Russia is surely accurate, as someone in the US wanting to go to math grad school should be doing more work in math than the bare minimum to get an undergraduate degree. Undergraduate math degree requirements in Europe (not just Russia) are much more substantial than in the US since math students in Europe take courses essentially only in math for all 4 years, and thus they graduate with more substantial knowledge, which would be assumed of the incoming math graduate students in Europe.

Answer 3

[Pre-emptive apologies for the anecdote nature of this answer...and standing by for my DS -1 bonk. But in case it helps you.]

I had interactions with two Russian (ex Soviet) chemists, shortly after the end of the Cold War. I was extremely impressed with their command of math and physics. And they were not even physical or theoretical physical chemists. They were lab guys. But they knew the Bessel functions and Drude model (a solid state physics thing) way better than I expected. I remarked to both of them on this in admiration and they said it was the norm. Now...I still think these two guys were smart, regardless...but all that said, the training was pretty hard corps.