If you watch US undergrad maths courses on YouTube, the content is essentially the last two years of German high school. Even at MIT or Harvard engineering and science students are first taught basics of derivatives and integrals with a focus on application and hardly any proofs. They later have advanced courses and the most talented students can fast track I hear, but that's the default.

In Germany you are expected to already know all that from day one. Aspiring engineers and (computer) scientists face proof after proof from the first week of the first semester. Logic, set theory, sequences, series, convergence, mean value theorem, intermediate value theorem, etc. You see hardly any numbers at all.

Where is Poland on this spectrum? I'm talking about major public universities.

by opolsce

24 comments

  1. Closer to Germany rather than US.

    I don’t speak German but I recognize some of equations from the screens above being used in first 1-2 years at my college.

  2. Well in set theory you learn set THEORY. I don’t know of anything like applied ST. Analysis, algebra it’s theory in lectures and exercises in uhh exercises.

  3. 3rd year of computer science faculty: we had to kearn how to solve systems of 60+ equasions /facepalm. Guess how many times I used it in my mature life.

  4. That kinda depends on the university (usually technical ones are more demanding regarding the study lines mentioned). Generally in the first years of Bachelor we are taught a lot of mathematics. I mean that we have subjects such as Probability, Math Analysis, Statistics, Linear Algebra, which are worth most ECTS in the whole Programme. And (at least) I have had to do all the topics mentioned by you. Also during the defense we normally are expected to present our project in a more business way, but l8r members of the ‘jury’ (usually one professor and 2 phd’s, but that’s not a rule) can ask u about whatever you’ve learned earlier during the whole programme and you rarely know what they will ask you about, because they draw the question from the ‘question bank’.

  5. Closer to germany but teachers are underfunded and hate their life.

  6. Integrals are taught in the first semester +- there is a short intensive math crash course then (it depends on Uni how they do this). After that it’s similar to what it’s in Germany.

    It works like that because Integrals are not required in High School advanced math programs and people go to IT studies from different school backgrounds – you don’t have to finish advanced math at high school to get to Uni, you need to pass abitur from required subjects at a good level.

    How theoretical is Uni depends on two factors
    – if it’s Polytechnique or University – Universities are usually less theoretical, and usually you don’t have Physics or more engineering subjects at them – but you end it with a title of “Licencjat” not “Inżynier”
    – what the school thinks is important

  8. Depends. University will almost always be more “theoretical” than Politechnika. Also depends on the university. I studied math at University of Warsaw and it was very “theoretical”. The only real life applications and numbers I saw in the undergraduate course was during numerical methods and statistics classes.

  9. Krakow university of technology has it as a first year maths

  10. Most of that screenshot, i.e. boolean logic and limits looks like my last high school year but limits were taught outside of the required curriculum when I attended. Now I think they are back in high schools?

    As others said, first two years in the STEM studies are almost all maths.

  11. I have read through those pages. I remember I had things like that in high school. So it really depends on the school you go to. I don’t think this is in the curriculum of high school tho, to that extent at least, so it would be repeated at Uni.

  12. Finance grad here but had plenty of math in my 1st and 2nd year that looked very similar to this – down to the font actually. So from that I would say definitely similar to Germany.

    But I wish that wasn’t the case. Finance is one of those where practical applications turned out to matter MUCH more than theory… I 100% understand for engineering, but for my field this theory turned out being pretty useless and I wish we had more of targeted practical application.

  13. Same in Poland, they assume you had extended math in high school, which I hadn’t. I remember my first semester at Computer Science, with all my colleagues fluent in integrals and calculus, and me being like “oh fuck me…”. That was a long and depressing semester, but I made it.

  14. I’m from U.S and can confirm the standards in Public Schools are so low. At least, in my State, I was able to take all of these courses in my first two years of High School. I was on an Engineering path for a long time so was done with all theoretical math early in High School. It was sad to see those students that just took all the basic classes and were doing geometry in their last year of High School

  16. It really depends – on my uni there is the same named track under two departments and they have very different reputations in that regard. So it will depend on uni and course you will take

  17. almost nobody has integrals during high school, but apart from that everything seems the same here as in Germany

  18. It looks like first semester of informatics or physics in the University. Not as detailed as pure maths, but quickly glossing over the main theoretical background before reaching stuff you need.

    I have watched some theoretical lectures from mathematics on YouTube and they usually start from like high school or even junior high school level.

    But it seems that Americans eventually catch on, they have less filler like foreign languages, some BS lectures that are there so you can have some useless subject BUT IN ENGLISH, PE, work and safety (ffs, I was studying mathematics, what are you thinking, that I will harm myself by licking the blackboard or what) etc

  20. I was in Warsaw Politechnic, Faculty of Mathematics and Information Science, Mathematic department.
    They were teaching derivatives and integrals from the basics, but we had a lot of proofs.
    On the first analysis exam you were supposed to be able to recreate around 60-80 pages of theorems and proofs as theoretical part of the exam and you must pass it to pass the whole subject. So you either know them all, or you need to be really lucky to pass. Also the subject was for a lot of points so if you fail it and any other subject, then you are out.
    If you pass it you could fail 2 other subjects and still be able to continue.

  21. It depends on university, i guess. But I can only speak about my uni (Rzeszów University of Technology, faculty of mechanical engineering and aeronautics).

    First 3 semesters were basically a “from zero to hero” course (aka meat grinder) about everything:
    Derivatives, matrices, sequences, series, integrals, simple differential equations, probability, statistics (in this order). 

  22. What I’ve been taught as a CS undergrad here is quite similar to what you’ve described as being the case in Germany. But where is your perception of the US system coming from? I remember referring to MIT recordings or American textbooks quite a lot (some of them explicitly recommended by lecturers) and they didn’t shy away from theory or proofs.

  23. My biggest grudge against Polish universities is that they are too theoretical, in the sense that practical applications are often overlooked which results in poor preparation for the job market. That’s why after a bachelor in Poland I went for a very practical Master in the Netherlands.

    But, to be clear, I studied economics in Poland, not Math. But that’s all the more reason why I found it to be too theoretical. It’s great for chit-chat and I guess a solid understanding of decades of economic thought but my employer cares little for that.

  24. This is a nice question which I will answer as a mathematician myself (currently my second phd year in Jagiellonian University). From my perspective the Undergraduate programme is complete in terms of which field you want to follow. If you are into Pure Mathematics, the Pure Math courses are very theoretical (as they should) and I would say dense in terms of material.

    Note that Polish school of mathematics is far more abstract than other western countries like France, Spain, Norway, Italy, at least in my field (complex analysis). Some of the best mathematicians who do research in Several Complex Variables are actually in Jagiellonian University. Topology and Functional Analysis is extremely well developed in Poland due to Banach too.

    I come from Greece, where the math bachelors is 4 years, and you need 42 courses to graduate, and this is more challenging compared to the undergrad programme in UJ, but the undergraduate programme in UJ is more focussed than what I followed in Greece.

    From my teaching experience here, I would say that Poland is the most Theoretical in Europe in terms of Complex Analysis and Functional Analysis , they focus on concepts that are quiete abstract by themselves.

    Last but not least. Polish math school might be introverted but they prosuce incredibly strong research in every field. It is a Polish trait to not be fancy or brag about anything. Thats why you may not know a lot of the Polish Mathematicians, but trust me there are many of them who thrived and still thrive. Jarnicki (rip), Łojasiewicz, Kanigowski (EMS awarded him), Dinew, Kosiński, Zwonek, Błocki among some of the matheticians with amazing work that everybody seems to neglect in other countries in europe except the ones inside the field.

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