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Is mathematical education better outside UK and USA? Studying in UK I noticed that the Uk syllabus of 3-4 modules per area of mathematics, is often easily covered by one module in central Europe, for instance Italy or Germany. Looking online, I found out (link in the comments) that each year students in UK study between 300 and 600 hours less than anyone else in EU. The result is that a second year student in Eu has more skills and knowledge of a Master student in the UK.

Someone might argue it is quality not quantity that matters, however if we compare the exercises or the exam papers, EU exam papers are clearly richer and harder. Also, I challenged my tutor to solve one tricky exercise from a first year module in mathematical physics and he didn't know how to solve it, despite being an internationally renewed professor.

Is mathematics really taught in a better (surely different) way in mainland Europe compared to UK? If so, then way is it common knowledge that UK/USA degrees are worth more? Is a maths degree from the UK or USA REALLY equivalent to one from mainland Europe?

Here is a link to lecture notes of a "Mathematical Physics" module in Italy, I know you won't understand the language, but most words are similar in the titles, so you can have an idea.

Fisica-Trento

EDIT: Here you can compare some lecture notes they are all from first years.

Foundation of Analysis - Imperial College

Analysis 1 - Imperial College

Mathematical Methods 1 - Imperial College

Mathematical Methods 2 - Imperial College

University of Pisa - Analysis 1

University of Rome - Analysis 1 -FOR ENGINEERS, not even mathematicians!

EDIT: The description of the bounty is wrong, I thought I was assigning the bounty to another question, I apologize, I got confused.

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    $\begingroup$ I have no experience in universities but there is one thing I want to point out: sometimes, the large amount of topics (especially in mathemathics) does not equal more knowledge. I have this experience with engineer students in Germany: they learn even differential and integral in high school, but when they go to university sometimes they cannot even multiply fractions (they forget it because they did not have the time to practice). So what I mean, that maybe the less amount of topics equal more depth. What you could also compare is the time spent in lectures + on doing homeworks altogether. $\endgroup$ – ylka Dec 6 '16 at 15:03
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    $\begingroup$ @ylka thank you for your comment! What you say is true, we do spend more time on things compared to them. And I guess this has it's pros! However, is not the quantity a bit important as well? I mean whether you want to do a PhD or go to work, it would be silly if they had to teach you a huge amout of maths in order for you to do research or to work. I mean, they hire maths undergraduate and they should already know a lot of things and techniques, I guess $\endgroup$ – Euler_Salter Dec 6 '16 at 18:41
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    $\begingroup$ @Euler_Salter When you do a PhD, 'they' don't teach you maths. You learn the maths. If you have a strong enough background, picking up new maths should be comparatively easy. $\endgroup$ – Jessica B Dec 8 '16 at 8:07
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    $\begingroup$ "they learn at least 5 times more things than I learn": I wonder if they really learn. To run through a topic before you are truely ready for it, is not really to learn that topic. $\endgroup$ – Joseph O'Rourke Dec 10 '16 at 2:47
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    $\begingroup$ You are focusing specifically on this mathematical physics module. First, I assume you are taking into account that the starred sections are "not necessary" for the course, i.e., the students are free to ignore that stuff. I would also assume (perhaps incorrectly) that the appendices are not necessary. It's entirely possible that the lecturer lectures one way and examines in another: the students may not be expected to understand it all and may just need to know how to calculate. It's also entirely possible that the lecturer is disastrously misjudging his audience. $\endgroup$ – Will R Dec 11 '16 at 5:23
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First off I would like to point out that at least one of the things you're comparing is a bad comparison. Mathematical Physics (or in my country just mathematics for Physics majors) will have a completely different breadth to any standard math course for mathematicians.

Physics majors don't have to care too much about proofs and theory but they need to get up to speed in calculations and basic understanding of mathematics extremely fast. Pretty much all of Physics assumes familiarity with decently hard differential equations, hard linear algebra and some to lots of numerical analysis and methods. They need to catch up very fast so the physics make any sense.

I remember back in my undergrad I was flabbergasted what my friend taking physics knew from Mathematical Analysis. He could solve complex differential equations at a time we were still developing a theory of the real numbers and could hardly do any limits. On the other hand he obviously had no clue what a real number was or how to construct it because it was useless for him.

Having that out of the way, I can't quite compare the UK, but I have a decent knowledge of the USA and the Czech republic. What I found is that what exactly you learn when you get a BC. in math in the USA is extremely student dependent. You can learn "almost no" math taking something like 16 credits worth of math courses or you can learn tons of math including taking advance MA/PHD levels courses. So how much you learn is often up to you rather than the institution.

In the Czech republic I ended my MA equivalent with roughly 200 credits of math courses for comparison and most of them would be high level undergrad or low level graduate type courses in the US.

That said in the USA there are some very considerable breadth level requirements meaning that you have to take lots of non math courses as well. And at the PHD level the US all of a sudden tightens up a huge amount and the courses are IMO often better (if not by a huge amount) than in Europe.

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    $\begingroup$ I am so sorry but I mislead your answer. "Course" and "Modules" are false friends for me. Of course I meant "Mathematical Physics" as a module of the Mathematics course, not the degree in Mathematical physics! So the lecture notes that you see attached, which cover tons of my modules and more, they are the lecture notes of ONE MODULE. In their first year. Which is extremely advanced! However, thank you a lot for your answer! $\endgroup$ – Euler_Salter Dec 6 '16 at 10:45
  • $\begingroup$ @Euler_Salter No you misunderstand me. I was also talking about once course/module. I'm just pointing out that courses in Physics (even when taught as part of a mathematics curriculum) often go to a very different level of depth. $\endgroup$ – DRF Dec 6 '16 at 11:13
  • $\begingroup$ okay now I understand. This could kind of justify that module, however this thing happens in every module. For example Analysis or Linear Algebra. With one course in Analysis, they study more things than 3 of my courses $\endgroup$ – Euler_Salter Dec 6 '16 at 12:48
  • $\begingroup$ I know you probably won't understand everything, but could you have a look at the hyperlink in the question and give me your opinion about it? Meaning, do you reckon it cover more or the right amount of stuff for a first year, undergraduate module in physics for mathematicians? Just based on your experience! Thanks $\endgroup$ – Euler_Salter Dec 6 '16 at 18:38
  • $\begingroup$ @Euler_Salter Reading a math book in italian is new for me and while I understood more than I expected I still understood nowhere near enough. That said the way I read the prerequisites for the course/book they seem to be differential and integral calculus general topology and fundamentals of mathematical physics. I would not assume a typical first year undergrad to have a thorough grounding in these. The actual contents of the book seem reasonable enough for a year long (rather then semester long) course. It doesn't seem the book goes into much detail. $\endgroup$ – DRF Dec 6 '16 at 20:11
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Part of the answer to your question is that the statement 'mathematics is considered good in the UK and USA' refers, I believe, to research mathematics, not to undergraduate teaching.

I don't have direct experience of education on the continent, although my colleagues do. There is a significant difference in standard. The culture and the education system are much more in favour of mathematics. The UK system, and even more so the US system on average, do not generally leave students well prepared to study maths at university level.

However, I still find it implausible that the difference is as much as you say. That your tutor can't do a first-year exercise raises a red flag for me. He will be an expert in the sense that he is good at using general understanding to address even unfamiliar questions. That he can't do it suggests the solution depends on some particular piece of information or a trick in the method. If you have been shown what to do, the question would be much easier to solve.

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I'm from Hungary and the level of physics education is pretty good compared to the UK (my graduate friends have no problem getting jobs there). However, I'm a bit confused, as A-levels exams are more difficult than our national exam, with the STEP exam much more difficult. I guess Cambridge is stronger than the best Hungarian universities.

Who is your tutor, if you don't mind?

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  • $\begingroup$ That's the point! Every person I know in Italy who studied mathematics and wanted to study further, after the bachelor, and decided to study abroad, had no difficulty in securing masters or PhDs at Cambridge, Imperial or Oxford. Whereas from a UK point of view is supposed to be very difficult. I haven't watched the A-levels exams to be honest, but also in high school, we do much more than A-levels, but again I think this happens often in Europe. I won't tell you his name, as he clearly wouldn't like other people to know he could not solve the problem ahah $\endgroup$ – Euler_Salter Dec 11 '16 at 23:55
  • $\begingroup$ @Euler_Salter Possibly the PhD places isn't a fair comparison. Are these people getting funded places, or are they bringing funding from Italy? Also, what proportion of students go to university in Italy? $\endgroup$ – Jessica B Dec 12 '16 at 7:40
  • $\begingroup$ STEP papers are very much not the norm, so shouldn't be used too much to judge standards. $\endgroup$ – Jessica B Dec 12 '16 at 7:40
  • $\begingroup$ @Euler_Salter What was the first-year problem? I think a good problem solver is not one who can solve something at first sight, but who knows how to get to the answer. Good problems are meant to perplex people at first sight. $\endgroup$ – GregT Dec 12 '16 at 10:40
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    $\begingroup$ @JessicaB I think he meant funded places, at least I did. I think A-levels is a pretty good standard, too, especially compared to SAT. STEP is harder than that, but IMO not that much harder. Maybe the UK has strong research because it has money to attract the best? $\endgroup$ – GregT Dec 12 '16 at 10:42

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