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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.

Euler_Salter
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    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. – ylka Dec 06 '16 at 15:03
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    @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 – Euler_Salter Dec 06 '16 at 18:41
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    @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. – Jessica B Dec 08 '16 at 08:07
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    "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. – Joseph O'Rourke Dec 10 '16 at 02:47
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    While it is interesting to compare different levels of mathematics and mathematics teaching in the world and delve into why they differ, parts of this question could be phrased more diplomatically and certain assumptions could be re-examined. For instance, can any first year student in mainland Europe easily beat a postgraduate student in the UK? I find that doubtful, to say the least. Furthermore, while I cannot speak for mathematicians in the UK and USA, I wouldn't be surprised if they do not overly appreciate the phrasing "childish game". – J W Dec 10 '16 at 11:57
  • @JW I admit I could have phrased it more diplomatically, my emotion was rushed into the question. About your question, it seems unlikely yeah. Although, can any second year or third year mainland student beat a postgrad? Well, if the /third year had a first, I would bet my money on him/her. I can give you an example: a guy in my Alevels used to be good at maths, but couldn't achieve my results. Now he studies in Trento, Italy and when we talk about maths, I always have to pretend I know what he is talking about, as we haven't done most of what he studied there. This is alarming! – Euler_Salter Dec 10 '16 at 15:11
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    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. – Will R Dec 11 '16 at 05:23
  • On a separate note, if your friend speaks about maths you don't know, you should just ask him; if he can understand it, what's stopping him from explaining it to you? And if he can't explain it to you, does he really understand it, or is he just saying words that he knows go together? For another matter, have you asked your friend how he found this module? Perhaps he didn't understand almost any of it at the time but then worked through books and pieced some things together over the summer. Either way, I'm sure there's some bit of maths (perhaps not in physics) that you know and he doesn't. – Will R Dec 11 '16 at 05:25
  • Finally, taking a look at the overall course structure of their bachelor's and master's degrees, I'm not seeing anything special. They focus on analysis, geometry, physics and computing in the first two years and in the third you get to specialize; in particular, Galois theory is a third year module, as is differential geometry, ODEs and "algebra". Assuming that the geometry in the first two years is mostly linear algebra, this more-or-less the standard in the UK. At Masters level they have algebraic geometry, topology, PDEs; nothing too surprising (perhaps Hodge theory? But maybe not). – Will R Dec 11 '16 at 05:34
  • @WillR I didn't ask him as I didn't wanna seem ignorant, as we all think education in UK is better than in Italy. However, this Christmas I might try to ask him how much he understood of it and how he found the module in general. The starred sections are not necessary yeah, although they are a very minority wrt the whole syllabus. And what you say is correct, it might be any of the possibilities you listed. Although it would be strange that a first year lecturer was unprepared. – Euler_Salter Dec 11 '16 at 14:50
  • @WillR So far, the only bits of mathematics that I studied and they didn't are Mathematical Modelling (Game Theory and markov chains (not sure about this one)mostly). Indeed, statistics they cover the syllabus of 2 of my stats modules, in linear algebra they cover Linear Algebra 1 and Linear algebra 2 and other modules, except from the topic of Group Theory, which they do in Algebra anyway. I'll try to put up a comparison between the syllabus so you'll actually see the difference, which from the outside might seem less than it is! Thank you for your research! – Euler_Salter Dec 11 '16 at 14:57
  • Yikes, dumping all the course descriptions to your entire baccalaureate program is totally unhelpful to the question. It doesn't even clarify what you're asking, and I think this currently the longest "question" I've seen on SE; total clutter. – Daniel R. Collins Dec 12 '16 at 23:38
  • OP: I cannot quite parse what you are asking. The only reason that I am not voting to close the question as unclear right now is because there is an open bounty preventing me from doing so. What is the actual question? – Benjamin Dickman Dec 13 '16 at 00:09
  • @BenjaminDickman I was hoping in somone with actual experience both in UK/USA and EU to tell me if there is actually a real difference. Furthermore if there is, how come globally we think Uk/Us education is the best – Euler_Salter Dec 13 '16 at 04:35
  • It is unreadable in its current form; I strongly suggest that you significantly abbreviate it and include only necessary details, along with a clear demarcation of where the well-formulated question is being asked. – Benjamin Dickman Dec 13 '16 at 04:38
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    @Benjamin Dickman , you are right, I've been adding too much information. Tomorrow I will edit it and cut off the unnecessary – Euler_Salter Dec 13 '16 at 04:41
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    Consider the distributions of learned ability by country. One country can have a lower mean, but a heavier upper tail. This is what happens in the US compared to some countries. There is no "system" in the US. There is no homogeneity. A talented student can progress much faster than she would in any kind of standard curriculum, while a typical student can finish a degree program without knowing some basic things. – Dan Fox Dec 15 '16 at 15:43
  • You never said whether or not your friend was comfortable with the material. I highly recommend asking your friend what he thinks; after all, he took the course and therefore knows how hard it was, how much of the material he was really required to learn, etc. – Will R Dec 24 '16 at 04:02
  • @WillR I haven't asked him exactly how much of the material he did yet. However, about being comfortable, he says he is, after all he loves maths and physics, although he complained that during term time he couldn't do much else apart from uni and skiing every once in a while and seeing friends in the weekend. On the other hand, in my uni most students joined 3-4 societies and go clubbing 3-4 times a week. So there clearly is a difference in the amount of material, considered that I havent met yet UK student who was ever taught how to study faster and smarter. – Euler_Salter Dec 24 '16 at 12:08
  • @WillR so he is comfortable, but it clearly takes much time to learn. I will probably see him after Christmas and let you know about the material – Euler_Salter Dec 24 '16 at 12:09

3 Answers3

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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.

Jessica B
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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.

DRF
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    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! – Euler_Salter Dec 06 '16 at 10:45
  • @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. – DRF Dec 06 '16 at 11:13
  • 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 – Euler_Salter Dec 06 '16 at 12:48
  • 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 – Euler_Salter Dec 06 '16 at 18:38
  • @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. – DRF Dec 06 '16 at 20:11
  • @Euler_Salter All together this does remind me somewhat of my first year of physics for mathematicians which was quite broad rarely went into much detail and I didn't understand most of the math we used until two years later. But it is really hard to estimate what the course actually covers without at least seeing a final exam or similar. It might be a really hard course (600 pages is quite a bit to cover even in a full year course) usually 200 is the limit for a semester if you're really trying to understand or it might be a first dip and quite easy if most things are skimmed. – DRF Dec 06 '16 at 20:14
  • Thanks for trying to read it; although mathematics is a universal language, Italian is not. However, the information about the length of the module and the year it is taken, is correct. Indeed, I got this information from the university website and even from the lecturer's webpage, who teaches it. It looks impossible to cover in a year, worse in a semester! Furthermore, they do a bit of topology in "Mathematical Analysis" so they do have a foundation in it. Also, in my "Introduction to Applied Mathematics" module, as a comparison, we only study classical and Lagrangian mechanics! – Euler_Salter Dec 06 '16 at 20:37
  • thank you for your comments and opinion, maybe I should have a closer look to the exam questions, which might indeed be easier! – Euler_Salter Dec 06 '16 at 20:38
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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?

GregT
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  • 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 – Euler_Salter Dec 11 '16 at 23:55
  • @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? – Jessica B Dec 12 '16 at 07:40
  • STEP papers are very much not the norm, so shouldn't be used too much to judge standards. – Jessica B Dec 12 '16 at 07:40
  • @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. – GregT Dec 12 '16 at 10:40
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    @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?

     – GregT Dec 12 '16 at 10:42
  • @JessicaB and GregT I will answer to both soon, right now I'm at uni. From my limited knowledge I think STEP papers are seen as some sort of higher proof of your mathematics abilities, required by only (i guess) the best universities. They are harder than A-levels and Exams of probably most countries in the world. However they are not harder than test used for the same reason by other universities. See Scuola Normale Superiore - Pisa, whose exercises for admission are often quite harder than International Mathematics Olympic games for our ages. So Step3 is average for that kind of test! – Euler_Salter Dec 12 '16 at 14:22
  • Also, I found a partial reason for all of this: https://en.m.wikipedia.org/wiki/European_Credit_Transfer_and_Accumulation_System . Total hours per year(both selfstudy and at uni) UK: 120×10 =1200. Total hours per year (both selfstudy and at uni) EU: 60× 25 or 60×30 = 1500 or 1800. Hence the rest of EU studies on average 300/600 hours more than UK. Considering that a semester in Uk has 60 credits of 10 hours, this meas that per year, they accumulate an extra whole semester, which means 4 MODULES MORE THAN UK! At the end of the bachelor will be 12 MODULES MORE! – Euler_Salter Dec 12 '16 at 14:36
  • The funny thing is that in the UK the cost is £27000 for a three year course and it is increasing with inflation. This is a very big case of false advertising, as usually done by english-speaking language countries. So again a second year student in EU, could be almost at the same level as a third year student, at least. Indeed EU student: 3000 or 3600 hours of study done, UK third year student 3600 hours. – Euler_Salter Dec 12 '16 at 14:40
  • Finally, "The state does not control university syllabuses" as can be found here https://en.m.wikipedia.org/wiki/Education_in_England – Euler_Salter Dec 12 '16 at 14:49
  • @Euler_Salter Thanks for telling us about SNS and it's admission exam. I didn't find practice exams, do you have it? My only objection is that SNS is not a university by itself; Hungary also has a similar special college, with a difficult entrance exam (but by no means Olympiad level). You are free to choose how much do you study for a particular subject :) What do you mean by false advertising? – GregT Dec 12 '16 at 21:12
  • For example http://www.sns.it/sites/default/files/documenti/07-09-2015/prove_di_ammissione_al_i_anno_di_scienze_a.a._2015-16.pdf just google them you can find them. Well mostly because I found out (I was ignorant, I have to say) that the league tables are written specifically by private organizations which clearly put certain universities in the first places when they shouldn't – Euler_Salter Dec 12 '16 at 21:40
  • On cost: the cost of a degree and what the student contributes are not the same thing. Tuition fees have rocketed in the UK because the state has massively reduced the share that it pays, not because the cost of provision has really changed. – Jessica B Dec 13 '16 at 06:38
  • On STEP papers: these are considered to be basically the Cambridge entrance test. They are not something you would typically get any teaching for, beyond what your teacher can spare after school. So it comes back to what you mean by difficult. Complex questions you've been taught to answer can be easier than simpler ones you have to work out for yourself. – Jessica B Dec 13 '16 at 06:44
  • @Euler_Salter Thanks for the document! I'll have it translated so I can see :) – GregT Dec 13 '16 at 12:52
  • @Euler_Salter Do you mean the "Top 100 universities" lists are biased?? Interesting. Do you have a link for proof? – GregT Dec 13 '16 at 12:54
  • Well the very top not, mit, oxford, cambridge standford for example. However I would say I wouldn't be surprised if the rest was biased. Clearly we know those 4 universities are probably the best for Stem subjects for the results of their graduates, for their lecturers and for the amount and quality of pubblication they have. However for the rest, I don't know now.. finding out all these things should make you doubtful! – Euler_Salter Dec 13 '16 at 14:29
  • @JessicaB, to be honest, I didn't know the reason for the drastic change in tuition fees! For steps, it makes sense yeah – Euler_Salter Dec 13 '16 at 14:31
  • @jessicaB http://www.istat.it/it/files/2016/11/Studenti-e-bacini-universitari.pdf page 24, 1.696.969 university students in Italy in 2013 (sum them up, politecnico is still a type of university which specialises in engineering). However notice at page 25 ONLY 72.223 are not Italian. Hence 1.624.736 are Italian university students. – Euler_Salter Dec 13 '16 at 16:17
  • @JessicaB, now notice http://www.universitiesuk.ac.uk/facts-and-stats/Pages/higher-education-data.aspx that there are 2,268 million students (2014) in Uk with 1.83 million UK students in total. However an important difference is the following: we do not have (apart from 1 or 2 in Milan) universities with "soft-courses" like theatre studies, dance, fashon etc. We have schools for them and therefore these students are not counted here. – Euler_Salter Dec 13 '16 at 16:26
  • @JessicaB hence you need to remove some students from the count. https://www.hesa.ac.uk/data-and-analysis/students/courses, here 166k students go to arts and creative studies at uni. To make a correct calculation then we can check at the same url and see that 42390 students study maths in UK. I couldn't find the same data from Italy but http://statistica.miur.it/Data/uic2008/Gli_Studenti.pdf here at page 45 table 2.2.2 73k students study natural sciences. That's the best information I can get, which means more maths undergraduate in UK – Euler_Salter Dec 13 '16 at 16:36