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This question is a bit off topic probably and is quite similar to my previous question posted on Mathematics for Education here. $\textit{(If you studied in both EU and Uk, possibly studying an undergraduate in EU, I'm waiting for your answer!)}$

However I have this question quite at heart and I'd like to give to this question more popularity, in order to reach students/teacher who actually have experience in the field, which surely I can find on MSE.

My question is then:

Is undergraduate mathematics in the English-speaking countries "lighter" than in other countries, especially in Europe?

It looks so, looking at the syllabus and the lecture notes.

Examples

  • In a applied mathematics course during 1 semester in Uk, you can start from vectors/point dynamics and get to central forces or sometimes a bit of calculus of variations/langrangian, doing only classical mechanics, with no electromagnetism, termodynamics or similar.
  • In Europe in a semester they start from the beginning, they do classical mechanics, they arrive to maxwell equations, they do termo dynamics, they deeply do lagrangian dynamics, they do multi-particle systems, rational mechanics a bit of relativity and often also some topology.

This is just one example of many. Also, if you take an exam-like problem (also a tutorial-sheet like problem) from Uk compared to one in EU on the same exact topic (for example : check if a series is convergent or not) you'll see the incredible difference in difficulty. In Uk is often not required to think when doing problems, problems are always already done in class so at the exam is just about doing the same thing in a slightly different fashion, whereas in EU you actually need to think! (For example I have a high first in one of the top uni for maths in Uk, obtaining over 90% in each exam, however I still can't get even 40% in their first year Analysis exams or applied mathematics or so on. And I'm in my second year)

If this is actually the case, why is it so? And also, how come mathematics is often thought to be harder and better-taught in English-Speaking countries?

Edit As a "funny" (or worrying) example here are the notes of a semester one course called Analysis 3. This module is taken both by engineers and mathematicians in their second year. Unluckily I could only find the engineering notes as the mathematicians ones are protected by passwords, however looking at the website, this module is a 9 credits course (compare with average of 7.5 credit courses in UK), whereas the one for mathematicians is 12 credits (hence much longer and harder, as seen by the syllabus on the website) and still holds for one semester (together with other 3 courses).

The module has 5 sections:

Manifolds, Multidimensional Integration,Vector Fields Integration,Theory of Differential Equations, ODEs

Notice the depth of the modules even for an engineer. And although you can't read italian, you can certainly read maths.

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    I'd want to see some answers to this too. – 2017-01-04
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    @Michael thank you for the support! I know there are many European students and teachers here, as well as from UK and other countries. I'm sure some of them know something! – 2017-01-04
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    Comment about closing the question: As I said this is a bit off topic, however if you can please give some time to the question so that it can reach the right people, then this question will get answers and I will be able to either close the question or assign the best answer to one of them! As you see from the views and the stars, this is a question of interest for many people and it's not about maths itself, however here's the right audience for it – 2017-01-04
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    I don't think you can generalise about the (rest of - UK is a part) of Europe like you do, there's bound to be major differences between countries. – 2017-01-04
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    @Henrik I didn't add much information in the question cause I didn't wanna make it too long. However I although I am study in my university I also study the lecture notes of the same (or similar, as sometimes they are not the same modules) modules in other UK universities, such as Imperial and Oxford which publish material on the web. However, no matter how you measure it, Oxbridge, Imperial and all the top 10 universities in Uk that I could find do much much less (and much easier!) than any university in Italy (I'm italian so I can read it) or germany – 2017-01-04
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    @Henrik , the point is that I can generalize exactly because the difference is much greater. It is not a small difference. If you look at first year analysis lecture notes in EU, it normally covers the material of Calculus 1, Calculus 2, Analysis 1 and maybe also half of linear algebra 1 in UK. Each module is much longer and much harder! And the problems as well. – 2017-01-04
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    Of course there are small differences between any UK university. Similarly, of course there are small differences between any EU university. However the differences between EU and UK universities are not negligible and big! – 2017-01-04
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    Here in France, your story about "40 % in analysis test" is practically every day life. Getting 90% is physically barely possible, as the fact that you have to write your answers by hand take too much of your time. I am in my second year, and in the analysis course, only 6 people out 100 scored the passing grade on the final last year, and the average is 3,5 out of 20. – 2017-01-04
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    @JohnMayne so how do people get their bachelor? And also, have you ever tried doing any UK examination question just for comparison? Before leaving for UK I used to be pretty good in my country, but now I feel awful. One of my friends doing maths in Trento is living that life you described, but his mathematics skills are already higher than I can ever hope by the end of my MMath course – 2017-01-04
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    @Euler_Salter Just a quick comment - I have to disagree with your suggestion that "his mathematics skills are already higher than I can ever hope by the end of my MMath course". The amount you learn is *entirely* up to you – 2017-01-04
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    @TheMathsGeek sure it is!! However the meaning behind my comment is: following my courses, studying for them and passing them with a high first and having a solid understanding of those courses, still won't allow me to know as much as a student who finished their second year in EU. Of course I can learn things on my own (as I'm trying to do staying on MSE and reading books). What you say is right though, it is entirely up to me, but the issue here was: is a degree from Uk really equivalent to a degree from Eu? If you look at my linked-question you'll see the difference in hours needed! – 2017-01-04
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    @Euler_Salter Yeah I see what you're saying. I can't compare really as I've not studied at a uni in mainland Europe, but having just finished my master's in the UK the links you sent do seem to be very thin on the ground. For example, the course I took for differential equations had course notes of ~300 pages. I think perhaps that studying so many different topics in one module actually leads to far less depth, and maybe even less actual knowledge of the subject, but rather being able to just solve problems – 2017-01-04
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    @Euler_Salter Equally, the way maths is taught before university in the UK is absolutely awful, it definitely leaves a gap to make up at the start of university! It's a very interesting question. Do you happen to have any of the problem sheets you mentioned (for tutorials etc)? – 2017-01-04
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    just a quick comment, "analisi 3" isn't a mandatory course for most (next to all?) engineering degrees in Italy – 2017-01-04
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    @TheMathsGeek interesting! Although here's another issue: looks like there's a HUGE difference in quality between undergraduate and postgraduate in UK and USA. Indeed most people try to get MSc or Phds in those countries. However I took a course in Differential Equations as well in my first year (quite basic I have to say) but it was very operational and with physical context (which I like!) but it wasn't as theoretical as those notes! – 2017-01-04
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    @TheMathsGeek so do you think that doing different topics in a module leads to confusion? Like so far I haven't done anything on manifolds, of course I've done vector calculus and the integral theorems, but the theory that they're doing and the problems are pretty harder! What you say is true, there is a gap before uni indeed, maybe that partially answers that! Do you mean a problem sheet from an italian/european university? I will give the link soon enough! – 2017-01-04
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    @Euler_Salter They struggle a lot to get their bachelor's degree. The French university accepts everybody, but not all of them graduate. Two things to take into account: you don't need to pass all of your courses, you need to have just a 10/20 overall grade in all courses combined in order to pass. Secondly, many just drop off. Me an my classmates worry a lot for our future, as the second year is very hard, and the third year is going to be toughest. I had about 40 classmates in first year, now I have around 20, with about 10 additional who repeat their second year because of failling it. – 2017-01-04
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    @AlessandroCodenotti I am ill-informed then. However, I was looking at Padua university and if you look at engineering courses/physics/astronomy you'll see they do that module. Maybe I am wrong with engineering, surely though they do it in the last two, you can look here https://www.youtube.com/channel/UCkPMH--mBhm-xJTifRFgTyw, which is a youtube channel on those lectures. Also, http://didattica.unipd.it/offerta/2016 here – 2017-01-04
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    @Euler_Salter I'm not 100% sure what you mean by 'quality'? Masters have become/ are becoming the norm in the UK just because as a society, the vast majority of people are expected to get a degree, thereby devaluing a BSc. I hope we aren't very weak anyway as I start my PhD in September... – 2017-01-04
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    @TheMathsGeek as quality I mainly mean: broadness, expertise.In UK/USA there are huge fundings on super interesting topics, spanning everywhere - hence you can study exactly what you like. Also there are a lot of experts from all over the world, so you can collaborate and learn from very good professors. So looks like because of money and the "lingua-franca" Uk manages to attract most minds for studying or teaching and hence there are very very good PhDs opportunities! – 2017-01-04
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    @AlessandroCodenotti I see you are studying at Trento, as my friend. Now, I will upload some material from my university and from other italian universities. Let me know if you think that the level of difficulty of similar modules is the same or not. Cause as I can see normally the "Prova d'Esame" are extremely harder than ours – 2017-01-04
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    @Euler_Salter I wouldn't say confusion exactly, but it wouldn't allow time to fully explore the topics. In my undergrad there was a large discrepancy of what was on the examinable syllabus and what was actually discussed. There were many lectures where probably half of the content was non-examinable, but really helped to explain concepts etc. I also think that the depth of content is likely better. They may be studying 'harder' content and problems - but do they *really* understand exactly what's going on? – 2017-01-04
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    @Euler_Salter Ah got it. Undergrad vs PG is a difficult one, especially with the rise of MMaths so that we're technically undergrads though studying some 'harder' material in the 4th year. Again I think a lot of the perceived difference in quality is that as a society we expect many people to have degrees, and so people with no interest in research maths are able to go and get a BSc (many of my friends included!) who wouldn't qualify as 'strong' mathematicians. I'm not sure what the general philosophy is like in mainland Europe though? – 2017-01-04
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    @TheMathsGeek hold on though, you did your Master in UK, but did you study Alevels and Undergraduate in UK too? Also, yes one should see what is actually examinable, although this is a harder information to find online for me! Well I've always thought that the ability of solving hard problems (except if you're a computer I guess? But that's not really a hard problem, rather a problem of hard programming ) shows how well you understand a concept. So you think they work on those problems in a "swiched-off-mind" mode, as in a "machine" mode? Like by memory or so? – 2017-01-04
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    @TheMathsGeek your point is really good. As you can see in the question on Mathematics for Educators, I posted some stats in the comments. In the UK many more people go to university. So do you reckon that this difference lies on the fact that in UK a degree is something "lighter" because people are expected to have it, whereas in EU maybe it's considered more like a distinction from the "others"? – 2017-01-04
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    Here are some old Analysis 1 exams for Physics http://www.mat.unimi.it/users/molteni/didattica/fisica/tema10an1q.pdf, here is Analysis 1 for Electrical Engineering http://users.dma.unipi.it/gobbino/Home_Page/Files/HP_AD/E99_CS.pdf, these are lecture notes for a first year analysis course for engineers http://calvino.polito.it/~fagnani/AnMatI/Analisi%20I.pdf , here are other lecture notes for a one semester course http://www.dm.unipi.it/~acquistp/analisi1.pdf, this is another exam with solutions http://www.math.unipd.it/~marson/didattica/Analisi1/aa1011/corapp1.pdf – 2017-01-04
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    http://www.unipd.net/download.php?mode=unipedia&id=264 here is a website where you can download more material, you'll download a pdf used by students to do exercises – 2017-01-04

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