University math curriculum comparison: US v UK

usmathstud

Disclaimer: Although my question is targeted toward the UK, I do not wish to exclude comparison with other countries e.g. Germany or Canada. Please, if you have studied maths at universities in another country, your experience is of value and interest.

Here in the United States, the usual undergraduate study is 4 years. Currently, that has grown to 5 or sometimes 6 years.
As a math major (= reading maths), all fours years are used in their preparation of their Math degree. Compared to the UK e.g. Cambridge, there they only spend 3 years with an optional 4th year.

What are the differences?

What is the typical UK math student's academic schedule throughout their 3 years at university?

In the USA, the typical undergrad math student follows this schedule:
freshman year (1st)
term 1 Calculus 1A-differential and integral calculus
term 2 Calculus 1B-integral techniques, series

sophomore year (2nd)
term 1 Calculus 1C-multivariable calculus
term 2 Diff Eq/Lin Alg-Differential Equations (ODEs) and Linear Algebra

junior year (3rd)
term 1 Linear Algebra
Abstract (Modern) Algebra
term 2 Real Analysis
Abstract Algebra 2/Galois Theory or Set Theory

senior year (4th)
term 1 Complex Analysis
some geometry such as Topology or Differential Geometry
term 2 PDEs, Cryptography, math thesis, or taking some graduate level course

If they were Applied Math majors, then they may do Stats or Probability instead of Set Theory or Galois Theory.

lurflurf

One big difference is that UK students usaully have Maths A-level and some times further Maths. All or almost all classes in the UK are taught by math faculty to almost all math students. In the US maybe half the classes are math, and many of those are taught by other departments or have students from other departments, this gives US students a broader but shallower perspective.

jtbell

These are included in the A-levels curriculum which is covered in secondary school, hence the UK student starts in university at a level corresponding to sophomore (2nd) year in the US.

See for example page 4 of the Edexcel GCE Mathematics specification.

A US student with a strong high school background can place out of the first two semesters of calculus at most colleges and universities via the Advanced Placement (AP) exam. When I entered college many years ago, before the advent of AP exams, my college placed me out of Calculus I and II, so I could have started with Calculus III, but I think I "sat in" on Calculus II anyway, without credit.

cristo

I think one of the major differences between the UK and the US is that here (in the UK), there is no "general education" requirement. That is, if you wish, you can take only courses in your subject, and not have to worry about ticking other boxes.

What is the typical UK math student's academic schedule throughout their 3 years at university?

This is quite difficult to answer, since there is generally so much choice at UK universities as to what you want to study. I studied for a four year masters, so here's a run down of my modules (though it's very applied orientated!), for the first three years.

1st year (this is standard for all):

Analytical & computational mathematics,
Calculus,
Linear mathematics,
Prob I
Statistics I
Intro to applied maths
Intro to pure maths (sets, functions, combinatorics (intro level),
mathematical structures (intro to axiomatic systems, groups, metric spaces, etc..)

2nd year (most modules optional):

vector calculus,
mechanics,
geometry and linear algebra,
mathematical analysis,
diff eqns and fourier analysis
dynamical systems
complex functions,
intro to quantum mechanics,
lagrangian and hamiltonian mechanics
algebra I
intro to numerical methods
fluid mechanics

3rd year:

elasticity
electromagnetism
special relativity
general relativity
semi-classical quantum theory
graph theory
cryptography
project

Admittedly, this probably isn't very useful, but the point to notice is that there isn't really such a thing as a 'typical' degree in the UK. Everything in the list above, apart from the first year, is optional. As you can see, my degree was heavily applied with a hint of pure, but one could construct a degree that was entirely the other way around. Also, there's basically no statistics in my degree: if you were interested in stats then you could pursue course in that area instead.

ice109

wow no general ed, you're lucky

Vid

It really depends on your high school preparations. In the UK, it seems to be standardized so that everyone enters at roughly the same level. In the US, some people enter not having taken Calculus at all and some enter already having 3 semesters of calculus plus other classes like diff eq. (For example, I took an Intro to Group Theory and a basic point set topology class in high school).

cristo

The idea over here is that students learn their general education at school, and then go on to specialise in their subject at university.

usmathstud

Wow! That is a lot to cover in a single academic year, even if divided between two or more terms. I read about 12 classes in the 2nd year. Even if divided, that is still 6 classes per term!

In the US, we do not normally take more than 3 or 4 classes per term. Aside from general requirements or elective courses, as a math major, one would not dare to take more than two math courses per term, not unless either repeating a class, one course is extremely easy, or the student is in a rush to graduate. For example, Real Analysis and Abstract Algebra are rough enough going in a single term without having to add Linear Algebra or even Differential Geometry. Here in the US if one did so, then they are either a genius or on a suicide path.

The content of the math courses are difficult without out having to study too much math.

Are the modules actual classes or topics UK maths students are expected to study during that particular academic year?
If that, then how are the classes organized? What are the assigned texts?

Thanks again.

cristo

They are actual classes that I took. So, say, in second year, there were 6 modules per semester, each had two hours of lectures and one tutorial (a class where you go and get help with any of the week's problems.. I'm not sure if the analog exists in the US) per week. That's only 18 hour's work each week! Rumor had it, however, that you were expected to put in at least two hours of private study per hour of class, so it quickly added up. I never did that much, though, and I doubt many people did. I was lucky that the university I went to had semester exams, so one didn't have to take 12 exams at the end of second year! As you increased up, and took less classes per year, the classes got more lectures, since they taught things in more detail.

As for textbooks: we didn't really have the same thing as you guys do in the US. That is, there is never an assigned textbook that one is told to buy and use throughout the course. Most lecturers make their notes available after the lecture, and you are encouraged to use a range of books to supplement your knowledge and study. A list is normally provided at the beginning of the course.

jtbell

You must be under the quarter system (three quarters per normal academic year). Under a semester system (two semesters per normal year, like), like where I teach, the typical load is five classes. A very energetic student might take six. Or are you counting only your physics and math classes?

Where I went to grad school, the equivalent of the "tutorial" was the "recitation." The intro physics lecture sections were very large, a couple hundred students or so, and the recitations were much smaller, maybe a couple dozen students. Some recitations were led by grad students (teaching assistants), others by professors.

I teach at a small college that doesn't distinguish between lectures and recitations. A class can be in either "lecture mode" or "recitation mode" depending on the day and what's going on in the class. We don't have teaching assistants either. The professor does everything.

We spread that rumor here, too. Some of us even write that expectation into our syllabi.