(Original post by Armpits)
It appears that maybe apart from Oxbridge/Warwick/Imperial, maths courses are completely mundane.
I have offers to study at KCL/Manchester/Nottingham (rejected from Warwick).
But after seeing the courses I am disinclined to attend any of these universities.
I check some other universities and the courses were equally mundane.
Yr1: Basic Analysis/Calculus/Set theory etc with a bit of dynamics, and stats, and introductory computational methods.
Moreover, judging from the content across the universities I looked at, I could complete Year 1 and 2 in one year.
So is there any point in studying maths at a non-COWI (and maybe UCL) university?
Is there a reason why undergrad maths (at most universities) is so plain and thin (for the first year at least)?
I think that this is quite an astute question. But before I attempt an answer, let me reflect it back to you: what would you hope to see in a first year university maths course?
So here are some reasons that the courses you are looking at might seem thin:
(a) School mathematics involves very little in the way of rigour or proof. When students arrive at university one of the biggest cultural adjustments to make is that things that were taken to be obvious in the past now have to be proved. First year mathematics is, in many ways, a recapitulation of late nineteenth century mathematics, where some very fundamental things were put on rigorous foundations. It is a preparation for doing real mathematics properly; which is what you get to by your third year (with a bit in the second if you are lucky). So, you will do differentiation and integration again; but this time you will do them properly! And it is really quite technically hard for a lot of students; the “thin” syllabus hides a lot of technical sweat.
(b) Mathematics and Further Mathematics at “A” level provides relatively little preparation in algebraic manipulation and, more generally, technical fluidity. For those students who have not been through an exam course like STEP, there is a lot to learn that is, again, foundational for what comes later. This is especially important in applied mathematics where you are fairly rapidly expected to manipulate long and complicated expressions.
(c) Some students do arrive with no Further Maths “A” level. Time has to be found in the syllabus to bring them up to speed.
(d) A lot of the substance of mathematics courses is to be found in the examples sheets that go with the lecture courses. It is a frequent experience of first year students that they find the lecture material relatively straight forward, and then find that they struggle with the example sheets. This is an example of having to learn that mathematics is about doing as much as it is about absorbing. The doing is hard; another culture shock.
Reasons (a) and (d) will apply at all universities; (b) and (c) slightly less so at places like Oxford/Cambridge/Warwick where entrance requirements are high. But I would urge you to give KCL/Manchester/Nottingham a chance! They run very good mathematics degree programmes.