# What is maths like at university? watch

1. I've always wondered about this after hearing my teacher say its very different from what it is in A-level . I've gone through some prospectuses, in terms of the listed topics, nothing seems out of the ordinary. Anyone care to enlighten me on this?
2. It's fast.
3. The main difference is that there's much more emphasis on proof. For example, at A Level, you might be asked to difference but at degree you would have to proof that is actually the derivative. Likewise, you may have to prove that the sequence tends to zero and that a matrix is only invertible if it's determinant is non-zero etc.
4. (Original post by electriic_ink)
The main difference is that there's much more emphasis on proof. For example, at A Level, you might be asked to difference but at degree you would have to proof that is actually the derivative. Likewise, you may have to prove that the sequence tends to zero and that a matrix is only invertible if it's determinant is non-zero etc.
how would you do that, out of interest
5. (Original post by hockeyjoe)
how would you do that, out of interest
It's to do with the strict definition of what is meant by a 'limit'.

See http://en.wikipedia.org/wiki/Limit_%..._of_a_function
6. (Original post by hockeyjoe)
how would you do that, out of interest
Well firstly let's call .

The definition of at some point is . Now all you have to do is substitute in for and in for and do a bit of cancelling.

I'm sure there's an even more rigorous way of doing it than this but I haven't done it yet.
7. (Original post by electriic_ink)
Well firstly let's call .

The definition of at some point is . Now all you have to do is substitute in for and in for and do a bit of cancelling.

I'm sure there's an even more rigorous way of doing it than this but I have done it yet.
I teach that in C1 .....
8. (Original post by H.C. Chinaski)
I teach that in C1 .....
You may do but it wouldn't be on the exam but it could easily be in a first year Maths exam.
9. (Original post by H.C. Chinaski)
I teach that in C1 .....
wish I went to your school..
10. (Original post by electriic_ink)
Well firstly let's call .

The definition of at some point is . Now all you have to do is substitute in for and in for and do a bit of cancelling.
Well, that's not exactly all you have to do. You either have to go to epsilons and deltas or argue that your reduced expression is continuous (and so has the desired limit).
I teach that in C1 .....
"Says it all" would be unacceptably snarky, but I'd say there's quite a big difference between:

", so set x = x_0 and get 3x_0^2"

and a proper epsilon-delta proof.
11. (Original post by fuzzybear)
I've always wondered about this after hearing my teacher say its very different from what it is in A-level . I've gone through some prospectuses, in terms of the listed topics, nothing seems out of the ordinary. Anyone care to enlighten me on this?
It's awesome.

Maths at A-Level I found incredibly dull - not because the material is that bad, but because nothing is ever really explained properly.

If you want, you can concentrate your degree on really understanding why the things everyone else takes for granted (calculus, algebra etc.) really works (that's what a 'pure' course is really about).

The great thing about a maths degree is that if that isn't really your thing, your focus can be entirely different. There are more than enough courses on mathematical physics, or statistics, or even plain old methods (that's where you learn to apply more complicated techniques but don't really have to prove they work) to get your fill. And towards the end of your degree you can check out courses in optimisation, mathematical finance, biology etc. etc. if you want to apply stuff you've learnt to other areas.

Its very different from an A-Level but in a good way. I absolutely loved my degree, and there's no reason why it shouldn't be the same for everyone else here too. Don't be fooled by course titles such as 'Calculus' or 'Algebra' or 'Mechanics'. Its definitely not just more of the same
12. (Original post by shamika)
It's awesome.

Maths at A-Level I found incredibly dull - not because the material is that bad, but because nothing is ever really explained properly.

If you want, you can concentrate your degree on really understanding why the things everyone else takes for granted (calculus, algebra etc.) really works (that's what a 'pure' course is really about).

The great thing about a maths degree is that if that isn't really your thing, your focus can be entirely different. There are more than enough courses on mathematical physics, or statistics, or even plain old methods (that's where you learn to apply more complicated techniques but don't really have to prove they work) to get your fill. And towards the end of your degree you can check out courses in optimisation, mathematical finance, biology etc. etc. if you want to apply stuff you've learnt to other areas.

Its very different from an A-Level but in a good way. I absolutely loved my degree, and there's no reason why it shouldn't be the same for everyone else here too. Don't be fooled by course titles such as 'Calculus' or 'Algebra' or 'Mechanics'. Its definitely not just more of the same
A few people on thos post mentioned about proofs being the main difference from A-level and the degree stage. So what would questions on homework/exams from a Calculus or Algebra topic be like?

In A-level, in every module (pure and applied), you're basically given problems like ''solve this....to find x'', ''show that...'', ''work out the angle/length/area/etc of...'', ''express this in the form...''. How would questions at university differ from that sort of format?

By the way, I totally get what you say about things never being explained properly in A-level. From what you've described, I think may potentially enjoy maths at uni. At the moment I'm set on applying for physics, but I'm thinking of applying for a joint degree with maths for 2-3 of my choices.
13. Browse this or this for plenty of examples (as a flavour, you might also want to look at stuff which you'll recognise from A-Levels)

See also a brief list of stuff for uni maths I wrote elsewhere.

You'll also find a lot of stuff which just looks like gobbledegook at the moment - and some courses where you won't even understand what a course is if you just look at the name (does Galois Theory mean anything to you?) But of course, that's all part of the fun. Of course, if you end up in a maths degree and after the end of the course it still looks like gobbledegook, that's when you should be worried

In case anyone's curious, here's what some university exam questions look like
14. (Original post by shamika)
Browse this or this for plenty of examples (as a flavour, you might also want to look at stuff which you'll recognise from A-Levels)

See also a brief list of stuff for uni maths I wrote elsewhere.

You'll also find a lot of stuff which just looks like gobbledegook at the moment - and some courses where you won't even understand what a course is if you just look at the name (does Galois Theory mean anything to you?) But of course, that's all part of the fun. Of course, if you end up in a maths degree and after the end of the course it still looks like gobbledegook, that's when you should be worried

In case anyone's curious, here's what some university exam questions look like

Those past undergrad questions look intense!

Can't wait to start my maths degree, hope I get into Cambridge as well.
15. Haha, a lot of it isn't so bad once you understand what's going on (on the other hand. there are some courses where it really is that bad and would give me nightmares...)

The trick of course is that you only take a few courses (around 8) to exam
16. (Original post by H.C. Chinaski)
I teach that in C1 .....
Yeah and it's not a proof, it's a heuristic jusification.

It's not a proof because you haven't defined what exactly you mean by "limit". At university mathematics two steps would be taken:

(1) Define rigorously what you mean by "limit"; and
(2) Prove, under this definition, that the limit of (f(x)=f(y)/x-y), as x tends to y, "the derivative of f(x) at y", both exists (limits don't always exist) and is equal to what you say it is equal to. In this case, you are saying that is equal to the function 3x^2.

Even if you have taken step (1), your proof isn't a proof. The generally agreed upon definition of "limit" refers to epsilons and deltas. Here epsilon and delta are variables representing positive real numbers, best thought of as small positive real numbers. Your proof doesn't actually mention anything in the nature of epsilons or deltas.

And you can't prove a theorem if you do not mention part of the statement of the theorem.
17. (Original post by Raiden10)
Yeah and it's not a proof, it's a heuristic jusification.

It's not a proof because you haven't defined what exactly you mean by "limit". At university mathematics two steps would be taken:

(1) Define rigorously what you mean by "limit"; and
(2) Prove, under this definition, that the limit of (f(x)=f(y)/x-y), as x tends to y, "the derivative of f(x) at y", both exists (limits don't always exist) and is equal to what you say it is equal to. In this case, you are saying that is equal to the function 3x^2.

Even if you have taken step (1), your proof isn't a proof. The generally agreed upon definition of "limit" refers to epsilons and deltas. Here epsilon and delta are variables representing positive real numbers, best thought of as small positive real numbers. Your proof doesn't actually mention anything in the nature of epsilons or deltas.

And you can't prove a theorem if you do not mention part of the statement of the theorem.
(i) Is there something wrong with you, or do you always post is this bizarre and aggressive fashion?
(ii) I think that you will find that I have not used the word proof anywhere in my post ..... I think that if you can actually manage to stop acting like such a ****, then you will find that I simply said that I teach that in C1.
(iii) You really do not need to tell me what I would need to do in order to write a proof ..... I did do Maths at University ...
You refer to my proof and say ...
(Original post by Raiden10)
Your proof doesn't actually mention anything in the nature of epsilons or deltas.
I haven't given a proof numbnuts..... what the hell you are on about is anyone's guess... Do you by any chance have a drinking problem or some other type of condition that turns you into a keyboard warrior ??? Or perhaps you just have a serious personality disorder .... You need help my friend, oh yes indeed, you need help.
18. (Original post by H.C. Chinaski)
I haven't given a proof .....
I think we've established that.
19. (Original post by Raiden10)
I think we've established that.
No, I think I established that. You went off on some peculiar rant making claims that I had said something other than I actually had.
Seek help, you need it. Seriously.
20. All H.C. Chinaski said was that he taught that (see above) in C1, which is perfectly legitimate, I don't see all the fuss. I learnt such stuff way before C1, and the point is that there is a difference between doing such manipulations (''getting to f'(x) = 2x) and the proper proof.

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