Advice for DS on studying Pure Maths

[polgareth]

Some background. DS1 just started 6th form. He got 7A* and 5A at GCSE and is doing Maths, FM, Physics, Chemistry and Biology for AS.
He was always good at Maths and on G&T for it. Sadly despite my best efforts I never managed to get the school to extend him in Maths with the result that he has spent years being bored at it.

So he turned his attention to physics. Loves it and has read very widely ( as recommended by people on MN ). He wanted to study physics in some form and to try for Cambridge.

Since starting A levels he has found a renewed love for pure Maths, less so for applied Maths. He has been buzzing about Maths since he September, for the first time in his life he is being stretched and challenged and has a teacher who gallops along at his speed. He's also getting very good grades. He is nothing like as excited about physics, which may be down to the curriculum.
I have said to him, and he agrees, that it seems to me that he ought to think about Maths as a degree. Any advice on some suitable reading or research for him would be very welcome? He was also wondering whether doing a Maths degree would rule out doing a post grad in Physics?

[schobe]

Why not get appointments for him (and you) to go and chat to some physics/maths lecturers in nearish universities.

I think students in this area are still much sought after, so I am sure they would make time to meet you and point your DS in the right direction.

[FraterculaArctica]

Can help with your second question: the preferred route into postgraduate study in theoretical physics at Cambridge is through the Maths tripos. So depending on his area of interest within physics, this could actually be a better first degree choice.

[polgareth]

Thank you
schobe I wouldn't have thought about that. Do you think they would talk to us even if DS doesn't plan to apply to them?
FraterculaArctica that's interesting, as he thought he might be closing the door to physics if he did a Maths degree. He's only just started 6th form so it's a way off yet but I think he needs to firm up which direction he is going to go.

[schobe]

Don't tell them where he's thinking of applying - say he doesn't know yet. You never know they might sell him on one of their courses.

[gfrnn]

I have professional experience in both disciplines and would agree with FraterculaArctica's comments and confirm a maths degree would not close the door to physics, but it is likely to result in a career involving theory / modelling based work rather than one involving experimental / practical skills.
Regarding maths at Uni, he may need to think about doing STEP in addition to further maths to get into one of the top Uni's. This would be good experience in any case for tackling more difficult questions. For reading outside the curriculum, the books by William Dunham ("Journey through Genius") and John Mason ("Thinking Mathematically") would be a good start.
Regarding physics, Muncaster is a superior course text which will stretch a brighter student. For further reading, the various popular books by Richard Feynman are good reads, as also is "Space, time and quanta" by Robert Mills.

[polgareth]

gfrnn Does he do STEP through the 6th form college?
He has read quite a lot of Feynman but not the Mills, will look at that. Do you have any suggestions for reading around Maths?

[boomting]

Has he considered doing a combined maths and physics degree? It's not offered at Cambridge (although all physics courses comprise a substantial bit of maths) but others do offer it.

[gfrnn]

some schools/sixth forms offer support for STEP; others do not. There are a number of free resources on the web for it, e.g. the guide by Stephen Siklos is a good start. For reading around maths: other than the books by Dunham/Mason which I mentioned in the previous post, you could try something by Eli Maor, or maybe "How to Solve it" by Polya.

[polgareth]

Thanks gfrnn.
I have tracked down most of those books so he will have some heavy reading to do.

[kingprawntikka]

Has he considered doing an BEng in some type of engineering. That combines physics and maths nicely.

[mummytime]

My DS is also enjoying Maths at present far more than Physics, I wonder what the problem is with the courses?

[LRDtheFeministDragon]

Do you mean 'pure maths' as in, just maths not a combined course, or 'pure maths' as in, not applied maths?

Most university maths courses are a mixture of pure and applied. If he did that, he could then specialize in the second and third year (depending on the course), and that sounds like a good bet for him, as he might change his enthusiasms again.

Lots of places would might let you change course mid-way through, though it'd not be something to rely on. It might be worth knowing that if you go to Cambridge, you can do a Part I in one subject (first year, or first two years) and a Part II in something else - so he could, if he liked, do Part I of the Maths tripos then Part II/III of the Physics?

I'm just suggesting in case he is wanting flexibility rather than the breadth of a combined degree, which is what it sounds like.

[polgareth]

mummytime I think that so far he hasn't covered anything in Physics that he didn't already know, mainly because he has "studied" it as a hobby, whereas at last in maths he's learning new stuff.
LRD I mean pure Maths as in not applied Maths. So engineering doesn't appeal.

[LRDtheFeministDragon]

Ah, I see. That is tricky, because physics shades more into the applied side, so he's really wavering between two quite different sides. I reckon a pure maths undergraduate degree would be really, really specialized and to be honest, quite narrow and restrictive. But if he did a normal maths degree with some pure and some applied in it, he could easily switch in to physics at postgrad.

[polgareth]

Thank you LRD, really useful for me as not only did I not go to university myself, I know nothing about Maths or Physics.

I will show him this thread and I think it should give him food for thought. I've also sent off for some prospectuses (?) so that he can see the content of different Maths / physics courses.

[IShallWearMidnight]

advice from DD1 (studying Maths at Bath) - if you need STEP - start working on it NOW, with as many practice questions as you can possibly fit in. She left it till Y13, and found it pretty tough. Also depending on your course, it may be possible to fit in some Physics modules into a Maths degree - Dd has dropped a maths module for a physics one this year, as she reckons it was easier and didn't involve programming.

[polgareth]

Programming he's a technophobe. I have told him about STEP. I think he needs to ask at college about it as well. He likes doing tests though so will have a go at some and see what's involved. They do A level maths in 1st year and A level Further maths in second year at his 6th form so it's quite intensive.

[LRDtheFeministDragon]

He sounds very like my big brother!

I've just thought - does his school do the maths/physics olympiads? They're competitions you can take, you don't have to do any training, they're just puzzle-solving. It's not a big thing and certainly not anything comparable to STEP, but they are interesting because the questions tend to be phrased and set up rather differently from the A Level style, so it's quite a nice way for him to see whether or not he gets a strong feeling of enjoying this sort of maths, or not.

School will know if they've done it before, I think.

[LRDtheFeministDragon]

This may be useful - though it is, I believe, designed for students a year older than him. But there are several podcasts on the same page that might also help give a sense of what maths at university involves. Here's the first:

www.themathsfaculty.org/a-levels/item/194-should-i-be-a-mathematician?

[LRDtheFeministDragon]

Btw: that is only one person's view - thank god not everyone speaks like that or gestures like that! It is just a bit fun to see if he thinks this makes sense or not.

[polgareth]

It's all Greek to me but I'll show DS when he gets home.

At college they are encouraged to do a few none exam related subjects to broaden their education. I suggested maybe Drama or Philosophy, and while he did see the girlfriend potential of doing something lighter he chose to do........ Scary Maths and Scary Physics.

[gfrnn]

IShallWearMidnight's information agrees with mine - STEP is designed to be tough and early preparation is advisable.

LRDtheFeministDragon - I do not intend to be argumentative but my view on one or two points differs from yours. Anyone who gets anywhere in an olympiad will typically have done an awful lot of training as the olympiads are extremely competitive. Also, a primary degree in pure maths is far from narrow or restrictive - it's a degree in problem solving in its most abstract/general form.

One further observation : it's much easier to move from a more theoretical discipline to a less theoretical one: going from pure to applied or from applied to physics is straightforward, but going the other way is hard.

[LRDtheFeministDragon]

gfrnn - oh, no worries, sorry if I've used the wrong term - is it the challenge at the early stages? The one qualifies you for the other IIRC, but as I say, his school will know about it. I mean the one you can just sit down and do.

A degree in Pure Maths would be quite narrow, I think: it's not a standard degree course for a reason. I did ask my brother (who lectures in Pure Maths) about that bit, and his view was that you'd be making yourself too narrow too early on. I expect that people who choose to do it do so for a reason, but it doesn't seem well suited to someone who thinks they might want to be a Physicist.

I agree with you about going from more theoretical to less theoretical.

[gfrnn]

LRD - yes, I think what you're thinking of is called the senior challenge. the olympiad follows from this and is rather more formidable. I would be inclined to make sure A level / STEP is under control first. I agree pure and applied would be a more direct preparation for physics and can avoid premature decisions for someone who is undecided. My difficulty with describing pure maths as "narrow" is that it might convey the impression that what is studied is restricted or lacking in breadth - not so: the material and mindset acquired are about as general as it gets; what gets squeezed is contact with practical applications. I'm in a (very) applied field and have no axe to grind.

[LRDtheFeministDragon]

Yes, that's what I was thinking of, thank you! I just remember enjoying them. Sorry to have got the names the wrong way around.

I didn't mean to offend by describing pure maths as 'narrow' - I did only mean it in this context. It would be daft of me to knock it since I have only (huge) respect for them as can do it!