Question about Oxford Maths

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Anonymous(
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#1
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Hello. I’m a Y12 student interested in becoming a theoretical physicist. I have been told time and time again that a maths degree is better preparation for theoretical physics. Does Oxford maths provide a good route into this? Cambridge obviously has a lot of theoretical physics courses in its maths degree, but what about Oxford? From looking at the website, I can tell that there are definitely applied maths/theoretical physics courses but not as much as Cambridge. They also don’t seem as comprehensive as Cambridge. Is the Oxford course too pure? Is that why they don’t have any mechanics on the MAT? As a side note, I haven’t been exposed to uni maths yet. From what I’ve heard, I think I would enjoy some aspects but I find myself more interested in physics in general and I don’t know whether I would enjoy such high levels of rigour. I also don’t know if I have the natural ability for this kind of maths. Do you guys think it’s worth doing a maths degree instead of a physics one just because it’s better prep, even if I think I would enjoy the physics degree more?
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CharlemagneDaDog
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Why not apply to Cambridge for maths?
Last edited by 22Pac; 3 months ago
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RichE
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(Original post by Anonymous()
Hello. I’m a Y12 student interested in becoming a theoretical physicist. I have been told time and time again that a maths degree is better preparation for theoretical physics. Does Oxford maths provide a good route into this? Cambridge obviously has a lot of theoretical physics courses in its maths degree, but what about Oxford? From looking at the website, I can tell that there are definitely applied maths/theoretical physics courses but not as much as Cambridge. They also don’t seem as comprehensive as Cambridge. Is the Oxford course too pure? Is that why they don’t have any mechanics on the MAT? As a side note, I haven’t been exposed to uni maths yet. From what I’ve heard, I think I would enjoy some aspects but I find myself more interested in physics in general and I don’t know whether I would enjoy such high levels of rigour. I also don’t know if I have the natural ability for this kind of maths. Do you guys think it’s worth doing a maths degree instead of a physics one just because it’s better prep, even if I think I would enjoy the physics degree more?
Firstly, I'd disagree with the idea that a maths degree is definitely better preparation for theoretical physics - Oxford's physics degree would be good preparation (it's highly mathematical) as would other similar degrees, as there are plenty of joint mathematics and physics degrees around the country.

Out of Cambridge's and Oxford's degrees it's arguable that Cambridge is better set up for this as their theoretical physics group are part of DAMTP and there is more applied maths and physics in their first year or two. e.g. can do tensors and special relativity in the first year and Oxford's first year is somewhat purer. That said, the route through Oxford's MMath or MMathPhys is definitely good preparation for theoretical physics.

None of this has anything to do with the MAT. The MAT syllabus more reflects its timing and is set from the traditional common core of the A-levels.

Overall I think my advice would be to do a physics degree with plenty of maths in it, but plenty of options through the degree too. If you're thinking of doing theoretical physics but also saying "I also don’t know if I have the natural ability for this kind of maths" I'm concerned the *very* mathematical nature of theoretical physics may be problematic. How are you finding maths and further maths A-level at the moment?
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(Original post by RichE)
Firstly, I'd disagree with the idea that a maths degree is definitely better preparation for theoretical physics - Oxford's physics degree would be good preparation (it's highly mathematical) as would other similar degrees, as there are plenty of joint mathematics and physics degrees around the country.

Out of Cambridge's and Oxford's degrees it's arguable that Cambridge is better set up for this as their theoretical physics group are part of DAMTP and there is more applied maths and physics in their first year or two. e.g. can do tensors and special relativity in the first year and Oxford's first year is somewhat purer. That said, the route through Oxford's MMath or MMathPhys is definitely good preparation for theoretical physics.

None of this has anything to do with the MAT. The MAT syllabus more reflects its timing and is set from the traditional common core of the A-levels.

Overall I think my advice would be to do a physics degree with plenty of maths in it, but plenty of options through the degree too. If you're thinking of doing theoretical physics but also saying "I also don’t know if I have the natural ability for this kind of maths" I'm concerned the *very* mathematical nature of theoretical physics may be problematic. How are you finding maths and further maths A-level at the moment?
Hi, thanks for your reply! When I said natural ability for ‘this kind of maths’, I meant the highly rigorous proof based maths and the very pure topics like number theory, analysis, category theory etc. The kind of maths that is all about proofs and rigour and nothing else is what I meant. Theoretical physics does use advanced maths, but it uses all the topics in an ‘applied’ sense, without much care for rigour, as I’m sure you already know. I don’t know whether I have natural ability, but I find A level maths trivial (for the topics we’ve done so far, FM starts in Y13 so can’t say yet). I’ve started looking at some MAT papers and I can do most of the MCQ’s on the recent ones.

Edit: I know that I’m going to be applying for Maths and Physics joint honours else where, just confused about the course at Oxbridge and Imperial, the 2 unis that I actually want to go to. After your reply, I think I would apply for Natsci at Cambridge/physics at Oxford and if at all I find myself doing well on STEP, then maybe give Cambridge maths a try.
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#5
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(Original post by 22Pac)
Why not apply to Cambridge for maths?
It is one of the courses I’m considering, just wanted to look at other options.
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Zuvio
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(Original post by Anonymous()
Hi, thanks for your reply! When I said natural ability for ‘this kind of maths’, I meant the highly rigorous proof based maths and the very pure topics like number theory, analysis, category theory etc. The kind of maths that is all about proofs and rigour and nothing else is what I meant. Theoretical physics does use advanced maths, but it uses all the topics in an ‘applied’ sense, without much care for rigour, as I’m sure you already know. I don’t know whether I have natural ability, but I find A level maths trivial (for the topics we’ve done so far, FM starts in Y13 so can’t say yet). I’ve started looking at some MAT papers and I can do most of the MCQ’s on the recent ones.

Edit: I know that I’m going to be applying for Maths and Physics joint honours else where, just confused about the course at Oxbridge and Imperial, the 2 unis that I actually want to go to. After your reply, I think I would apply for Natsci at Cambridge/physics at Oxford and if at all I find myself doing well on STEP, then maybe give Cambridge maths a try.
Some universities have specific 'theoretical physics' or 'mathematical physics' degrees. I know Imperial does 'physics with theoretical physics', although Oxford and Cambridge don't. It may be worth considering these as well as a joint honours course.

I don't know if you're aware, but on the Cambridge maths course, there is a first year option called 'mathematics with physics'. Basically, you swap out a quarter of the maths course for the physics course from natsci. After the first year, you could continue with the maths if you liked that, or you could transfer to natsci and specialise in physics. However, the entry requirements are the same as regular maths, so I would make sure you're OK with STEP.
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(Original post by Zuvio)
Some universities have specific 'theoretical physics' or 'mathematical physics' degrees. I know Imperial does 'physics with theoretical physics', although Oxford and Cambridge don't. It may be worth considering these as well as a joint honours course.

I don't know if you're aware, but on the Cambridge maths course, there is a first year option called 'mathematics with physics'. Basically, you swap out a quarter of the maths course for the physics course from natsci. After the first year, you could continue with the maths if you liked that, or you could transfer to natsci and specialise in physics. However, the entry requirements are the same as regular maths, so I would make sure you're OK with STEP.
Yes I’m aware of imperial’s course but I’m also considering their maths with applied maths/mathematical physics course. I’m also aware of the ‘Maths with Physics’ option at Cambridge. If I apply to Cambridge’s Mathematical Tripos then I will choose the ‘Maths with Physics’ option.
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_gcx
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(Original post by Anonymous()
Hi, thanks for your reply! When I said natural ability for ‘this kind of maths’, I meant the highly rigorous proof based maths and the very pure topics like number theory, analysis, category theory etc. The kind of maths that is all about proofs and rigour and nothing else is what I meant. Theoretical physics does use advanced maths, but it uses all the topics in an ‘applied’ sense, without much care for rigour, as I’m sure you already know. I don’t know whether I have natural ability, but I find A level maths trivial (for the topics we’ve done so far, FM starts in Y13 so can’t say yet). I’ve started looking at some MAT papers and I can do most of the MCQ’s on the recent ones.

Edit: I know that I’m going to be applying for Maths and Physics joint honours else where, just confused about the course at Oxbridge and Imperial, the 2 unis that I actually want to go to. After your reply, I think I would apply for Natsci at Cambridge/physics at Oxford and if at all I find myself doing well on STEP, then maybe give Cambridge maths a try.
There isn't really any kind of maths that's all about proofs and rigour and nothing else, most of what you will cover at undergraduate is applicable somewhere. (often in physics)

There isn't really a hard border between applied and pure either - you might say fluid dynamics is "applied" but a lot of it is just analysis no different to what you might do as "pure maths", just applied to physically applicable models. Similar deal with probability, sounds "applied" but draws heavily on measure theory, functional analysis, etc. In some physics courses you might not care as much about smaller technical details (often people interchange limits, integrals, sums, etc. without thinking too much) but they will still have derivations/proofs of some kind that will demand technical understanding. Point being "applied" doesn't necessarily mean you're black-boxing everything with no proofs. (it can do, it kind of varies depending on what you're doing)

Imo an issue with A-level maths is that they teach "proof" as if it can be separated as a topic. "Proof" is fundamental to how maths is done. You build up a theoretical framework on which you can do calculations, and building up that theoretical framework will need the kind of "Definition, Theorem, Proof" maths. You might not build up that framework yourself, but someone will, and doing calculations will often require a good understanding of the theoretical underpinnings.

Have a read of some elementary number theory or introductory real analysis over the summer (you don't need anything from A-level maths, confusingly - it's much more reliant on mathematical maturity) and see how you like university maths.
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(Original post by _gcx)
There isn't really any kind of maths that's all about proofs and rigour and nothing else, most of what you will cover at undergraduate is applicable somewhere. (often in physics)

There isn't really a hard border between applied and pure either - you might say fluid dynamics is "applied" but a lot of it is just analysis no different to what you might do as "pure maths", just applied to physically applicable models. Similar deal with probability, sounds "applied" but draws heavily on measure theory, functional analysis, etc. In some physics courses you might not care as much about smaller technical details (often people interchange limits, integrals, sums, etc. without thinking too much) but they will still have derivations/proofs of some kind that will demand technical understanding. Point being "applied" doesn't necessarily mean you're black-boxing everything with no proofs. (it can do, it kind of varies depending on what you're doing)

Imo an issue with A-level maths is that they teach "proof" as if it can be separated as a topic. "Proof" is fundamental to how maths is done. You build up a theoretical framework on which you can do calculations, and building up that theoretical framework will need the kind of "Definition, Theorem, Proof" maths. You might not build up that framework yourself, but someone will, and doing calculations will often require a good understanding of the theoretical underpinnings.

Have a read of some elementary number theory or introductory real analysis over the summer (you don't need anything from A-level maths, confusingly - it's much more reliant on mathematical maturity) and see how you like university maths.
Definitely makes sense. I guess what I meant was that I’m aware of the drastic difference between a level and uni maths and it’s hard for me to tell whether I would do well in it. I’ve been told that the maths done in a physics/tp degree whilst very advanced is akin to the style of A level M and FM, so I have a better judgement of my ability. I was thinking of reading ‘How to think like a mathematician : a companion to undergraduate mathematics’ by Kevin Houston. Do you think this book will give me a good idea or should I look at something else? Any recommendations?
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_gcx
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(Original post by Anonymous()
Definitely makes sense. I guess what I meant was that I’m aware of the drastic difference between a level and uni maths and it’s hard for me to tell whether I would do well in it. I’ve been told that the maths done in a physics/tp degree whilst very advanced is akin to the style of A level M and FM, so I have a better judgement of my ability. I was thinking of reading ‘How to think like a mathematician : a companion to undergraduate mathematics’ by Kevin Houston. Do you think this book will give me a good idea or should I look at something else? Any recommendations?
I think so - I haven't done any physics so can't really comment much. Only intended to point out the artificial distinction between pure and applied maths that is often made.

If you can do very well in STEP-like questions there's no reason why you wouldn't have a good shot at university maths.

I've never read that book - I liked Apostol mathematical analysis for analysis. It wasn't exactly what I was thinking of but Beardon's Algebra and Geometry looks like a decent first taste of undergraduate maths too. (the book I used for my number theory module was Ireland & Rosen but it probably has too much algebra) Wouldn't recommend buying these books if you can settle for reading them off a screen.
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(Original post by RichE)
Firstly, I'd disagree with the idea that a maths degree is definitely better preparation for theoretical physics - Oxford's physics degree would be good preparation (it's highly mathematical) as would other similar degrees, as there are plenty of joint mathematics and physics degrees around the country.

Out of Cambridge's and Oxford's degrees it's arguable that Cambridge is better set up for this as their theoretical physics group are part of DAMTP and there is more applied maths and physics in their first year or two. e.g. can do tensors and special relativity in the first year and Oxford's first year is somewhat purer. That said, the route through Oxford's MMath or MMathPhys is definitely good preparation for theoretical physics.

None of this has anything to do with the MAT. The MAT syllabus more reflects its timing and is set from the traditional common core of the A-levels.

Overall I think my advice would be to do a physics degree with plenty of maths in it, but plenty of options through the degree too. If you're thinking of doing theoretical physics but also saying "I also don’t know if I have the natural ability for this kind of maths" I'm concerned the *very* mathematical nature of theoretical physics may be problematic. How are you finding maths and further maths A-level at the moment?
Hi again. I noticed that the 4th year at Oxford has plenty of theoretical physics. Is it possible to take maybe 1 or 2 4th year courses in the third year? A lot of them only have prerequisites that are already covered in 1st/2nd year.
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RichE
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(Original post by Anonymous()
Hi again. I noticed that the 4th year at Oxford has plenty of theoretical physics. Is it possible to take maybe 1 or 2 4th year courses in the third year? A lot of them only have prerequisites that are already covered in 1st/2nd year.
It's not formally possible to study 4th year options in the 3rd year; you could attend lectures and possibly even classes, but not take the paper to examination. But in my experience, theoretical physicists need background courses from all over mathematics so they, more than any other specialist, need to be picking up a range of courses as they progress through the degree.
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(Original post by RichE)
It's not formally possible to study 4th year options in the 3rd year; you could attend lectures and possibly even classes, but not take the paper to examination. But in my experience, theoretical physicists need background courses from all over mathematics so they, more than any other specialist, need to be picking up a range of courses as they progress through the degree.
I hope I can reach out to you later on when I actually have to apply and have more information about my interests and abilities. Thanks for all your help.
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(Original post by RichE)
It's not formally possible to study 4th year options in the 3rd year; you could attend lectures and possibly even classes, but not take the paper to examination. But in my experience, theoretical physicists need background courses from all over mathematics so they, more than any other specialist, need to be picking up a range of courses as they progress through the degree.
Hi again RichE _gcx. I will be applying to Imperial for theoretical physics and UCL, Warwick and Edinburgh for Maths and Physics. As a result, I would have to include lots of Physics in my personal statement as well. Would I be at any disadvantage for Oxford if my personal statement is a mix of Maths and Physics? How would tutors look at this? Will it leave a bad impression, will they doubt my dedication to study pure maths? Is it common or rare? Also, does Oxford differentiate on the basis of predicted grades? I.e. if someone is predicted 4A*s and another is predicted 2A*s and 2A's, would the candidate with 4A*s have any advantage over the one with 2A*s? Or do they not care once you've met the entry requirements? Thanks.
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