# Maths at uni

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Hi

I am applying to university later this year and I am planning on doing maths. However, I am not very fond at all of physics or mechanics and I was wondering if there was a way to avoid these modules? Also, which out of Oxford and Cambridge has less mechanics in their course? I don't mind statistics but at the moment at A-level I enjoy pure maths the most.

Also, if anyone could give me opinions on what the best universities are to study maths that would also be appreciated.

Thanks

I am applying to university later this year and I am planning on doing maths. However, I am not very fond at all of physics or mechanics and I was wondering if there was a way to avoid these modules? Also, which out of Oxford and Cambridge has less mechanics in their course? I don't mind statistics but at the moment at A-level I enjoy pure maths the most.

Also, if anyone could give me opinions on what the best universities are to study maths that would also be appreciated.

Thanks

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#2

(Original post by

Hi

I am applying to university later this year and I am planning on doing maths. However, I am not very fond at all of physics or mechanics and I was wondering if there was a way to avoid these modules? Also, which out of Oxford and Cambridge has less mechanics in their course? I don't mind statistics but at the moment at A-level I enjoy pure maths the most.

Also, if anyone could give me opinions on what the best universities are to study maths that would also be appreciated.

Thanks

**ABC789**)Hi

I am applying to university later this year and I am planning on doing maths. However, I am not very fond at all of physics or mechanics and I was wondering if there was a way to avoid these modules? Also, which out of Oxford and Cambridge has less mechanics in their course? I don't mind statistics but at the moment at A-level I enjoy pure maths the most.

Also, if anyone could give me opinions on what the best universities are to study maths that would also be appreciated.

Thanks

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#3

(Original post by

I don't mind statistics but at the moment at A-level I enjoy pure maths the most.

**ABC789**)I don't mind statistics but at the moment at A-level I enjoy pure maths the most.

Also, if anyone could give me opinions on what the best universities are to study maths that would also be appreciated.

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#4

Look at some of the stuff in e.g. the new edexcel further pure maths 2, particularly the number theory, group theory, and proof by induction of sequences and series. This is the kind of stuff that maths degrees are made of (also you'll get some more calculus with differential equations and vector calculus).

Also the differentiation by first principles is actually a hand wavy formulation of the fundamental theorem of calculus.

Also the differentiation by first principles is actually a hand wavy formulation of the fundamental theorem of calculus.

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#5

(Original post by

Are you doing a maths degree? What a level subjects did you do?

**MajorFader**)Are you doing a maths degree? What a level subjects did you do?

But as other posters stated, it's a huge difference in style of how it's "done"; in fact you'll probably realise that you weren't actually "doing" maths at A-level, you were just "using" maths

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#6

(Original post by

Also the differentiation by first principles is actually a hand wavy formulation of the fundamental theorem of calculus.

**artful_lounger**)Also the differentiation by first principles is actually a hand wavy formulation of the fundamental theorem of calculus.

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#7

(Original post by

Uh... what?

**Zacken**)Uh... what?

Which you can work backwards from to the definition of the integral, if you were so inclined and careful with your definitions.

My point being, that consideration of how the derivative is built up (and by extension the integral i.e. the FΘC ) is an important result and also by considering it very carefully and being very precise in your definitions this is actually how the rest of maths (well certainly analysis) gets put together.

For the purposes of an A-level student it's sufficient to look at it further and more carefully, I'm not proposing mathematicians start using "differentiation from first principles" as an approach to constructing the integral

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#8

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Well the construction of the derivative part anyway :P

**artful_lounger**)Well the construction of the derivative part anyway :P

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#9

It's hand wavy in the sense that it doesn't precisely discuss where it's applicable, the necessary conditions for it to be so etc; it obscures this by using a more intuitive sense of the concept of the limit.

I am aware you need the definition of a derivative but this is not really a definition so much as an intuitive derivation of it. Hence handwavy.

Equally I loathed "proper" calculus and analysis so...I'll stick with the handwavy concepts xD

I am aware you need the definition of a derivative but this is not really a definition so much as an intuitive derivation of it. Hence handwavy.

Equally I loathed "proper" calculus and analysis so...I'll stick with the handwavy concepts xD

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#10

I was a bit like you as I hated (and still hate) mechanics, so I looked at all the university's (that I was interested in) modules lists to see if they had too many compulsory mechanics courses eg dynamics. I applied to Oxford (as they had less mechanics than Cambridge), Southampton, Bath, Exeter and Reading. Some have one compulsory mechanics type module first year but after that they are all optional.

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#11

(Original post by

It's hand wavy in the sense that it doesn't precisely discuss where it's applicable, the necessary conditions for it to be so etc; it obscures this by using a more intuitive sense of the concept of the limit.

I am aware you need the definition of a derivative but this is not really a definition so much as an intuitive derivation of it. Hence handwavy.

Equally I loathed "proper" calculus and analysis so...I'll stick with the handwavy concepts xD

**artful_lounger**)It's hand wavy in the sense that it doesn't precisely discuss where it's applicable, the necessary conditions for it to be so etc; it obscures this by using a more intuitive sense of the concept of the limit.

I am aware you need the definition of a derivative but this is not really a definition so much as an intuitive derivation of it. Hence handwavy.

Equally I loathed "proper" calculus and analysis so...I'll stick with the handwavy concepts xD

I can't see the link to FoC. It might not be explained so rigorously at A-Level (which is what you might have been talking about) but then it's a hand-waving of limits, not FoC.

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#12

Also OP, if you're interested in maths at uni, the age old suggestion of finding a copy of Spivak's Calculus (not calculus on manifolds, stay away from that until you've got at least a year of uni maths under your belt lol) and working through that isn't a bad idea. I'd look in your local library possibly, or maybe see if you can get a copy off ebay or something for ~£20ish or under. There are always the dark corners of the internet as well...

It should be challenging, but theoretically accessible, and is the kind of thing maths students will encounter. If anything, even if you can't necessarily do all (or any) of the problems, you'll have a chance to start thinking about things in a more formal way as you would in an undergrad maths course (although it works through from your intuition of calculus as has been developed in A-level/equivalent to developing the formal statements).

In fact most maths students (at least, once they get to the PhD level) seem to be of the opinion that attempting all the problems will make you a much better mathematician and it's generally quite popular due to the style of it's writing.

It should be challenging, but theoretically accessible, and is the kind of thing maths students will encounter. If anything, even if you can't necessarily do all (or any) of the problems, you'll have a chance to start thinking about things in a more formal way as you would in an undergrad maths course (although it works through from your intuition of calculus as has been developed in A-level/equivalent to developing the formal statements).

In fact most maths students (at least, once they get to the PhD level) seem to be of the opinion that attempting all the problems will make you a much better mathematician and it's generally quite popular due to the style of it's writing.

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#14

(Original post by

I think we may be talking about different things: to me, differentiation from first principles refers to the definition of a derivative. That is, a real-valued function is differentiable at if the limit if exists (and we call it ), where limit refers to .

I can't see the link to FoC. It might not be explained so rigorously at A-Level (which is what you might have been talking about) but then it's a hand-waving of limits, not FoC.

**Zacken**)I think we may be talking about different things: to me, differentiation from first principles refers to the definition of a derivative. That is, a real-valued function is differentiable at if the limit if exists (and we call it ), where limit refers to .

I can't see the link to FoC. It might not be explained so rigorously at A-Level (which is what you might have been talking about) but then it's a hand-waving of limits, not FoC.

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#15

Also I can confirm Southampton doesn't have a lot of mechanics, you do about ~1/3 of a first year module of mechanics, and then you can pretty much drop it for the rest of the course (barring a bit of fluid mechanics in second year, which is a fairly decent way to introduce vector calculus anyway since otherwise the concept of grad div curl are kind of ambiguous and EM isn't as intuitively obvious in the physical implication of them).

You would have to do at least 3 modules of stats then though, so your mileage may vary...you may prefer the treatment of mechanics in a maths degree (i.e. derived as differential equations and through vector calculus) as opposed to "formula collecting" as in A-level.

You would have to do at least 3 modules of stats then though, so your mileage may vary...you may prefer the treatment of mechanics in a maths degree (i.e. derived as differential equations and through vector calculus) as opposed to "formula collecting" as in A-level.

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#16

**ABC789**)

Hi

I am applying to university later this year and I am planning on doing maths. However, I am not very fond at all of physics or mechanics and I was wondering if there was a way to avoid these modules? Also, which out of Oxford and Cambridge has less mechanics in their course? I don't mind statistics but at the moment at A-level I enjoy pure maths the most.

Also, if anyone could give me opinions on what the best universities are to study maths that would also be appreciated.

Thanks

An example of analysis would be calculus, in particular, google Riemann Integrals. If that's too easy, proceed to Ito and Stratonovich Integrals.

Algebra would be vectors and matrices, specifically proving theorems (check out fundamental theorem of algebra).

It does have its uses. In stats, you have something called degrees of freedom. That stems from the Rank Nullity Theorem in algebra.

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#17

(Original post by

There are broadly two branches of pure maths at uni - analysis and algebra.

**dugdugdug**)There are broadly two branches of pure maths at uni - analysis and algebra.

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#18

(Original post by

Geometry, number theory, logic, set theory, topology, ...

**RichE**)Geometry, number theory, logic, set theory, topology, ...

Number theory is separate, although usually not developed extensively except through optional modules usually (typically you might do a single number theory module vs 2-4 in algebra and analysis).

Geometry is very variable; basic elements of euclidean geometry tend to be covered alongside linear algebra (in the main algebra sequence) while differential geometry. algebraic geometry etc are a) optional type modules that may or may not be offered and b) often more algebra or analysis leaning.

I mean yes those are all things that come up in the course of a maths degree but the original statement that it's primarily algebra/analysis isn't incorrect or misleading.

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#19

(Original post by

Topology is kind of a branch of analysis, logic and set theory aren't commonly done as subjects unto themselves so much as tools to develop the necessary theorems in other subjects.

**artful_lounger**)Topology is kind of a branch of analysis, logic and set theory aren't commonly done as subjects unto themselves so much as tools to develop the necessary theorems in other subjects.

Number theory is separate, although usually not developed extensively except through optional modules usually (typically you might do a single number theory module vs 2-4 in algebra and analysis).

Geometry is very variable; basic elements of euclidean geometry tend to be covered alongside linear algebra (in the main algebra sequence) while differential geometry. algebraic geometry etc are a) optional type modules that may or may not be offered and b) often more algebra or analysis leaning.

I mean yes those are all things that come up in the course of a maths degree but the original statement that it's primarily algebra/analysis isn't incorrect or misleading.

Geometry is very variable; basic elements of euclidean geometry tend to be covered alongside linear algebra (in the main algebra sequence) while differential geometry. algebraic geometry etc are a) optional type modules that may or may not be offered and b) often more algebra or analysis leaning.

I mean yes those are all things that come up in the course of a maths degree but the original statement that it's primarily algebra/analysis isn't incorrect or misleading.

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#20

(Original post by

If you're saying that then I suspect you've only met elements of general point-set topology.

You're of course welcome to your opinion but I do think the statement is incorrect. It's a view that aligns with how a first year might be set up but would become more false during the degree. That there may well be more algebra and analysis is a function of what's missing in school maths and what's deemed useful material for instilling an appreciation of rigour and abstraction, not about some primacy of algebra and analysis within pure maths.

**RichE**)If you're saying that then I suspect you've only met elements of general point-set topology.

You're of course welcome to your opinion but I do think the statement is incorrect. It's a view that aligns with how a first year might be set up but would become more false during the degree. That there may well be more algebra and analysis is a function of what's missing in school maths and what's deemed useful material for instilling an appreciation of rigour and abstraction, not about some primacy of algebra and analysis within pure maths.

Yes each of those is within it's own right a very deep and broad area of expertise at the graduate level. Most universities will have few opportunities to do much if any work beyond very basic topics taught in first year until the final year.

Within the specific context of an undergraduate degree which was what the thread is about, this is broadly correct, as the first two years tend to have a significant compulsory portion of analysis and algebra. This is not to suggest any "primacy" as you indicated, merely an observation of undergraduate maths course structures (outside of Cambridge level courses).

And your comment about topology was broadly correct, but again I am referring specifically to the content of an undergraduate degree and they're unlikely to see much more beyond that unless there a significant research group in topology at a given university.

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