_gcx
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I'm a maths student at Warwick and I've just finished my first year. I'm happy to answer any questions you might have about studying maths at university, or studying maths at Warwick in particular.

I feel this thread is particularly important since there's a lot of difference between maths at school and maths at university!

Also answering questions here:
  • RDKGames - MMath Mathematics (Fourth Year), University of Loughborough
  • astrotemp - BSc Physics and Applied Mathematics (graduate, 2018), UTAS
  • deathbySTEP- Maths (offer holder), University of Cambridge
  • peaerhead7997- Maths (offer holder)

This AMA is part of the 'Ask a University Student 2.0' initiative. If you want to find out more about other courses or universites, please check out the main list of threads:

https://www.thestudentroom.co.uk/sho....php?t=6431108

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HS_1
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(Original post by _gcx)
TSR has decided to run some university AMA threads seeing as many university open days have been cancelled.

I'm a maths student at Warwick and I've just finished my first year. I'm happy to answer any questions you might have about studying maths at university, or studying maths at Warwick in particular.

I feel this thread is particularly important since there's a lot of difference between maths at school and maths at university!

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wht sort of topics do u cover in first yr?
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RogerOxon
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(Original post by _gcx)
I'm a maths student at Warwick and I've just finished my first year. I'm happy to answer any questions you might have about studying maths at university, or studying maths at Warwick in particular.

I feel this thread is particularly important since there's a lot of difference between maths at school and maths at university!
Thanks for doing this. Whilst I went to university decades ago, I discounted a Maths joint degree because I thought that the Mathematics would be too pedantic. I wanted to be able to state the obvious, so did Engineering (and CS) instead. That may be an issue for some considering it now.

How pedantic do you find university-level maths?
Do you feel that you have to prove things that are obvious?
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_gcx
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wht sort of topics do u cover in first yr?
Fairly standard first year modules would be:

  • Linear Algebra - Expands upon what you've looked at with matrices in A-level further maths (or equivalent). You might generalise some of the calculations you've done with matrices (such as finding the determinant and inverse) to matrices of larger sizes, learning more computationally efficient ways to do these calculations, and applying to solving systems of linear equations among other things. You will expand upon this by studying more general objects called vector spaces, which you'll likely build upon in your second year. Tools of linear algebra turn out to be very important in further study of stats and mechanics!
  • Foundations - Warwick calls this module Foundations but it is called different things at other universities (for example, Numbers and Sets at Cambridge), but you will probably cover everything in here at some point. You will look at how the sets of numbers that you are familiar with (integers, rationals, building up to the real numbers) from scratch, and the challenges this brings. You'll look at some theory about sets and functions, building on what you've already looked at in A-level maths.
  • Analysis - Essentially here, you restart your study of calculus. (the current understanding you have is only really sufficient for use in applied fields) You will get a better understanding of infinity, studying concepts such as limits (which you may have encountered briefly before) and convergence. You'll move on to studying functions and their various properties. You'll revisit differentiation from first principles (which you may have already done at university). You may also look at integration from first principles, which is in general much trickier. (to summarise, you can split up the area under a curve into "infinitely many" rectangles that are "infinitely thin" and sum over these areas)
  • Differential Equations - This is where you get into your more immediately applicable maths. You'll expand on your study of differential equations from A-level here. The differential equations you'll have studied so far at A-level will be very nice, and will have solutions that you can (mostly) write nicely out. However, situations that may appear in the real world aren't exactly carefully crafted and so may be a little trickier. Then comes the need for more realistic approximations, as well as studying how we can analyse the solutions of a differential equation without explicitly finding them. You'll learn how to build up diagrams called phase portraits, which give us a very good idea of how solutions to a differential equation might behave. This has quite wide-reaching uses particularly in physics. You'll build upon this in later years, with a particular interesting application being the study of dynamical systems, which look at how a system, for example a population, grows and evolves over time.
  • Applied Maths - You will also probably study some more applied maths, such as statistics and classical mechanics, maybe some special relativity. In the first year at Warwick, you take a probability module as core. This essentially, consistent with other modules, goes back and defines probability in a much more general setting (with probability spaces), and goes from there. If you're into "puzzle style" maths, you'll probably enjoy some of the problems probability has to offer. (for example: if 10 sweets are randomly distributed to 6 children, what is the probability they all receive a sweet?) You may have the option to study some classical mechanics, which will probably be a far more mathematical approach than you've seen so far. I didn't take the mechanics option offered here so I can't offer much of an insight unfortunately!
You may also study modules in vector calculus and group theory, though this will vary from university to university.

The style of university maths you'll find to be much different. Instead of focusing on computation, you'll be mainly focused at understanding how the maths works. A proper understanding of the theory of maths is essential to creating new mathematics, (and indeed, developing the mathematical tools and foundations that we need for these calculations!) as well as making sure any work you do in more applied realms is mathematically sound. You may be surprised to find that calculators are hardly used in university level maths because they simply aren't needed. Essentially, you've progressed beyond that type of maths!

Apologies if I've made these sound quite boring!
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zetamcfc
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(Original post by _gcx)
Fairly standard first year modules would be:

  • Linear Algebra - Expands upon what you've looked at with matrices in A-level further maths (or equivalent). You might generalise some of the calculations you've done with matrices (such as finding the determinant and inverse) to matrices of larger sizes, learning more computationally efficient ways to do these calculations, and applying to solving systems of linear equations among other things. You will expand upon this by studying more general objects called vector spaces, which you'll likely build upon in your second year. Tools of linear algebra turn out to be very important in further study of stats and mechanics!
  • Foundations - Warwick calls this module Foundations but it is called different things at other universities (for example, Numbers and Sets at Cambridge), but you will probably cover everything in here at some point. You will look at how the sets of numbers that you are familiar with (integers, rationals, building up to the real numbers) from scratch, and the challenges this brings. You'll look at some theory about sets and functions, building on what you've already looked at in A-level maths.
  • Analysis - Essentially here, you restart your study of calculus. (the current understanding you have is only really sufficient for use in applied fields) You will get a better understanding of infinity, studying concepts such as limits (which you may have encountered briefly before) and convergence. You'll move on to studying functions and their various properties. You'll revisit differentiation from first principles (which you may have already done at university). You may also look at integration from first principles, which is in general much trickier. (to summarise, you can split up the area under a curve into "infinitely many" rectangles that are "infinitely thin" and sum over these areas)
  • Differential Equations - This is where you get into your more immediately applicable maths. You'll expand on your study of differential equations from A-level here. The differential equations you'll have studied so far at A-level will be very nice, and will have solutions that you can (mostly) write nicely out. However, situations that may appear in the real world aren't exactly carefully crafted and so may be a little trickier. Then comes the need for more realistic approximations, as well as studying how we can analyse the solutions of a differential equation without explicitly finding them. You'll learn how to build up diagrams called phase portraits, which give us a very good idea of how solutions to a differential equation might behave. This has quite wide-reaching uses particularly in physics. You'll build upon this in later years, with a particular interesting application being the study of dynamical systems, which look at how a system, for example a population, grows and evolves over time.
  • Applied Maths - You will also probably study some more applied maths, such as statistics and classical mechanics, maybe some special relativity. In the first year at Warwick, you take a probability module as core. This essentially, consistent with other modules, goes back and defines probability in a much more general setting (with probability spaces), and goes from there. If you're into "puzzle style" maths, you'll probably enjoy some of the problems probability has to offer. (for example: if 10 sweets are randomly distributed to 6 children, what is the probability they all receive a sweet?) You may have the option to study some classical mechanics, which will probably be a far more mathematical approach than you've seen so far. I didn't take the mechanics option offered here so I can't offer much of an insight unfortunately!
The style of university maths you'll find to be much different. Instead of focusing on computation, you'll be mainly focused at understanding how the maths works. A proper understanding of the theory of maths is essential to creating new mathematics, (and indeed, developing the mathematical tools and foundations that we need for these calculations!) as well as making sure any work you do in more applied realms is mathematically sound. You may be surprised to find that calculators are hardly used in university level maths because they simply aren't needed. Essentially, you've progressed beyond that type of maths!

Apologies if I've made these sound quite boring!
Very good summary of 1st year maths.
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(Original post by RogerOxon)
Thanks for doing this. Whilst I went to university decades ago, I discounted a Maths joint degree because I thought that the Mathematics would be too pedantic. I wanted to be able to state the obvious, so did Engineering (and CS) instead. That may be an issue for some considering it now.

How pedantic do you find university-level maths?
Do you feel that you have to prove things that are obvious?
I don't really find it too pedantic. I appreciate the need for going through things so carefully, because often things you suspect to be true have quite elaborate counterexamples you can craft. And I like seeing how things build up anyway. Set theory is particularly troublesome, the axiom of choice for example seems extremely obvious but isn't accepted by some mathematicians! Russell's paradox is a fairly good example of why we should be careful with these things.

Some modules I've read were very dense and were crammed with very long proofs. This can get quite tiresome, but I wouldn't say these were pedantic! More I felt that there wasn't a clear direction with all of the theorems being introduced.
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What made you choose Warwick, and which other universities did you look at and/or apply for?
What has been your favourite topic to learn so far?
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What made you choose Warwick, and which other universities did you look at and/or apply for?
What has been your favourite topic to learn so far?
I knew to look at Warwick from the wisdom on here and elsewhere that it was the third/fourth best for maths. I liked the look of the course, and the breadth. I also applied to Cambridge, Bath, UCL. I didn't like Bath because it looked a bit too slow and there wasn't enough pure maths, and I didn't want to go to UCL because the atmosphere there is very distant and impersonal. I firmed Cambridge and insured Warwick.

I like analysis. Real analysis is a bit dry, but complex analysis is where things get exciting. (it all works out nicer and tools from complex analysis are much more useful for computations) I've also quite enjoyed group theory/abstract algebra and I've started reading the second year abstract algebra module over the summer.
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(Original post by _gcx)
Fairly standard first year modules would be:

  • Linear Algebra - Expands upon what you've looked at with matrices in A-level further maths (or equivalent). You might generalise some of the calculations you've done with matrices (such as finding the determinant and inverse) to matrices of larger sizes, learning more computationally efficient ways to do these calculations, and applying to solving systems of linear equations among other things. You will expand upon this by studying more general objects called vector spaces, which you'll likely build upon in your second year. Tools of linear algebra turn out to be very important in further study of stats and mechanics!
  • Foundations - Warwick calls this module Foundations but it is called different things at other universities (for example, Numbers and Sets at Cambridge), but you will probably cover everything in here at some point. You will look at how the sets of numbers that you are familiar with (integers, rationals, building up to the real numbers) from scratch, and the challenges this brings. You'll look at some theory about sets and functions, building on what you've already looked at in A-level maths.
  • Analysis - Essentially here, you restart your study of calculus. (the current understanding you have is only really sufficient for use in applied fields) You will get a better understanding of infinity, studying concepts such as limits (which you may have encountered briefly before) and convergence. You'll move on to studying functions and their various properties. You'll revisit differentiation from first principles (which you may have already done at university). You may also look at integration from first principles, which is in general much trickier. (to summarise, you can split up the area under a curve into "infinitely many" rectangles that are "infinitely thin" and sum over these areas)
  • Differential Equations - This is where you get into your more immediately applicable maths. You'll expand on your study of differential equations from A-level here. The differential equations you'll have studied so far at A-level will be very nice, and will have solutions that you can (mostly) write nicely out. However, situations that may appear in the real world aren't exactly carefully crafted and so may be a little trickier. Then comes the need for more realistic approximations, as well as studying how we can analyse the solutions of a differential equation without explicitly finding them. You'll learn how to build up diagrams called phase portraits, which give us a very good idea of how solutions to a differential equation might behave. This has quite wide-reaching uses particularly in physics. You'll build upon this in later years, with a particular interesting application being the study of dynamical systems, which look at how a system, for example a population, grows and evolves over time.
  • Applied Maths - You will also probably study some more applied maths, such as statistics and classical mechanics, maybe some special relativity. In the first year at Warwick, you take a probability module as core. This essentially, consistent with other modules, goes back and defines probability in a much more general setting (with probability spaces), and goes from there. If you're into "puzzle style" maths, you'll probably enjoy some of the problems probability has to offer. (for example: if 10 sweets are randomly distributed to 6 children, what is the probability they all receive a sweet?) You may have the option to study some classical mechanics, which will probably be a far more mathematical approach than you've seen so far. I didn't take the mechanics option offered here so I can't offer much of an insight unfortunately!

You may also study modules in vector calculus and group theory, though this will vary from university to university.

The style of university maths you'll find to be much different. Instead of focusing on computation, you'll be mainly focused at understanding how the maths works. A proper understanding of the theory of maths is essential to creating new mathematics, (and indeed, developing the mathematical tools and foundations that we need for these calculations!) as well as making sure any work you do in more applied realms is mathematically sound. You may be surprised to find that calculators are hardly used in university level maths because they simply aren't needed. Essentially, you've progressed beyond that type of maths!

Apologies if I've made these sound quite boring!
I find it strange that you have not mentioned any programming. Does your 1st year not cover any of it?

Programming in Excel / Maple / MATLAB / R / etc... is extremely important for us as mathematicians and is done to death in the Applied part of maths to solve ODE's and PDE's numerically that cannot be solved algebraically so that the solutions can be seen and analysed. You mention phase portraits which indeed give us some insight into how a dynamical system behaves, but seeing the well approximated solutions is also important in these scanarios and allow us to answer more direct questions.
Programming also comes up a lot in managing statistical data in R, but I'm not a statistician so I digress.

A compulsory introductory module is set in place at my university for 1st years and it has very good foundations for developing the skills required for research in Applied maths or some sort of relevant specialization. I suspect something of this caliber is true across most universities, so it's worth mentioning.


P.S. Maybe mentioning group-work assessments in Maths is also worthwhile, since it's not really a thing at A-Level or GCSE and may come as some sort of surprise to many in those positions.
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I’m hoping to start maths at nottingham in september! I only did maths at a-level, so what would you recommend looking over during this free time I have?
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_gcx
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I find it strange that you have not mentioned any programming. Does your 1st year not cover any of it?

Programming in Excel / Maple / MATLAB / R / etc... is extremely important for us as mathematicians and is done to death in the Applied part of maths to solve ODE's and PDE's numerically that cannot be solved algebraically so that the solutions can be seen and analysed. You mention phase portraits which indeed give us some insight into how a dynamical system behaves, but seeing the well approximated solutions is also important in these scanarios and allow us to answer more direct questions.
Programming also comes up a lot in managing statistical data in R, but I'm not a statistician so I digress.

A compulsory introductory module is set in place at my university for 1st years and it has very good foundations for developing the skills required for research in Applied maths or some sort of relevant specialization. I suspect something of this caliber is true across most universities, so it's worth mentioning.


P.S. Maybe mentioning group-work assessments in Maths is also worthwhile, since it's not really a thing at A-Level or GCSE and may come as some sort of surprise to many in those positions.
I forgot about this! Warwick does have Maths by Computer compulsory for straight maths students, in which Matlab is taught. (assignments included probability, graphs, root finding) There was an option to work in pairs. But beyond this module, there's no group work in maths and a small amount for some stats modules. I'm not really a fan personally, purely because I don't want to be assessed on what's partly someone else's work, I'd like to have control over it all. (not because of an aversion to group work itself)

There were a few other modules you could take involving programming like Stats Lab (whose overall purpose was to teach basic stats in a more practical setting primarily using R) and Programming for Scientists. (mathematical programming challenges/projects somewhat comparable to CATAM at Cambridge, but using Java. there were oddly no write-ups involved either)

Our Linear Algebra assignments had a small amount of Matlab but these were pretty insignificant and generally just involved a few lines of code. I was told this was mainly just to give a flavour of Maths by Computer, but it did save having to calculate rrefs by hand.
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I’m hoping to start maths at nottingham in september! I only did maths at a-level, so what would you recommend looking over during this free time I have?
I'm not OP but while I am here I suggest you are comfortable with most topics at normal A-Level, with heavy emphasis on Calculus and its applications.

But if you are already at this stage, it goes without saying that if you invest time in self-teaching yourself Further Maths with all the free time you got, then you will have an extremely smooth transition to uni maths.

And if you get through that, then you can prepare directly for your courses by starting to read up on some new stuff by looking at the material provided in your module reading lists for 1st year maths. E.g. reading list for the 'Calculus' 1st year module is here: https://rl.talis.com/3/notts/lists/8...99898F7B0.html
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I’m hoping to start maths at nottingham in september! I only did maths at a-level, so what would you recommend looking over during this free time I have?
Not certain how Nottingham's programme is structured, but the main issue new maths students face is having to adapt to the new style of university maths. Warwick throws you into this straight away but I understand that some may ease you into it more. I'd recommend looking at a basic university-level textbook, for example in analysis or elementary number theory, just to get a feel for the sort of style. These shouldn't need any further maths knowledge to start.

I wouldn't worry too much about covering all of A-level further maths, since that will be presumably be taught during your degree, but I would recommend having a look over complex numbers, (tbh, among the most important things you learn A-level FM [should be in normal maths imo]), matrices (similar) and maybe FM-level calculus/differential equations just so you have a good grasp of these things going in.

Definitely make sure you're comfortable with A-level maths above all things!
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zetamcfc
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(Original post by RDKGames)
I find it strange that you have not mentioned any programming. Does your 1st year not cover any of it?

Programming in Excel / Maple / MATLAB / R / etc... is extremely important for us as mathematicians and is done to death in the Applied part of maths to solve ODE's and PDE's numerically that cannot be solved algebraically so that the solutions can be seen and analysed. You mention phase portraits which indeed give us some insight into how a dynamical system behaves, but seeing the well approximated solutions is also important in these scanarios and allow us to answer more direct questions.
Programming also comes up a lot in managing statistical data in R, but I'm not a statistician so I digress.

A compulsory introductory module is set in place at my university for 1st years and it has very good foundations for developing the skills required for research in Applied maths or some sort of relevant specialization. I suspect something of this caliber is true across most universities, so it's worth mentioning.


P.S. Maybe mentioning group-work assessments in Maths is also worthwhile, since it's not really a thing at A-Level or GCSE and may come as some sort of surprise to many in those positions.
Don't scare people away, not all of us are one with technology
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Do you think not having Further Maths A-level would hold me back? I'm a year 12 studying Maths, Physics and History. I wasn't sure what I wanted to do when I started A-levels so kept my options open but am now thinking of studying maths at uni! It stresses me out a bit as I get mixed responses from teachers. Thank you for doing this
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Do you think not having Further Maths A-level would hold me back? I'm a year 12 studying Maths, Physics and History. I wasn't sure what I wanted to do when I started A-levels so kept my options open but am now thinking of studying maths at uni! It stresses me out a bit as I get mixed responses from teachers. Thank you for doing this
It will only stop you from applying to a few universities at the top - namely Cambridge, Warwick (for the flagship maths course - some joint honours will accept you without further maths) and Imperial. (who seem to strictly only allow a lack of FM where it is not offered at the applicant's school)

Other universities will give you offers, but these might be higher than they would be with further maths. Some universities take the position of - if further maths is offered, you should take it, (for example, Oxford) for other courses they merely (in some cases, strongly) recommend FM. (I think when I was at an open day for Bath they mentioned that your application may be disadvantaged without FM at at least AS level)

You may be interested in doing an AS in further maths which lowers entry requirements for some universities, if you have the time. (so does AEA/TMUA/MAT/STEP, but the latter of these is known to be quite scary and the AEA is less popular these days)

However, there are equally plenty of courses that don't require A-level further maths at all. These would introduce these concepts from complete scratch, so you wouldn't have to worry about not having further maths.

Overall - if you like maths this shouldn't hold you back!
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(Original post by _gcx)
TSR has decided to run some university AMA threads seeing as many university open days have been cancelled.

I'm a maths student at Warwick and I've just finished my first year. I'm happy to answer any questions you might have about studying maths at university, or studying maths at Warwick in particular.

I feel this thread is particularly important since there's a lot of difference between maths at school and maths at university!

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What is the main difference between A-level maths/further maths and University maths - is uni maths similar to further maths/ does further maths give sufficient preparation for uni?
Do you have the opportunity to explore optional modules in other departments at Warwick, for example physics or economics?
Also, how is the maths that you learn applicable in real life, like how will it been used in jobs?

Thank you!
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(Original post by _Mia101)
What is the main difference between A-level maths/further maths and University maths - is uni maths similar to further maths/ does further maths give sufficient preparation for uni?
Do you have the opportunity to explore optional modules in other departments at Warwick, for example physics or economics?
Also, how is the maths that you learn applicable in real life, like how will it been used in jobs?

Thank you!
The main difference between A-level and university is definitely the style! At A-level, you'll typically be introduced a concept, (a lot of things being given without proof) given a few examples, and then be given a load of questions which will often be closely tied to said examples. The way you're taught maths at university will be more centred around the theory, and actually understanding the maths rather than just learning things to immediately apply in samey computations. Proof will become a central part of your learning, rather than just an aside/afterthought.

Of course, you will have computation but these will should be less routine and require more thought than you've seen at A-level. You'll find only a small proportion of assignments are routine computations. To take Warwick Differential Equations sheets for example - section A has quite routine computations (solving ODEs for example), but this only ends up contributing 2/20 marks. In assignments you might explore important consequences of results you've seen in lectures, look at generalisations (for example - many theorems say if x then y, you might prove that in fact - if y then x, meaning that the two statements are equivalent, [both true or both false] or indeed find that there are examples where y holds, but x doesn't) and perhaps apply some of the more abstract results you've learnt to more concrete examples.

I'd say no, honestly. Proof-based maths is a shock to many people and unfortunately, some people find that [at least pure] university maths isn't for them despite liking school maths. I'll get onto this in answering your next question, but many of these people instead decide to take more applied routes through their degree, focusing on for example statistics, physics or economics. (Warwick is quite flexible in allowing people to transfer to joint degrees like MORSE, provided the correct modules are taken) STEP is a good transition to university-based maths with its emphasis on problem solving, and I'd strongly recommend trying some STEP questions even if your offer does not require STEP.

Yes. At Warwick there are "usual" options, that you can take freely, and unusual options which require departmental approval from the department offering the module. (you can take up to 30 CATs of modules, which is 25% of the year if you are taking only the standard load) Usual options include physics, statistics, economics, computer science, philosophy, business, engineering, film and even a practical teaching module! (involving a placement at a secondary school) Unusual options can be from any department, provided departmental approval which is often simply a matter of having the correct prerequisites. If you take the correct options in your first year, you can transfer to a joint degree program like MORSE, maths and economics, maths and philosophy, maths and stats, maths and physics, and so on. This might prove a useful escape for people who don't like university level maths.

Virtually every topic you learn in your first two years will be applicable. Differential equations and linear algebra, for example, are an integral part of physics, (for example - linear algebra is used quite heavily in relativity) and heavily used in statistics as well. Even something as abstract as topology is used in areas of physics such as quantum field theory. I assume applications to statistics will prove practical in the real world, but it's not often something I consider because I just do maths because I like it lol. As RDK said above you'll learn programming skills which will be useful in industry. How things relate directly to jobs I wouldn't know, sorry!
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Also, how is the maths that you learn applicable in real life, like how will it been used in jobs?
I will give a little bit here.

> Programming is useful if you aim to go into any related work to do with that.

> You can also focus on specialising in Statistics to become a statistician and work for private companies to help with data. E.g. Pharmaceutical companies like PAREXEL seek out statisticians to help analyse developing drug data in phases I and II of the development cycle. Not to mention the lovely bonuses you get for working for these companies...

> If you want to teach Maths then obviously the maths you learn at uni definitely helps you understand the field a whole lot better and hence be able to pass this knowledge along.

> If you want to go into any science related research then you will undoubtedly have the benefit of problem-solving skills when it comes to logical problems.

> There are jobs for mathematical modelling where you use lots of theory (mostly related to mathematical physics) to help construct mathematical models that describe different scenarios of a situation the company would want you to predict. For instance, the whole 'flatten the curve' saying nowadays is related to a curve which originates from solving a system of ordinary differential equations; i.e. mathematical modelling brought this curve to life. By playing around with the different parameters of the model, the experts have been able to flatten it. And to an average Joe, this is where social distancing comes from.


Truth be told, the skills you learn on a Maths degree do not imply you will excel at a particular job tied to it, this is why most companies would just train you. But they want you to have the experience of a uni degree so that they know you have been exposed to all the good background skills that come with it. High salary jobs like acturial work would require you to have a decent degree in a numeric subject before they decide to take you in and train you to build on top of all those problem solving skills so that you're ready to specialise in that work.
Last edited by RDKGames; 9 months ago
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(Original post by _gcx)
The main difference between A-level and university is definitely the style! At A-level, you'll typically be introduced a concept, (a lot of things being given without proof) given a few examples, and then be given a load of questions which will often be closely tied to said examples. The way you're taught maths at university will be more centred around the theory, and actually understanding the maths rather than just learning things to immediately apply in samey computations. Proof will become a central part of your learning, rather than just an aside/afterthought.

Of course, you will have computation but these will should be less routine and require more thought than you've seen at A-level. You'll find only a small proportion of assignments are routine computations. To take Warwick Differential Equations sheets for example - section A has quite routine computations (solving ODEs for example), but this only ends up contributing 2/20 marks. In assignments you might explore important consequences of results you've seen in lectures, look at generalisations (for example - many theorems say if x then y, you might prove that in fact - if y then x, meaning that the two statements are equivalent, [both true or both false] or indeed find that there are examples where y holds, but x doesn't) and perhaps apply some of the more abstract results you've learnt to more concrete examples.

I'd say no, honestly. Proof-based maths is a shock to many people and unfortunately, some people find that [at least pure] university maths isn't for them despite liking school maths. I'll get onto this in answering your next question, but many of these people instead decide to take more applied routes through their degree, focusing on for example statistics, physics or economics. (Warwick is quite flexible in allowing people to transfer to joint degrees like MORSE, provided the correct modules are taken) STEP is a good transition to university-based maths with its emphasis on problem solving, and I'd strongly recommend trying some STEP questions even if your offer does not require STEP.

Thank you so much!

Yeah, that is my biggest worry - the change in style between school and university. I'm only in year 11, so I still have time to explore all this stuff, so I'll definitely get involved in the STEP classes at my sixth form.

I think it was mentioned that calculators aren't really used in maths at uni, does that mean it is majorly proof work and mental maths? Also, do you prove things yourself or are you taught the proofs?

Yes. At Warwick there are "usual" options, that you can take freely, and unusual options which require departmental approval from the department offering the module. (you can take up to 30 CATs of modules, which is 25% of the year if you are taking only the standard load) Usual options include physics, statistics, economics, computer science, philosophy, business, engineering, film and even a practical teaching module! (involving a placement at a secondary school) Unusual options can be from any department, provided departmental approval which is often simply a matter of having the correct prerequisites. If you take the correct options in your first year, you can transfer to a joint degree program like MORSE, maths and economics, maths and philosophy, maths and stats, maths and physics, and so on. This might prove a useful escape for people who don't like university level maths.
I didn't realise there was so much flexibility module-wise. Does that mean if you applied for MORSE you could potentially switch to maths and economics?

Virtually every topic you learn in your first two years will be applicable. Differential equations and linear algebra, for example, are an integral part of physics, (for example - linear algebra is used quite heavily in relativity) and heavily used in statistics as well. Even something as abstract as topology is used in areas of physics such as quantum field theory. I assume applications to statistics will prove practical in the real world, but it's not often something I consider because I just do maths because I like it lol. As RDK said above you'll learn programming skills which will be useful in industry. How things relate directly to jobs I wouldn't know, sorry!
That makes sense :yep:. Although, I was thinking a bit more about pure maths... but it seems that how pure maths is seen at uni is very different to how it is in school, and resultingly is more applicable in the real world.
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