in general, what's the difference between pure and applied mathematics. Watch

Toasticide
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so i know there is no easy answer to this question for many reasons. but basically, what i mean is (corresponding to the edexcel non-further maths A level course) is C1-4 pure maths and the S/M chapters the applied ones? i need to make a decision as to wether i want to do pure or applied as i have to make a decision as soon as possible as to what uni's i want to go to so i can get a personal statement done, i strongly prefer trigonometry and all the C chapters to the S chapters and M chapters (i havent actually done this in maths yet, but based on physics experience, its an utter nightmare) so i THINK im a pure student rather than applied
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smartalan73
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(Original post by Toasticide)
so i know there is no easy answer to this question for many reasons. but basically, what i mean is (corresponding to the edexcel non-further maths A level course) is C1-4 pure maths and the S/M chapters the applied ones? i need to make a decision as to wether i want to do pure or applied as i have to make a decision as soon as possible as to what uni's i want to go to so i can get a personal statement done, i strongly prefer trigonometry and all the C chapters to the S chapters and M chapters (i havent actually done this in maths yet, but based on physics experience, its an utter nightmare) so i THINK im a pure student rather than applied
In A level terms C1-4 are pure maths, and mechanics and stats are the applied units. However I have been told by uni students that you don't really learn any actual pure maths at A level, all the stuff you get told is pure like calculus and trig is actually applied when you get to uni
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Toasticide
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(Original post by smartalan73)
In A level terms C1-4 are pure maths, and mechanics and stats are the applied units. However I have been told by uni students that you don't really learn any actual pure maths at A level, all the stuff you get told is pure like calculus and trig is actually applied when you get to uni
ah many thanks, the reason i prefer calculus and trigonometry is because it is something bizarre that (at my level) has little to no applcation and is generally new therefore i think id prefer pure. i dont really like stats, it's generally simple stuff, but boring, and mechanics in physics (i presume similar to maths) is just sheer difficult. thanks for your answer, really helps
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qno2
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Generally speaking, pure maths is done for the sake of maths while applied is done to solve or model something different. At undergraduate, there tends to be four different types of courses on offer: methods, pure, applied and statistics though statistics does sometimes come under applied.

Methods courses are normally the core stuff you "need" to do all the other things. This will mainly be calculus and algebra in a broad sense but should include some numerical analysis. Most of the stuff you will do at school falls into this category.

Pure courses will focus more on proofs and more abstract mathematical concepts. Number theory, geometry and topology are normally examples of this. You'll have done little to no real pure maths in school so wait and see if you like it.

Applied courses, as the name suggests, will involve using maths in other subject areas generally. Physics, biology and finance all benefit greatly from mathematicians solving problems they themselves can't deal with, amount other areas. Modern maths education in schools tries to make it more relevant to people by making the subject more applied but don't let those boring cases put you off more interesting applications.

Statistics tends to be considered its own subject as statistical distributions and probabilities change most maths at a fairly fundamental level. It does sometimes come under the heading of applied maths.

I'd also like to emphasise that courses won't nessicssarly sit in isolation as methods courses often have a pure or applied slant on them in later years. A module on partial differential equations might concern itself with standard methods for solutions and studies of property and structure of those solutions whereas at another university, it might be about standard methods for solving and then looking at how certain types of equations model physical systems. Nothing like this is ever as black and white as some people make them out to be.


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Toasticide
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(Original post by qno2)
Generally speaking, pure maths is done for the sake of maths while applied is done to solve or model something different. At undergraduate, there tends to be four different types of courses on offer: methods, pure, applied and statistics though statistics does sometimes come under applied.

Methods courses are normally the core stuff you "need" to do all the other things. This will mainly be calculus and algebra in a broad sense but should include some numerical analysis. Most of the stuff you will do at school falls into this category.

Pure courses will focus more on proofs and more abstract mathematical concepts. Number theory, geometry and topology are normally examples of this. You'll have done little to no real pure maths in school so wait and see if you like it.

Applied courses, as the name suggests, will involve using maths in other subject areas generally. Physics, biology and finance all benefit greatly from mathematicians solving problems they themselves can't deal with, amount other areas. Modern maths education in schools tries to make it more relevant to people by making the subject more applied but don't let those boring cases put you off more interesting applications.

Statistics tends to be considered its own subject as statistical distributions and probabilities change most maths at a fairly fundamental level. It does sometimes come under the heading of applied maths.

I'd also like to emphasise that courses won't nessicssarly sit in isolation as methods courses often have a pure or applied slant on them in later years. A module on partial differential equations might concern itself with standard methods for solutions and studies of property and structure of those solutions whereas at another university, it might be about standard methods for solving and then looking at how certain types of equations model physical systems. Nothing like this is ever as black and white as some people make them out to be.


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ahhh that's interesting, thanks, i mean, stats i dont like and i noticed that courses can be one or more of "pure" "applied" or stats and got confused why the last two were different. also sciences i dont really like, im doing all three for a level but so far biology is more stats than methods and physics is sheer difficult. This actually helps as it makes module lists that will be covered a lot easier as before i thought calculus and trigonometry were pure when its just methods parts. now i know what they actually mean!
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