[Request] How to be a good maths student and applicant Watch

Athematica
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#1
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Hi

I'm a y12 student, studying for maths, further maths, chemistry and physics. My intention wasn't to study maths initially but I've warned to the idea. We recently started M2 and C2 (as our structure is C1-3 and M1-3 in y12 then FP1-2, C4 and S1-3 in y13.) and by far it is the most interesting subject I am studying. Vector mechanics is the first subject I've felt myself actually having to think about what is happening and I love it. Though, I feel I have a lot of catching up to do if I am to attend one of the 'Big 5' (COWIB) compared to those who've known and practiced maths since they were young.

Recently I picked up the Art of Problem Solving vol 1: The Basics so to become a more proficient problem solver and understand beyond the syllabus with a little more nuance (while also acting as a springboard for trying olympiad and MAT style questions then Silko and STEP). However, otherwise, what can I be doing to become a more proficient mathematician, improve my number sense, mathematical intuition, etc.? "Do lots of maths!" is clearly the general idea but something a bit more specific might be useful to aspiring mathematicians here Are there any resources in particular that you might recommend? I've heard about the Nrich website recently so may give that a try.

Appreciate any advice you can offer.
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Jai Sandhu
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(Original post by Athematica)
Hi

I'm a y12 student, studying for maths, further maths, chemistry and physics. My intention wasn't to study maths initially but I've warned to the idea. We recently started M2 and C2 (as our structure is C1-3 and M1-3 in y12 then FP1-2, C4 and S1-3 in y13.) and by far it is the most interesting subject I am studying. Vector mechanics is the first subject I've felt myself actually having to think about what is happening and I love it. Though, I feel I have a lot of catching up to do if I am to attend one of the 'Big 5' (COWIB) compared to those who've known and practiced maths since they were young.

Recently I picked up the Art of Problem Solving vol 1: The Basics so to become a more proficient problem solver and understand beyond the syllabus with a little more nuance (while also acting as a springboard for trying olympiad and MAT style questions then Silko and STEP). However, otherwise, what can I be doing to become a more proficient mathematician, improve my number sense, mathematical intuition, etc.? "Do lots of maths!" is clearly the general idea but something a bit more specific might be useful to aspiring mathematicians here Are there any resources in particular that you might recommend? I've heard about the Nrich website recently so may give that a try.

Appreciate any advice you can offer.
If you are serious, I would love to help you out so drop me a message. Quick couple of notes while I am here:

1.) I would not include Bath up there in the ranks of COWI, there is a pretty stark difference, even though Bath is a great uni (it was my backup for Maths if I did not get into Warwick)

2.) If you get examined on your yr12 modules in yr12, doing M1-3 seems absurd as M3 in my opinion should not be being examined at the end of yr12. I personally believe you are unlikely to have the mathematical maturity to ace that module then, (if you do, you probably don't need to be asking for help) I couldn't even do M2 to a good enough standard (i.e. being able to regularly score 90+) at that point, then again I am not the best mathematician.

3.) Is there anyway your school would let you do FP1-3, I personally believe it is much more valuable to do all the pure maths modules, than an extra applied one.
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TimGB
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You seem to be a cool person who enjoys maths. Don't get caught up in bureaucratic world of university applications though, I mean it sure is important and needs to be done, but there's no point getting hung up about it. Take a step back and appreciate the beauty of the mathematical world - there's so much cool stuff out there, like how the sine function can be written as a combination of all odd positive powers of x, and how φ can be written as 1/(1+1/(1+1/....)) etc, making it the most irrational number, and how any function that is differentiable on the complex plane has nth derivatives for all positive n.

Let the offers come to you. They will, by the way, as long as you keep exploring maths and you tell universities about what you learn. A whole world of mathematics awaits - there's no time to waste! Quickly now, which is bigger, π^e or e^π?

There are many good books out there that you can read, too. I'd recommend 'the number mysteries' by Marcus Du Sautoy, but there are plenty of others out there. Go above and beyond and completely outside what you learn in school. School maths shouldn't be the limit. Read up on stuff like ε-δ proofs, partial derivatives, images and kernels. Read some mathematical papers or watch talks - even if you don't really understand them, they can still be interesting and insightful.
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