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Maths Problem Solving

How and where can I start getting better at solving maths problems like the UKMT challenge? Are there any courses/methods or books I can use that will dramatically improve my maths abilities?
Reply 1
Original post by Utomic
How and where can I start getting better at solving maths problems like the UKMT challenge? Are there any courses/methods or books I can use that will dramatically improve my maths abilities?


What level / year, what problems do you think youre having, have you done any challenges, ....? Im not sure it will dramatically improve your maths ability, but it should make you more flexible, get you to think about problems from different viewpoints and give you a bit more appreciation of the historical stuff.
Reply 2
Original post by mqb2766
What level / year, what problems do you think youre having, have you done any challenges, ....? Im not sure it will dramatically improve your maths ability, but it should make you more flexible, get you to think about problems from different viewpoints and give you a bit more appreciation of the historical stuff.

I am in year 12 and I ve recently done the senior maths challenge and got a bronze. I am a bit disappointed as the other peers in my further maths lessons got silver and are way better at maths than I am. I find maths sort of boring but I want to study general engineering at imperial college university
Reply 3
Original post by Utomic
I am in year 12 and I ve recently done the senior maths challenge and got a bronze. I am a bit disappointed as the other peers in my further maths lessons got silver and are way better at maths than I am. I find maths sort of boring but I want to study general engineering at imperial college university


Cant remember exactly, but imperial (general engineering, does it exist?) usually requires some form of mat/step test and that would be the key thing to aim towards. However, spending a few months doing some ukmt (smc/bmo) type practice would be a step in that direction, although mat is gcse+maths AS syllabus (some problem solving) and step 2 is maths A + further AS syllabus. smc and bmo is largely based on gcse maths so youd be consolidating that and practising some problem solving.

Obviously practice is the key thing, so going over past papers and reflecting on the solutions, both for the questions you get right as well as the ones you cant do. The extended solutions on the ukmt site have some supplementary questions for the harder ones and theyd be worth doing for the ones you couldnt start. For the practice, Id do some timed but also do a few questions untimed/open book where you simply think about the problem, before looking at the solutions. It would also be worth doing a few imc if youre ~bronze smc as its a similar syllabus but the questions are a bit easier.

For this years smc, I did an elementary/problem solving approach thread
https://www.thestudentroom.co.uk/showthread.php?t=7412326
so you dont really need a level maths, never mind further for pretty much all the questions. Maybe go through that and see what you did/think. For a book about problem solving I like
https://www.worldscientific.com/worldscibooks/10.1142/9478#t=aboutBook
and that would probably benefit both smc and mat (somewhat), but its got little to do with a level maths. The reimann zeta stuff at drfrost is aimed at smc/mat/step
https://www.drfrostmaths.com/downloadables.php?noid=917
though the slides are good, its worth skimming them to begin with. Similarly in y12, the step foundation modules are worth going through
https://maths.org/step/assignments
as are having a peek at the mat liverstream stuff.

There are quite a few other resources (mentoring sheets, parallel (imc), ....), but honestly hitting a few smc papers, asking for some advice about things you find hard, reflecting on the solutions and learning a bit problem solving would be the things that would bump up your performance in the short term and keep in mind that youre really doing it as a step towards the step/mat stuff. Theres no silver bullet, so regular practice/a bit of reading each week, is the key thing. If youre aiming for a top uni (imperial - engineering), youre going to have to get over the finding maths boring somehow.
(edited 4 months ago)

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