Getting to Cambridge: STEP by STEP!

If you can get your hands on "Pure Maths 1and 2" by S L Parsonson, it'll make interesting reading.

Me? I think that's a bit useless at this stage. I'd rather read more rigorous things like "Algebra and Geometry" by A.B or other books off the Cambridge tripos reading list (A first course in analysis looks lovely as well!) - but thank you for the recommendation!

Not sure what level you're at (I know you're still at school but you could be IMO level) but the books I suggested are aimed at pre-uni students but are very old 1950s A-Levels, so is quite different to modern day books.

Might even be able to download a copy.

Re analysis, I was using Mathematical Analysis by K G Binmore.

Aye, but it'd just be the same content or pre-uni content taught in a different (albeit more rigorous way), I'll have a look anyway, thanks.

Re: analysis, I was recommended this book just today itself, what were your thoughts?

It's been a VERY long time since I graduated, (to give you an idea, S-Levels were still around and STEP 1 and 3 were on the same day, to prevent you taking both) but as far as I can remember, it was quite a good read.

Analysis is a course most undergrads find difficult because it's not something they've encountered before.

Algebra is less daunting, as school used to cover group theory and matrix algebra.

I particularly liked the "tests" eg D'Alembert's ratio test or nth root test.

I'll give it a look in that case, thanks!

Aye, the tests are fun but from the little I've been doing, I seem to really like fiddling about with epsilon-deltas proofs. By the way, I've been meaning to ask - would things like injectivity, surjectivity and their nitty gritty definitions be covered in Analysis or Algebra?

I am NOTa strong mathematician unfortunately but I am blessed with a good memory,

From what I can recall, these were covered in analysis. Definitions such as bijection means "one to one and onto" whatever that means!

Algebra contained defns such as isomorphism, congruence, etc.

Alg courses included groups, group rep, rings, alg number theory, lin alg and geom.

Analysis had complex analysis, functional analysis, real analysis, prob from a pure perspective, analytical geometry (as oppsed to differential geom) and analytical number theory.

Most people at school would not have come across pure, so really chooses between applied and stats.

Why are you so interested in pure?

Yikes, that sounds very heavy. Thanks for it!

I haven't quite sworn myself to pure or applied yet, I'm keeping my options open, which is partly why I did M1-3 and S1-3. I'll settle on something once I've had some proper exposure to it.

But partly, I seem to feel an inexorable attraction to pure, it's what makes the most 'sense' to me and the feeling after grasping a concept that you've struggled with after ages is very nice. It's more abstract than the 'applied' stuff (from what I've heard: applied at uni is pure at A-Level, so that checks out) which is more computational and technique-y and hence carries (in my opinion) less reward.

That wasn't explained very well, but that's abouut the gist of it.

Yes, school pure maths is called methods and is classed, if anything, as applied.

I did MEI maths, which consisted of 2 papers for A-Level and 2 for FM.

Paper 2 included mechanics and mathematical physics, as well as stats, though my school only taught stats, so I was penalised very heavily, as the FM paper was choose 7 questions from 18, meaning for my class, it was choose 7 from 9!

Naturally I could only do pure and stats at uni, severely limiting my options.

Uni pure is an acquired taste I feel. A comtemporary of mine was like yourself, adamant on doing applied but eventually ended up with a PhD in Group Theory!

What's your liking of programming? A good applied mathematician cannot get away from it.

I personally hated it, we did FORTRAN in my days, yet now I'm a programmer!

You prefer analysis or algebra?

For example Riemann Integrals or The Rank Nulity Theorem, which believe it or not, has it's practical uses in stats!

Pure horror

PRSOM It doesn't feel like two days... doe

Time flies when you're having fun

Wait, people are enjoying Easter and not revising? What has this world come to? Idek myself anymoar!

I'm really sick atm so the "enjoying myself" part cancels out Neutral holiday

I'm really sick atm so the "enjoying myself" part cancels out Neutral holiday

I'm really sick atm so the "enjoying myself" part cancels out Neutral holiday

Hope you feel better soon!

Aww shaz man, feel better soon! Meanwhile on #PlanetBrokeAF

Thank you both Happy Easter if you guys celebrate!

This thread did.. For 2 whole days