# What is you favourite area of Maths? watch

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1. Most A-Level students will say Calculus, though after being torn apart and put back together with infinite detail, first in terms of Riemann Integration, and then Lebesgue Integration, I'd be very surprised if this was still the same answer upon graduation. Having said that, Lebesgue integration is so important for higher level mathematics, that it's hard to scoff at it's significance.

I myself, am very into probability: Stochastics (esp. differential equations), Brownian Motion, Time Series, and outside probability: Dynamical systems, and Functional Analysis.
I've become quite taken with Complex Analysis too. Far more satisfying and challenging than Real Analysis. The difference in Taylor's Theorem between real and complex cases is astounding.

I think probability is very underrated as a Mathematical discipline. The proofs are less technical, and generally need to be cleverer.
2. (Original post by GordonP)
Out of interest, anyone know what we use sec, cosec and cot for, the answers I got from my maths teachers were all 'uh, dunno, try Mr/s x'
They crop up all the time in applied maths, when you've got things like 1/tan or 1/sin. It's like asking "What do we use i for?".
3. This has to have been question of the year for Mathematics interviews... It rather irritates me, to be honest, as it's quite hard to pick on a single area, although I definitely gravitate more towards the pure modules.
4. I've loved all the algebra I've done. Galois theory in particular is just so pretty. Group theory, ring theory, module theory, automata... it's all good with me.

I did a really fun course called Designs & Codes that involved a little bit of Galois theory and some combinatorics. I also loved the basic number theory I did, but at the higher levels it's so hard.

Complex analysis was good, but I hated real analysis. Could manage calculus, DEs, etc. but nothing remotely applied (mechanics... ugh!)
5. i'm doing A level and my favourite is differentiation and intergretion. esp with all the In and cos and cosec and stuff. all the more complicated the funner
6. Not far into the realms of calculus, but got to say that I love it. Personally, differentiation is much more exciting than integration.

But doesn't anyone else find that you get a nice feeling of achievement after you have worked a particularly demanding question and that you have actually enjoyed it?
7. I love number theory ("the Queen of Mathematics") and prime numbers.
Apparently they are paying \$100,000, to the first person who discover a prime number with more than 1 million digits.

www.mersenne.org/
8. Favourite in terms of difficulty level? Induction hands down.

Favourite in terms of how challenging/stimulating the topic is: Statistics.
9. (Original post by Knogle)
Favourite in terms of how challenging/stimulating the topic is: Statistics.
You Crazy?

..and hello The D , welcome to (I like me number theory too )
10. (Original post by KAISER_MOLE)
You Crazy?

..and hello The D , welcome to (I like me number theory too )

Well it does involve a fair amount of cracking your brain, but once you arrive at the answer, you feel like you're on cloud no. 9.
11. (Original post by The D)
Apparently they are paying \$100,000, to the first person who discover a prime number with more than 1 million digits.[/URL]
You mean 10 million. I've a 4 million digit prime saved on my PC, and the largest known prime is 9 million digits long
12. Brilliant. I'm such a geek. I read about AlphaNumeric's 4 million digit prime number and there's nothing I can do to stop the sheer envy well up inside me as I realise that *his prime is bigger than mine*.

Some poetic licence there. In fact I don't have any primes saved on my computer
13. mechanics is the most enjoyable aspect of maths alevel and with pure maths it feels your on top of the world when you get that tricky question right!
14. (Original post by AlphaNumeric)
You mean 10 million. I've a 4 million digit prime saved on my PC, and the largest known prime is 9 million digits long
Yes. It should be 10 million. The largest prime known is 9,152,052 digits long.
15. differential equations and discrete maths
16. I'm only at the end of the A-level syllabus (1st year college, but doing maths in a year so we do all of FM next year), but since starting A-level I've really found the calculus interesting. Luckily we've got a really good teacher who goes a bit beyond the syllabus (we're a class of about 11 specifically aimed at FM - everyone got As in core 1 so he can afford to :P) and really explains topics. This means we can cover the derivations of some formulae which would normally be taught but not explained.

In maths outside school, I'm really interested in pure topics like prime numbers, complex numbers, set theory etc. What I'm currently looking into is Maclaurin series - they look pretty nifty.

I think it's the abstraction of the pure maths that makes it rewarding for me. I don't find mechanics or stats that interesting because the results are normally just predictions about a real world scenario, which you could obtain just as easily through an experiment. With the pure stuff, you're not modelling a real process, you're finding answers because they're valuable in themselves - to me, this seems like a more satisfying way to do maths.
17. group theory, stats, decision maths are all boring.

complex numbers have interesting parts, although to be honest i^i being real was pretty much the most interesting thing there. a lot of boring algebra, essentially just another form of geometry, especially with nth roots and expansions of (sin x)^n and (cos x)^n. some interesting calculus applications i guess.

calculus is where it's at as far as a-level f.maths is concerned. and step (although the mech questions on step are oftenthe easier ones....)
18. (Original post by Bigcnee)
Most A-Level students will say Calculus, though after being torn apart and put back together with infinite detail, first in terms of Riemann Integration, and then Lebesgue Integration, I'd be very surprised if this was still the same answer upon graduation. Having said that, Lebesgue integration is so important for higher level mathematics, that it's hard to scoff at it's significance.

I myself, am very into probability: Stochastics (esp. differential equations), Brownian Motion, Time Series, and outside probability: Dynamical systems, and Functional Analysis.
I've become quite taken with Complex Analysis too. Far more satisfying and challenging than Real Analysis. The difference in Taylor's Theorem between real and complex cases is astounding.

I think probability is very underrated as a Mathematical discipline. The proofs are less technical, and generally need to be cleverer.
Having just taken a first course in complex analysis this term (and more real analysis last term) it feels as if the proofs are very repetitive - they all seem to involve the same ideas and steps which makes them extremely dull to work on. The results themselves are very significant; it's just that one often finds it too pedantic to prove them.

I personally enjoy applied mathematics, group theory and dynamics (although I do find the latter topic very difficult to comprehend at the moment).

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Updated: April 10, 2006
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