Most interesting area of mathematics?

Michael Collins

What would you say was the most interesting area of maths you ever studied?

Someone asked me this question there the other day and I had to think a bit, in the end I came up with:

For pure Maths I'd have to say: Complex Analysis - since it's such a "beautiful" area, if I may use that word! With lots of powerful theorems including a nice easy proof of the Fundamental Theorem of algebra.

For applied Maths it'd probably be: Differential Equations - they are the language of nature after all. Nearly everything can be modelled using these somehow.

I liked Linear Algebra too...it crops up all over the place in other areas and I think if you have a good knowledge of this, it helps your maths in general.

So what's your favourite area!?

Pherekydes

My favourite area was number theory. Its application to cryptography is fascinating.

I was also very taken by Combinatorics, which I found great fun, and probability.

Starting a Masters on monday and complex analysis is an option, so I'm strongly leaning towards taking it.

hivizman

I loved Galois Theory, and also mathematical logic and recursive function theory - the more abstract the better. Forgotten all the details now, alas, but still have a vague recollection of the general principles and the major results, such as Kurt Gödel's Incompleteness Theorem and Alan Turing's work on computation and decidability. I studied this under Robin Gandy (sadly now dead), who had been a student and colleague of Alan Turing's, so perhaps that made the course particularly stimulating.

Sadly, complex analysis didn't turn me on.

Fremen

Probability theory and stochastic analysis. Brownian motion is freaking awesome.

LeixlipRed

Number Theory and it's applications to crytpography. Anyone disagrees and two month ban straight off.... :P Also, linear algebra, I'd roooiiiidddeee her out if it.

ramanujan

LeixlipRed wrote: »

Number Theory and it's applications to crytpography. Anyone disagrees and two month ban straight off.... :P Also, linear algebra, I'd roooiiiidddeee her out if it.

always taught of linear algebra as a tool, never really did it for me!!!


on the other hand combinatorics is the bizz, funny seeing youngsters grasp concepts professors struggle with. maths is littered with boring repetitive tasks until college, so it's like a haven for young 'n old!

Fremen

ramanujan wrote: »

always taught of linear algebra as a tool, never really did it for me!!!


on the other hand combinatorics is the bizz, funny seeing youngsters grasp concepts professors struggle with. maths is littered with boring repetitive tasks all through college, so it's like a haven for young 'n old!

Fixed that for you

Honestly, I saw very few interesting/elegant problems as an undergrad. In the first couple of years when you're mixed in with business and science students, it's even worse since they need to keep things relatively easy.