This is sort of an odd request I guess...I'm a math buff, I love maths. I'm sort of feeling bored though, I need stimulating mathematical challenge.
Can anyone suggest some hypothesis's and stuff I could read up on and mess with? Anything which is just complex, involving and makes you really really think will do! I was thinking the riemann hypothesis but I looked into that before and I'm after something new...
__________________ Omnis mico antequam dominus Spookster!
What level math are you in? I could give you some fun problems I had from Multivariable Calculus, or you could try proving the explicit formula for the nth term in the Fibonacci sequence using various topics from Linear Algebra, or I could give some some differential equations from my DiffEq class, or heck, I could even give you some proofs from my Topology seminar, or a nifty problem we recently had in Real Analysis. But you wouldn't be able to solve any of them without the appropriate background.
But I mean like, have you had Real Analysis? Differential Equations? Linear Algebra? Multivariable calculus? If I was to mention topology of the real number line, bernoulli's method, eigenvalues, or directional gradients (examples from each of those classes respectively), would you know what I'm saying?
If you want some fun, prove:
The area underneath the normal bell curve is in fact 1. That's a pretty simply exercise in multivariable calc to get you started. For more calc fun, find the 2 curves which satisfy x^y = y^x.
Originally posted by bcarl314 Well, you could look into group, ring, and field theory. Very intense stuff and should keep you busy. (Of course I'm assuming you don't have a Masters in Math, otherwise this would be old hat.)
Yeah, that used to be my favorite topic back in the day (and today I barely remember what a group is ). I could discuss those cyclic groups for ages. If you like algebra and number theory then that's the way to go.