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Thread: Fascinating mathematics

01292004, 11:06 AM #1
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Fascinating mathematics
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!
01292004, 12:20 PM
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01292004, 12:23 PM
#3
Baire Category theorem? Pretty important to the branch of Topology....
01292004, 12:26 PM
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Excellent! That should keep me busy for a while.
Omnis mico antequam dominus Spookster!
01292004, 12:46 PM
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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.)
01292004, 01:54 PM
#6
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.
01292004, 02:18 PM
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I'm not sure what level you would consider me over there but over here I'm doing 3 unit mathematics. I would be doing 4 unit but I don't have the time (being HSC year and all)..
Usually if I can't do something I ask dad and he explains it ... feel free to throw anything fun at me, if I don't know how to do it, it becomes all the more fun finding out how ..
Has anyone ever dealt with quadrics? Part of anylictic calculus I think. I've never really looked at them but dad mentioned they can be quite a challenge!
Omnis mico antequam dominus Spookster!
01292004, 03:27 PM
#8
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.
01292004, 03:28 PM
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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.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.)
shmoove
01302004, 05:15 AM
#10
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Hey Mhtml, would you be willing to do a mathtype problem for me; even though I use coloured scrollbars on my site?
<div>  putting your mind in a box since 1997
01302004, 08:48 AM
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lol, depends what it is!
I'll have a go at those things you suggested Jason. Also I've done differentiation/integration/multivar calc but I haven't touched topology (at least I don't remember doing it!) ...
Omnis mico antequam dominus Spookster!
01302004, 03:48 PM
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"For more calc fun, find the 2 curves which satisfy x^y = y^x."
or die trying...
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01302004, 04:07 PM
#13
Really not that tough, I'll do half of it. y = x . Find the other one . Really not that bad though, I can show you the writeup I did of it for a math major problem if you have Maple.Originally posted by whackaxe
"For more calc fun, find the 2 curves which satisfy x^y = y^x."
or die trying...
01302004, 05:54 PM
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Just a guess, but isn't the other solution either
y = ln (x)
or
y = e^x
???
01302004, 08:23 PM
#15
No. Plug in and see for yourself. It actually cannot be expressed as y=f(x). Rather, only as a parametricization.