cool Math topics

[cragar]

As you took math classes what were some of the interesting topics that you came across that you thought were interesting? I thought transfinite numbers and infinite series were interesting. What did you guys think was interesting, it doesn't matter what level.

[micromass]

I personally like mathematical theories where you can see a connection between to completely different branches of mathematics. To see the interplay between the two fields is fascinating.

For example, algebraic topology is a very nice field of study. You can study geometric objects very nicely by examining algebraic invariants.

Topics that I really liked where of course the transfinite numbers. Also complex numbers and complex analysis is really cool. Point-set topology and its generalization to pointless topology is also quite nice.

[MrNerd]

I liked calculus.

[mathal]

Continued Fractions. Every Real number has an associated CF -a string of positive integer numbers. A finite series is a rational number and an infinite series is irrational.

mathal

[FlexGunship]

As you took math classes what were some of the interesting topics that you came across that you thought were interesting? I thought transfinite numbers and infinite series were interesting. What did you guys think was interesting, it doesn't matter what level.

Math isn't cool... pffft.

http://www.sabotagetimes.com/wp-content/uploads/henry-winkler-the-f_683943c.jpg

Just kidding... I loved the moment when I finally internalized the meaning of a differential equation. It happened a few months after "learning" it. It was a eureka moment, and the significance hasn't left me yet.

[jobyts]

My coolest moment was when I rediscovered the following property of prime numbers:

p^2 = 24*n + 1
where p is a prime number > 3
n is an integer.

5^2 = 24.1+1
7^2 = 24.2+1
11^2 = 24.5+1 etc.

[gravenewworld]

Computability theory and logic. It's way, way out there and is practically philosophy.

[bp_psy]

Last night I was going trough Wikipedia from page to page and stumbled upon knot theory.Looks pretty cool.

[Jack21222]

My favorite math topic is one I came across in a "computers in physics" class: Chaos theory. Our project was to model two damped driven oscillators in the computer, and make a few plots comparing the two with varying parameters. At certain parameters, the tiniest difference in initial conditions made the two pendulums wildly diverge.

Plus I was hypnotized by the double pendulum the professor brought in.

[cragar]

And also Banach–Tarski paradox is pretty interesting.

[DoggerDan]

I enjoyed differential equations. They were complex enough to be a challenge, but not so much that I'd get lost.

[gakushya]

I hated the epsilons and deltas. I figured that was sorta my right of passage to learning the higher math. But, I'm not it for the theorems, I'm more interested in the philosophical aspects of math. So I was never really moved by any undergrad topics.

But, when I read that manifolds can be modeled over infinite dimensional Banach spaces. Just, wow. That **** still blows my mind. Maybe one day I'll even finish my topology book and get into the more general geometric stuff. Damn. Just warps my mind. I need to go sit down.

[Cyclopse]

Calculus is a great subject.

[1MileCrash]

I find fractal geometry intriguing, but I know little about it.

[gakushya]

Actually, something I thought was cool. Mapping the interval [0,1)⊂ℝ into the unit 1sphere S1⊂ℂ2 with the exponential function as such a(s)=e2πis. So this is a continuous bijective function, but its not a homeomorphism between [0,1) and S1⊂ℂ2 (its image space). Wait! What!? Does it make intuitive sense that a bijective continuous function does not necessarily admit a continuous inverse (despite the bijectiveness implying that the inverse does indeed exist)? I mean, what more do the gods of homeomorphisms want beyond a god damn bijective continuous map!?

[cragar]

also the Banach–Mazur game seems interesting.

[fletch-j]

The coolest thing so far for me was learning about Taylor series expansion..
At first I was thinking 'what is the point of this?' but then when my teacher subbed in (i theta) to the Taylor series for ex my mind was blown...

[Jimmy Snyder]

Professor Paulos' work on the connection between humor and catastrophe theory.

[Infinitum]

I like the game theory and various mathematical series, especially Taylor.

eiπ + 1 = 0.

Ah, bliss...

[cragar]

the cantor set is uncountable and no-where dense.

[Alfi]

attractors got me . chaos theory studies began , :)

[redrum419_7]

Taylor series and expansions are really interesting. The fact that you can describe most functions by an infinite series is amazing and an insight to the ingenuity of humans.