Interesting Math Topics: Transfinite Numbers & Infinite Series

[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.

[PLAIN]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 sort of 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)=e^2πis. 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 e^x 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.

e^iπ + 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.