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Cool Math topics

  1. Oct 6, 2011 #1
    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.
  2. jcsd
  3. Oct 6, 2011 #2
    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.
  4. Oct 7, 2011 #3
    I liked calculus.
  5. Oct 7, 2011 #4
    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.

  6. Oct 7, 2011 #5


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    Math isn't cool... pffft.

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

    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.
    Last edited by a moderator: May 5, 2017
  7. Oct 7, 2011 #6
    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.
  8. Oct 7, 2011 #7
    Computability theory and logic. It's way, way out there and is practically philosophy.
  9. Oct 7, 2011 #8
    Last night I was going trough Wikipedia from page to page and stumbled upon knot theory.Looks pretty cool.
  10. Oct 7, 2011 #9
    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.
  11. Oct 7, 2011 #10
    And also Banach–Tarski paradox is pretty interesting.
  12. Oct 7, 2011 #11
    I enjoyed differential equations. They were complex enough to be a challenge, but not so much that I'd get lost.
  13. Apr 28, 2012 #12
    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.
  14. Apr 28, 2012 #13
    Calculus is a great subject.
  15. Apr 28, 2012 #14
    I find fractal geometry intriguing, but I know little about it.
  16. Apr 29, 2012 #15
    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!?
    Last edited: Apr 29, 2012
  17. Apr 30, 2012 #16
    also the Banach–Mazur game seems interesting.
  18. May 6, 2012 #17
    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...
  19. May 6, 2012 #18
    Professor Paulos' work on the connection between humor and catastrophe theory.
  20. May 6, 2012 #19
    I like the game theory and various mathematical series, especially Taylor.

    e + 1 = 0.

    Ah, bliss...
  21. May 6, 2012 #20
    the cantor set is uncountable and no-where dense.
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