ℝolliℵg M∀th Thr∑a∂

Yeah

it would be an interesting history of math to classify what programmes have led to the most research -- i suspect classification programmes themselves would probably lead the pack.

classification of surfaces seemed like it didn't take very long once they figured out what they were doing

oh yeah, finite simple groups, too

arguably, figuring out what you're doing is typically the hard part.

great little history of the classification of surfaces on appendix D of this book http://download.springer.com/static/pdf/997/bbm%253A978-3-642-34364-3%252F1.pdf?auth66=1387259121_9a9118105634f100257c6f624c9329f0&ext=.pdf (full pdf)

gah i should be studying for my analysis exam... blegh

which 2 should i take next semester out of these 4

real analysis 4 (measure theory, functional analysis)
differential geometry
topics in geometry & topology course on cube c0mplexes
discrete mathematics of paul erdos (taught by the great vasec chv4tal http://users.encs.concordia.ca/~chvatal/6621/)

real and discrete OR differential and cube complexes

i sort of hated analysis 3 but while studying for it and memorizing all those theorems i became really impressed with it and now have the urge to take the 4th. also i've heard measure theory is one of those things you've just *got* to learn and this guy would teach it properly

interesting, why those 2 diff pairings?

(xp)

i've always had better luck in school when i take courses with some connection to each other rather than courses which have different approaches

although ... is real analysis useful in differential geometry?

yes

pairing of most similar would be cubes + discrete, diff geo + ana

oh okay. that's what i'd do then.

(higher math n00b)

cube complexes was developed by algebraic topologists & geometric group theorists, people who exploit an analogy (functor or whatever) between topological spaces, infinite groups, and cayley graphs of infinite groups, to prove results in group theory & 3-manifold theory. so graph theory would come up

the simplest vers of diff geo is, like, in multivariable calculus taking a surface integral

yeah that's about as far as i got in geometry

that article i posted upthread goes into the CC stuff, with some quotes by dude who is teaching the course (and is like world champion of cube complexes)

yeah i read it but my head started to spin halfway through and i definitely got real confused around when the cube complexes came in

word

2 much cool math

How can you not take Erdos class?

i know, right

Students who will make significant progress towards the solution of any open problem on the list posted here will get the grade of A+ regardless of their numerical score.

This is kind of old news, but I enjoyed this article. I never tire of these kinds of stories about unknown mathematicians toiling on hard problems in obscurity for years and then reaching a breakthrough, plus it does a good job of explaining the topic in layman's terms:

https://www.simonsfoundation.org/quanta/20130519-unheralded-mathematician-bridges-the-prime-gap/

yeah that one's great

there was a great slate article where they explained why twin primes conjecture is an obvious conjecture (because primes behave *as if* they are randomly distributed, even though they're not)

this interview with the guy is awesome http://nautil.us/issue/5/fame/the-twin-prime-hero

I am working on a problem related to the Goldbach conjecture.

TIL

flopson: what courses did you end up registering for? Real Analysis 4, I hope. :-)

i have until third week of the semester, probably gonna feel it out. not sure if ana will work out though, it's a pretty heavy workload

you like analysis?

One of the songs on Fade I don't care for, but the math is very good:

https://www.youtube.com/watch?v=4IwA9IimYSc

http://www.cut-the-knot.org/

Reminds me I need to change my screenname.

HI DERE

merry xmas math nerds

^ let xmas be any holiday

man this thread needs some actual words in its title

i cracked open a graph theory book, been doing some problems to relax

i realized that when i tried to 'write math', i automatically write a symbol (kind of a backward epsilon, though it was never quite that before when i used it) for 'such that'—which i/we NEVER do now when writing logic.

what is wrong with logicians?! why don't they write it? ('logically unnecessary', prob.)

do you mean existential quantification? as in ∃ x. x > 5 ?

You need it in higher order logic obv, but it tends to be implicit in first order logics.

yes, i mean after the quantifier and before the statement of the condition involving the bound variable

ah, as opposed to just the dot?

yeah; we certainly never used dots in any of the informal math style/notation i learned. backwards 'epsilons' or words.

maybe it's because logicians tend to be writing formulas after quantifiers which they just intend to be satisfied by values for the relevant quantified variables,

whereas a mathematician writing down an existential quantifier usually intends the subsequent conditions to say something meaningful about the 'x' (etc.) whose existence is being asserted (usually in terms of some conditions stated initially, or a principle or theorem etc.), so that he reaches for a piece of notation that emphasizes the subordination of the condition to the existential quantifier.

(i find that when i'm writing math, i will even put in a comma after a universal quantifier, for somewhat analogous reasons maybe)

do you mean '∍' ? I think that it might have to do with set theoretic roots there. You can read it as there exists an x drawn from the set of 'x > 5' for example. But if you're working without a set-theoretic model in mind then its terribly confusing. or if you have exists x ∍ R, then that's more like giving a 'type' than a condition -- x drawn from the reals.

i do mean that, but in concert with a membership epsilon, and w/in the general background of a naive set theory (the 'jargon of mathematicians' kind)

so it may be e.g. there exists x epsilon R backwards-epsilon x > 5

I wasn’t familiar with ∋ in a set-theoretic context. Nonetheless, Wikipedia’s article on Elements: http://en.wikipedia.org/wiki/Element_(mathematics) mentions it:

Another possible notation for [x ∈ A] is:

A ∋ x

meaning “A contains x”, though it is used less often.

I assumed you were talking about the traditional notation for “such that.” Most contemporary mathematicians, however, use a semicolon.

The relevant Unicode code point: http://www.fileformat.info/info/unicode/char/220b/index.htm