## Search found 17 matches

Thu Dec 08, 2011 12:35 am UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 158914

### Re: Math: Fleeting Thoughts

I've been taking a course on Riemann Surfaces and the Riemann-Hilbert Problem with applications to partial differential equations. So far we've only really seen the Riemann-Hilbert Problem arise in elliptic pde's, and even then only linear ones. It seems unlikely that hyperbolic or parabolic pde's w...
Thu Dec 08, 2011 12:17 am UTC
Forum: Food
Topic: Childhood Defining Foods
Replies: 39
Views: 9022

### Re: Childhood Defining Foods

Nothing brings back summer memories like grilled burgers with barbeque sauce.
Sat Feb 06, 2010 10:37 pm UTC
Forum: Mathematics
Topic: [Solved] Fractional Integral Question
Replies: 2
Views: 899

### Re: Fractional Integral Question

Nevermind, solved. Change some variables and it's the Euler Beta function.
Fri Jan 29, 2010 8:40 pm UTC
Forum: Mathematics
Topic: [Solved] Fractional Integral Question
Replies: 2
Views: 899

### [Solved] Fractional Integral Question

I'm currently reading some lecture notes online regarding fractional integrals and derivatives. Somewhere in the middle of a proof for the semigroup property of fractional integrals, the author states that : (I^{\alpha}_{a+}f)(x) = \frac{\Gamma(\beta)}{\Gamma(\alpha + \be...
Sun Nov 29, 2009 11:59 pm UTC
Forum: Mathematics
Topic: Getting into Mathematics
Replies: 10
Views: 1833

### Re: Getting into Mathematics

I wouldn't fret about intuition. That sort of thing, believe it or not, takes time and practice to develop properly. Very few people are experts at calculus upon their first introduction, especially at the high school level. If your interest is indeed a keen one, that together with some hard work wi...
Fri Oct 30, 2009 8:40 pm UTC
Forum: Mathematics
Topic: Discontinuous derivative of an explicitly defined function
Replies: 18
Views: 4887

### Re: Discontinuous derivative of an explicitly defined function

It should be noted that derivatives of differentiable functions cannot have jump discontinuities. This is called Darboux's theorem . Fixed, because the derivative of |x| definitely doesn't satisfy the mean value theorem. I took me a second, but I see now how Darboux's Theorem implies no jump discon...
Fri Sep 25, 2009 3:57 pm UTC
Forum: Mathematics
Topic: What's the coolest thing you've ever learned in math class?
Replies: 58
Views: 6721

### Re: What's the coolest thing you've ever learned in math class?

E. Hopf's Extension Theorem, combined with the refinement of an outer measure to a countably-additive measure. Freaking awesome that if you have a slightly well-behaved way to measure a weak collection of sets, then you automatically get a measure that's as nice as you could ask for. Even better tha...
Fri Sep 11, 2009 10:08 pm UTC
Forum: Mathematics
Topic: There's some way to calculate this, right?
Replies: 6
Views: 2141

### Re: There's some way to calculate this, right?

The "kind" of math from which nCk (also said/written "n choose k") most naturally arises is called Combinatorics, which is roughly the study of different ways of organizing and combining discrete (countable) objects. Sometimes order is considered, other times not. While it is a b...
Tue Sep 08, 2009 11:30 pm UTC
Forum: Mathematics
Topic: Morphisms and Isomorphisms of Fnctnl Structures (Sheaves)
Replies: 3
Views: 855

### Re: Morphisms and Isomorphisms of Fnctnl Structures (Sheaves)

Ah, damn it. Yeah, it'd be real easy if g was already injective, and I see now how I'm assuming its injectivity. It's too late now, however, since I turned in the homework today at noon. Thanks for the help and insight, per usual.
Mon Sep 07, 2009 7:56 pm UTC
Forum: Mathematics
Topic: Morphisms and Isomorphisms of Fnctnl Structures (Sheaves)
Replies: 3
Views: 855

### Morphisms and Isomorphisms of Fnctnl Structures (Sheaves)

I'm in a topology course dealing with smooth manifolds at the moment, and for one of the homework problems I need to show that a certain morphism f is injective. I think I've done it right, but I arrive at a statement that seems to be false, that "every morphism f: (X, F x ) ---> (Y, F y )[/mat...
Sat Jul 04, 2009 11:50 pm UTC
Forum: General
Topic: Skateboarding in the rain
Replies: 8
Views: 1640

### Re: Skateboarding in the rain

If you're using a regular skateboard (grip tape, deck, bolts/nuts, trucks, bearings, wheels), I can't imagine anything worse for your board. Rain, and water of any kind, weakens your deck, loosens the grip tape, de-lubricates the bearings on your wheels, and rusts the nuts and bolts connecting your ...
Sat Jul 04, 2009 11:20 pm UTC
Forum: General
Topic: Hype your ripe snipes 'n' gripes
Replies: 28619
Views: 3531249

Ah, the safety of anonymity... Fuck Brad. What a piece of shit ass hole. I've never met a more fickle, bitchy, passive-aggressive little bitch in my whole life. For almost 5 years I've tried to establish a stabilized friendship with this guy, and all he does is fucking turn his back on me and active...
Wed Jun 17, 2009 8:01 pm UTC
Forum: Music
Topic: Psychedelic (or "Stoner" Metal)
Replies: 41
Views: 3885

### Re: Psychedelic (or "Stoner" Metal)

I'm a little surprised that no one has mentioned this yet, but Ozric Tentacles. Freakin' great psych-rock. I'd recommend them to anyone who likes interesting music. I'll also second Porcupine Tree, although they're of a decidedly more mellow flavor. I especially recommend the album "Up the Down...
Fri May 15, 2009 9:28 am UTC
Forum: Mathematics
Topic: Courses, Abridged
Replies: 19
Views: 2436

### Re: Courses, Abridged

Undergraduate Analysis: Distance is an important and fundamental concept: it extends naturally (and sometimes not very naturally) to very many mathematical objects and spaces, and provides them with structure that's more than just topological. Other equally important ideas are boundedness and (Cauch...
Sat Apr 18, 2009 12:43 am UTC
Forum: Music
Topic: Perfect Moments In Music
Replies: 396
Views: 201950

### Re: Perfect Moments In Music

In no particular order: Claude Debussy - Toccata (pour le piano) When, near the very end (last 30 seconds-ish), after tons of build up, the upper register is doing very active arpeggios and the mid register is just going insane with heavy chords. Miraculous. Shpongle - Levitation Nation (Nothing Las...
Fri Apr 17, 2009 11:57 pm UTC
Forum: Music
Topic: Music you put off listening to and now love
Replies: 29
Views: 2966

### Re: Music you put off listening to and now love

Simon & Garfunkle. Good god, I can't believe it took me so long to listen to them, but they're FANTASTIC. Acoustic/folk has never been better.
Wed Apr 01, 2009 3:22 pm UTC
Forum: Mathematics
Topic: Immeasurable Sets
Replies: 5
Views: 961

### Immeasurable Sets

Studying Measure Theory has led me to a question that I can't find an answer to: Given a Measure Space (X,M,m), do the non-measurable sets of X form a set algebra? If not in general, does there exist such a Measure Space?