## Search found 114 matches

Fri Jun 29, 2012 1:16 am UTC
Forum: Mathematics
Topic: Matrices with incoherent columns
Replies: 2
Views: 2437

### Re: Matrices with incoherent columns

http://en.wikipedia.org/wiki/Mutual_coherence_(linear_algebra) That should do it for you. As a more general source of information, it sounds like you're working on things in the area of compressed sensing (woo!). You might find something like http://www-stat.stanford.edu/~markad/publications/ddek-c...
Thu Jun 14, 2012 4:22 pm UTC
Forum: Mathematics
Topic: Hi/Game structure for financial markets
Replies: 36
Views: 8184

### Re: Hi/Game structure for financial markets

This might have some relevant information for you:

http://en.wikipedia.org/wiki/Dunning%E2 ... ger_effect
Sat Mar 10, 2012 12:47 am UTC
Forum: Mathematics
Replies: 40
Views: 7623

With his requirements that it be translation invariant and finitely additive, it pretty much has to look like this. As I said, bounded sets cannot matter (ie, they're all probability 0), so a set's size must be determined by it's asymptotic behaviour. You could do just the positive direction, or ju...
Sat Mar 10, 2012 12:12 am UTC
Forum: Mathematics
Replies: 40
Views: 7623

Here's a simple 'linear' one, ie u(aA+b) = |a|u(A). Define the size of a subset to be \mu(A) = \lim\inf \frac{|A \cap [-n,n]|}{2n} Any bounded set must be size 0, by finite additivity and translation invariance, which is why I say that actually 'picking' numbers based on this is going to be...
Fri Mar 09, 2012 11:38 pm UTC
Forum: Mathematics
Replies: 40
Views: 7623

Answers like mike-l's are quickly becoming a pet peeve of mine. Sure, a probability distribution as defined in mathematics has to be countably additive. But that doesn't mean the question is "wrong". It just means that its not asking about what mathematicians call a probability distributi...
Fri Mar 09, 2012 10:49 pm UTC
Forum: Mathematics
Replies: 40
Views: 7623

This isn't a mystery, this isn't a paradox, this is, quite exactly, a situation where the probability distribution you are trying to use does not exist . There is no uncertainty here, mathematicians have studied these problems, and if you were to take the time to study elementary probability theory ...
Mon Mar 05, 2012 10:48 pm UTC
Forum: Mathematics
Topic: Just what am I doing wrong here? (homework)
Replies: 14
Views: 2988

### Re: Just what am I doing wrong here? (homework)

They have to pay extra for it?!? If students don't generally have to pay humans to grade their homework (except as part of the usual tuition), why do they have to pay more for computers that do a worse job? Why don't they just employ some undergrad math majors to do grading? In my experience, there...
Mon Mar 05, 2012 10:16 pm UTC
Forum: Mathematics
Topic: Just what am I doing wrong here? (homework)
Replies: 14
Views: 2988

### Re: Just what am I doing wrong here? (homework)

That's ridiculous. How are you supposed to know what form of the expression is the one form that the submission system will accept? Often, you don't. I'm a TA down at UMCP currently, and the lower-level students have to use something called WebAssign for some of their homework. It's awful - I can't...
Sat Mar 03, 2012 3:56 am UTC
Forum: Mathematics
Topic: Pi in fraction form
Replies: 17
Views: 5371

### Re: Pi in fraction form

Well, I don't know for sure, but it seems unlikely. Why store pi as the seventh root of some nasty fraction when you can store it as the finite decimal sequence 3.1415926535898 or whatever? Then, it can just be looked up when needed - computing seventh roots is costly, computationally.
Sat Mar 03, 2012 1:55 am UTC
Forum: Mathematics
Topic: Pi in fraction form
Replies: 17
Views: 5371

### Re: Pi in fraction form

That's just an artifact of the calculator's finite number of decimal places, it's not really a fraction. Pi is a transcendental number, so no equation involving powers and sums of pi will ever yield a rational number.
Tue Jan 10, 2012 7:20 pm UTC
Forum: Mathematics
Topic: Are conversations considered markov chains?
Replies: 9
Views: 3601

### Re: Are conversations considered markov chains?

Perhaps you could get an interesting toy model with an n-history Markov model for some n, but that's not really representative of the full breadth of human discourse. First of all, consider that we don't have access to previous statements, only our memories of them. That alone is a substantial real-...
Tue Jan 10, 2012 12:57 am UTC
Forum: Mathematics
Topic: What's the point of rationalizing?
Replies: 61
Views: 9315

### Re: What's the point of rationalizing?

gfauxpas, you seem like someone who is very interested in math but fairly new to rigorous mathematical proofs. That's ok, we were all there at one point. However, in time you'll come to understand them in a broader context of "doing" mathematics (or at least ought to, if you want to be goo...
Tue Dec 20, 2011 11:02 pm UTC
Forum: Mathematics
Replies: 6
Views: 2004

I'm currently a math grad student. This probably isn't what you want to hear, but I hope you can appreciate that I'm trying to give you a realistic answer: A math minor with what is apparently a very shallow exposure to higher math is unlikely to land you a spot in a math graduate program. How much ...
Mon Dec 19, 2011 12:21 am UTC
Forum: Mathematics
Replies: 6
Views: 2004

What math did you do as part of your minor? What do you intend to do in graduate school?
Sun Dec 11, 2011 9:07 pm UTC
Forum: Mathematics
Topic: Traveling Doctor Problem
Replies: 5
Views: 1331

### Re: Traveling Doctor Problem

In your model, do the doctors have different specialties? i.e. are there some patients that can only be seen by certain doctors and not others? Also, how are you modeling patient arrivals? Are they scheduled far enough in advance that we can assume the clinics know each week's schedule before the we...
Wed Oct 26, 2011 10:40 pm UTC
Forum: Mathematics
Topic: What do you think the most underrated area of math is?
Replies: 13
Views: 4000

### Re: What do you think the most underrated area of math is?

Baseball theory didn't get interesting until theorists abandoned the parallel postulate, though.
Wed Oct 26, 2011 9:41 pm UTC
Forum: Mathematics
Topic: What do you think the most underrated area of math is?
Replies: 13
Views: 4000

### Re: What do you think the most underrated area of math is?

Eh, in my experience, they just need to see the applications. Hit a prof a few times with a bat and they start agreeing with you.
Wed Oct 26, 2011 8:23 pm UTC
Forum: Mathematics
Topic: What do you think the most underrated area of math is?
Replies: 13
Views: 4000

### Re: What do you think the most underrated area of math is?

Oh, you again.

I'm gonna go with "literary criticism".
Fri Sep 09, 2011 10:43 pm UTC
Forum: Mathematics
Topic: Elliptic geometry or Hyperbolic geometry
Replies: 10
Views: 1578

### Re: Elliptic geometry or Hyperbolic geometry

Sorry, I do all my geometry on the Dehn plane.
Thu Jun 09, 2011 6:50 pm UTC
Forum: Mathematics
Topic: Cardinality Confusion
Replies: 3
Views: 1256

### Re: Cardinality Confusion

The confusion here stems from the ambiguity of the notion of one set being "bigger than" another. There are many ways we could try to define this. For finite sets, a simple way to do so is to say that S "is bigger than" T if there are more elements in S than there are in T. The i...
Wed Feb 16, 2011 2:51 am UTC
Forum: Mathematics
Topic: Derivative of x^(ln(x))?
Replies: 4
Views: 17032

### Re: Derivative of x^(ln(x))?

Just note that [imath]x^{\ln(x)}=e^{\ln(x)\cdot\ln(x)}[/imath] by definition, and then chain rule.
Fri Jan 21, 2011 1:36 am UTC
Forum: Mathematics
Topic: Does this series converge!?
Replies: 32
Views: 4321

### Re: Does this series converge!?

Well, when something that you suspect is trivial (such as an infinite sum of zeros being equal to 0) doesn't fall out immediately from whatever angle you're looking at, always go back to definitions. What is the definition of \sum_{i=1}^{\infty}0 ? It is the limit of the sequence {0, 0+0, 0+0+0, ......
Sun Dec 12, 2010 9:57 am UTC
Forum: Mathematics
Topic: Modern Cryptanalysis
Replies: 12
Views: 4123

### Re: Modern Cryptanalysis

Classic cryptography was more of an art than a science: Come up with an encipherment system that "seems" hard to break, and use it until someone finds a way to crack it. Modern cryptography is much more mathematically rigorous, starting with agreed-upon assumptions (an adversary is computa...
Sun Dec 05, 2010 12:58 am UTC
Forum: Mathematics
Topic: Would this be a proof?
Replies: 14
Views: 1763

### Re: Would this be a proof?

One of my favorite parts of learning proofs in high school was proving that all odd numbers are part of a unique Pythagorean triple during one of my classes when I should have been paying attention. So once you get the hang of some of the basics, see what other stuff you can show with the Pythagore...
Tue Oct 26, 2010 5:54 am UTC
Forum: Mathematics
Topic: Yo momma's so nerdy...
Replies: 40
Views: 7176

### Re: Yo momma's so nerdy...

Her wedding ring is non-noetherian!
Wed Sep 08, 2010 4:52 am UTC
Forum: Mathematics
Topic: i suck at proofs...
Replies: 8
Views: 2167

### Re: i suck at proofs...

Hint: a is being drawn from a field, which has multiplicative inverses. Suppose a is nonzero, what happens? Full answer spoilered, think about it for a bit Suppose a is not 0. Then, we have: ax = O (1/a)ax=(1/a)O, OK since a is not 0 by hypothesis 1x=O x=O So, we can show that a bein...
Fri Sep 03, 2010 7:37 pm UTC
Forum: Mathematics
Topic: Computing eigenfunctions for nonlinear operators
Replies: 7
Views: 1751

### Re: Computing eigenfunctions for nonlinear operators

Hey Yakk, in a bit I'll read over what you said carefully, but just a couple notes: First note that in the 1D case, the infinity Laplacian is the same as the standard Laplacian on graphs. So that is a thing to consider. Also, in describing how we get some sort of propagation in maximal/minimal adjac...
Fri Sep 03, 2010 3:45 pm UTC
Forum: Mathematics
Topic: Computing eigenfunctions for nonlinear operators
Replies: 7
Views: 1751

### Re: Computing eigenfunctions for nonlinear operators

Alright Yakk, I'll buy that. I suppoooose I can go into a little more detail. Your non-pink shirt point is apt. The operator is called the infinity-Laplacian, defined on graph domains as \Delta_{\infty}u(x) = \frac{1}{2}\left(\max\limits_{y\sim x}u( y) + \min\limits_{y\sim x} u&#...
Wed Sep 01, 2010 11:18 pm UTC
Forum: Mathematics
Topic: Computing eigenfunctions for nonlinear operators
Replies: 7
Views: 1751

### Computing eigenfunctions for nonlinear operators

Is there a general method for this? If A is a non-linear operator, and I am approximating it by computing the discrete analog of A on a graph approximation to my domain, how can I compute eigenfunctions for given boundary data? Or, at the very least, show that none exist.
Wed Aug 11, 2010 10:09 pm UTC
Forum: Mathematics
Topic: Revised Simple Proof of Beal's Conjecture
Replies: 29
Views: 4224

### Re: Revised Simple Proof of Beal's Conjecture

Very good, you fixed the flaw, that \$100,000 should be yours in no time. The next step you should take is to email math professors at several universities. Explain to them what you've done exactly as you explained it to us. Pick your favorite university, go to its website, and find its math faculty....
Tue Aug 10, 2010 3:00 am UTC
Forum: Computer Science
Topic: P!=NP
Replies: 1
Views: 1587

### P!=NP

http://www.win.tue.nl/~gwoegi/P-versus-NP/Deolalikar.pdf Vinay Deolalikar out of HP Labs recently posted a potential proof that P!=NP. I saw this on Slashdot the other day, and wondered if anyone here knew enough about the various areas of math, physics, and CS used in the proof to point out a poten...
Tue Jul 27, 2010 11:29 pm UTC
Forum: Mathematics
Topic: Polygon inside a polygon: A surprisingly tricky problem
Replies: 20
Views: 3612

### Re: Polygon inside a polygon: A surprisingly tricky problem

Let the vertices of the inner polygon be x_1,x_2,\ldots,x_n , so that there is an edge e_{i,i+1} for all i\in[1,n-1] and an edge e_{n,1} . Pick some point p in the interior of the smaller polygon, and draw rays from p to each x_i , letting the rays go on to intersect the larger polygon. Each two suc...
Tue Jun 01, 2010 7:30 pm UTC
Forum: Mathematics
Topic: Math discovered or invented?
Replies: 110
Views: 17910

### Re: Math discovered or invented?

The thing that is created when we do mathematics is the proof that connects axiom to theorem. The space of "true statements" that are implied even by axioms (and the conceptual framework that lets you prove things with them) is vast, and speaking of the consequences as being "already...
Wed May 12, 2010 12:00 am UTC
Forum: Mathematics
Topic: Can we truly prove anything?
Replies: 86
Views: 11634

### Re: Can we truly prove anything?

So the most ridiculous option is that there is a supernatural power, and you make a straw man argument, creating a stupid scenario that virtually no one believes, of brains in a vat and an infinitely intelligent mad scientist? Since our argument is about logic, I'd expect a little more seriousness ...
Tue May 11, 2010 1:51 pm UTC
Forum: Mathematics
Topic: Can we truly prove anything?
Replies: 86
Views: 11634

### Re: Can we truly prove anything?

First, a definition: The way I am interpreting the question "Can we truly prove anything" involves "prove" to be proving something in the physical world around us. Perhaps that is the origin of this disagreement, as you may be thinking of only theoretical mathematics. If not, th...
Fri Apr 23, 2010 6:28 am UTC
Forum: School
Topic: Private vs. Public school, and some underlying stereotypes
Replies: 44
Views: 7911

### Re: Private vs. Public school, and some underlying stereotyp

Well, that depends on what you value in life, doesn't it? There's no real blanket answer. But the truth is, there's probably a reason why the belief that hard work and studiousness during adolescence is so important. Inevitably at some point, a kid leaves home and has to start a life for themselves ...
Wed Apr 21, 2010 10:26 pm UTC
Forum: Mathematics
Topic: Finding H_1(R,Q)
Replies: 1
Views: 588

### Finding H_1(R,Q)

So this is indeed for homework, computing H_1(R,Q) , specifically showing it's free abelian and finding a basis. I think i still don't grasp relative homology groups exactly, so I'm trying to start with the chain \ldots\stackrel{\partial_3}{\longrightarrow} C_2(R,Q)\stackrel{\partial...
Thu Apr 15, 2010 3:35 pm UTC
Forum: Mathematics
Topic: What do you do with that?
Replies: 12
Views: 1956

### Re: What do you do with that?

Bus driver, waiter, etc.
Wed Oct 07, 2009 5:54 am UTC
Forum: Mathematics
Topic: Math College
Replies: 13
Views: 2604

### Re: Math College

If you had the scholarship you would choose RPI over Cornell? Please explain. Because I'm also applying to Cornell. Hi! I am currently a student doing pure math at Cornell, a junior, though i went to Dartmouth for my first year and a half of college. I can tell you that the math program here is pre...
Wed Aug 19, 2009 5:47 am UTC
Forum: Science
Topic: Von Neumann machines and the Fermi paradox
Replies: 54
Views: 4303

### Re: Von Neumann machines and the Fermi paradox

We talked about this subject extensively a while back. Lemme see if I can find the thread. Ah: http://forums.xkcd.com/viewtopic.php?f=9&t=41400 Bottom line: The reason the Fermi paradox is called a paradox is because it is a paradox. None of the explanations are very attractive. 1) Aliens don't...