Search found 40 matches

by Fluid_Dynamic
Wed Nov 02, 2011 2:18 am UTC
Forum: Mathematics
Topic: Help to spot my errors (Measure theory, two questions)
Replies: 5
Views: 1171

Re: Help to spot my errors (Measure theory, two questions)

We also know that for some positive integer p, a_n < \frac{1}{n} \text{ when } n \ge p . This is not necessarily true. We know a n < 1/n for infinitely many n, but we don't know it for cofinitely many n. Even if this were true, this statement is counterproductive to the proof, as \sum \frac{1}{n} i...
by Fluid_Dynamic
Thu Aug 26, 2010 4:21 am UTC
Forum: Mathematics
Topic: A duck swimming
Replies: 7
Views: 1407

Re: A duck swimming

Going back to the original question, that being the distance d = vt traveled when at a distance x = \frac{v\sin(at)}{a} . Notice that implies t = \frac{\arcsin(\frac{ax}{v})}{a} Therefore, the distance traveled d = \frac{v}{a}\arcsin(\frac{ax}{v}) for x < \frac{v}{a} and t < ...
by Fluid_Dynamic
Fri Jun 25, 2010 2:43 am UTC
Forum: Mathematics
Topic: Ackermann function, please check.
Replies: 3
Views: 935

Re: Ackermann function, please check.

If it speeds things up, I see that

[math]A(3,n) = 2^{n+3} - 3[/math]
by Fluid_Dynamic
Sat Jun 12, 2010 5:29 am UTC
Forum: Mathematics
Topic: Infinite random walks
Replies: 6
Views: 1235

Re: Infinite random walks

It seems to me much easier to calculate the probability the first time you come back to the origin is after 2n step, and then just convolving that solution on itself k times to figure out the distribution for it taking some many steps to get back to the starting point k times, and then just bound th...
by Fluid_Dynamic
Sun May 30, 2010 5:49 am UTC
Forum: Mathematics
Topic: Most interesting mathematician?
Replies: 35
Views: 5256

Re: Most interesting mathematician?

I'm gonna have to say Turing life was pretty amazing
(and his death rather tragic, and a testament that humanity still had a ways to go ...).

If the OP's question is just a veiled test to see who thought Turing was interesting,
would this be a Turing test?
Did I pass the Turing test?
by Fluid_Dynamic
Sun May 30, 2010 3:36 am UTC
Forum: Mathematics
Topic: Tricky Differential Equations Problem
Replies: 13
Views: 2516

Re: Tricky Differential Equations Problem

x(t,u) = x_0(t) + ux_1(t) + u^2x_2(t) + \cdots It should be mentioned that the key to this ansatz working is that u must be assumed small, so that increasing powers of u quickly tend to zero. That's a valid question. So, I worked out the solution atleast for x_0(...
by Fluid_Dynamic
Sun May 16, 2010 5:02 am UTC
Forum: Mathematics
Topic: How to model a spinning rubber band
Replies: 11
Views: 1986

Re: How to model a spinning rubber band

$$\frac{\partial}{\partial t}\rho(\theta,t)=-\omega \frac{\partial}{\partial \theta}\rho(\theta,t)+\epsilon\frac{\partial^2}{\partial \theta^2} \rho(\theta,t).$$ Maybe this is just me, but isn't that's just the advective-diffusion equation? So the solution would just be the diffusion equation with ...
by Fluid_Dynamic
Sun May 02, 2010 6:10 pm UTC
Forum: Mathematics
Topic: Top Colleges for Undergraduate Mathematics
Replies: 30
Views: 9326

Re: Top Colleges for Undergraduate Mathematics

I cannot speak for most programs out there other than what one can find in various college prep books. However, I can attest to MIT's program being pretty solid, and given the skills of those I met who came there from Cambridge through the Cambridge-MIT exchange program, Cambridge is exceptionally g...
by Fluid_Dynamic
Sat Apr 10, 2010 3:53 pm UTC
Forum: Mathematics
Topic: Repeated Integral (kinda) proof
Replies: 2
Views: 840

Re: Repeated Integral (kinda) proof

Before I get too far into this, I'm seeing integrals. Since this is a first order linear system of ODEs, wouldn't a proof by plugging in your guess be really quick? (I assume derivatives are easier than integrals). Simply showing your answer satisfies the ODE and initial conditions for some r=n, and...
by Fluid_Dynamic
Sat Jan 23, 2010 6:16 pm UTC
Forum: Mathematics
Topic: Give these Word Problems a Try
Replies: 19
Views: 1987

Re: Give these Word Problems a Try

I choose to disregard the initial instructions. 6: We do not know how many more or fewer students took the second test than took the first, whether by adding or dropping the course, or missing a test. Incomplete problem statement means there is not a unique correct answer. 6:Your answer makes more ...
by Fluid_Dynamic
Mon Dec 28, 2009 3:59 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0681: "Gravity Wells"
Replies: 205
Views: 57233

Re: "Gravity Wells" Discussion

Earth's gravity well depth has 3 different figures: 5478, 6000, 6379km. The last one should be the correct one. That's what my calculations say as well. The 6000 is obviously an approximation, but why 5478? Is it a simple error, or is there something more subtle behind it? -- Claus It looks to be j...
by Fluid_Dynamic
Thu Nov 26, 2009 3:09 am UTC
Forum: Mathematics
Topic: Help with probability problems please .....
Replies: 9
Views: 1404

Re: Help with probability problems please .....

I really hope problem 4 is easier to solve than the way I solved it. Let Q_n = Probability that the couple hasn't had at least 2 boys and at least 2 girls after n kids. Clearly Q_n = 1 for n = 1, 2, 3, so let n >= 4 Let p = 1/2 = probability of having a boy, and likewise 1/2 for having a girl. O...
by Fluid_Dynamic
Wed Aug 26, 2009 1:08 am UTC
Forum: Mathematics
Topic: probability density function question
Replies: 3
Views: 821

Re: probability density function question

Could you show what work you've done so far?
Also, you may want to consider using the cdf on Wikipedia instead of the pdf.
by Fluid_Dynamic
Tue Jul 21, 2009 2:18 pm UTC
Forum: Mathematics
Topic: 1=2?
Replies: 9
Views: 1309

Re: 1=2?

[imath]i = \sqrt{-1} = \sqrt{\frac{1}{-1}} = \frac{\sqrt{1}}{\sqrt{-1}} = \frac{1}{i}[/imath]

So [imath]i^2 = 1 = -1[/imath], do a little more math manipulation, and you get 1 = 2.
by Fluid_Dynamic
Thu Jul 16, 2009 4:50 am UTC
Forum: Mathematics
Topic: A Happy Prime Problem
Replies: 11
Views: 1913

Re: A Happy Prime Problem

Consider N = 3, in base B = 29; 3^2 = 9 = 9 9^2 = 81 = 2*29 + 23 2^2 + 23^2 = 533 = 18*29 + 11 18^2 + 11^2 = 445 = 15*29 + 10 15^2 + 10^2 = 325 = 11*29 + 6 11^2 + 6^2 = 157 = 5*29 + 12 5^2 + 12^2 = 169 = 5*29 + 24 5^2 + 24^2 = 601 = 20*29 + 21 20^2 + 21^2 = 841 = 1*29^2 So 3 is happy in base 29. Als...
by Fluid_Dynamic
Sun Jul 12, 2009 9:36 pm UTC
Forum: Mathematics
Topic: Post your interesting/challenging/fun integrals
Replies: 53
Views: 9699

Re: Post your interesting/challenging/fun integrals

Here's one that I stumped my high school class with for a few days:

[imath]\int \frac{1}{x \log x} \,dx[/imath]

Try solving it through integration by parts ( [imath]u = \frac{1}{\log x}, dv = \frac{1}{x} \,dx[/imath] )
by Fluid_Dynamic
Mon Jul 06, 2009 3:27 am UTC
Forum: Mathematics
Topic: Finding time for math with a job
Replies: 4
Views: 1102

Re: Finding time for math with a job

My answer is somewhat dependent on your job. If there are many programmers you work with, I would recommend finding some that, like you, enjoy math puzzles. Create a mailing list where you can post math puzzles you think up or hear about, so that others on the mailing list can think about them too. ...
by Fluid_Dynamic
Fri Jul 03, 2009 3:28 am UTC
Forum: Mathematics
Topic: Need a function that looks like
Replies: 4
Views: 1431

Re: Need a function that looks like

I'd say something like [imath]y = x + e^{((1-z)*x)} - 1[/imath]
Maybe throw some constants in there, but yeah, data points would be good.

EDIT: Sorry, didn't read the part about y = 2 asymptote.
by Fluid_Dynamic
Sat Jun 27, 2009 4:12 pm UTC
Forum: Mathematics
Topic: Numerically computing the Cauchy Integral
Replies: 3
Views: 880

Re: Numerically computing the Cauchy Integral

So it looks like you're analyzing a harmonic function f(z). For a given point a near the boundary, you're getting the "weighting" element 1/(z-a) to be really large at some point near the boundary. A couple of possibilities: 1) If a is so close the boundary, why not interpolate using a num...
by Fluid_Dynamic
Wed Jun 24, 2009 4:53 pm UTC
Forum: Mathematics
Topic: Statistics -- permutation question
Replies: 3
Views: 1698

Re: Statistics -- permutation question

According to the article, the probability of at least one element staying in place approaches 1-e^{-1} as n\to\infty . To put things in perspective, the error term for a given n on that limit is |(1 - \frac{d_{n}}{n!}) - (1-e^{-1})| \leq \frac{1}{(n+1)!} meaning that for n >...
by Fluid_Dynamic
Wed Jun 24, 2009 3:32 pm UTC
Forum: Mathematics
Topic: Binomial or normal distribution?
Replies: 2
Views: 747

Re: Binomial or normal distribution?

It would appear what you found was the probability that a given person's reaction time is over 20, and then built a binomial distribution on that. What you seem to be looking for is that the average is over 20, and shouldn't care as much what the individual values are. I would consider the central l...
by Fluid_Dynamic
Mon Jun 22, 2009 7:32 pm UTC
Forum: Mathematics
Topic: Part-time math hobbyist, I just took ODE. Any applications?
Replies: 30
Views: 3375

Re: Part-time math hobbyist, I just took ODE. Any applications?

I can understand your initial impression of pure math. I suppose I would like to remark that, while language / grammar is constantly in flux, 1 + 1 will always equal 2 (not talking about Z 2 guys). To that end, though we sometimes give theoretical mathematicians a hard time, their intense rigour is ...
by Fluid_Dynamic
Mon Jun 22, 2009 3:14 am UTC
Forum: Mathematics
Topic: Part-time math hobbyist, I just took ODE. Any applications?
Replies: 30
Views: 3375

Re: Part-time math hobbyist, I just took ODE. Any applications?

Linear Algebra is one of those math courses that can be theory intensive if you want it to be, but more often than not is just taught from an applied standpoint, which is, I think, what you are looking for. Unequivocally, it is important in a practical sense. Personally, I think practical lin alg co...
by Fluid_Dynamic
Mon Jun 22, 2009 1:23 am UTC
Forum: Mathematics
Topic: Part-time math hobbyist, I just took ODE. Any applications?
Replies: 30
Views: 3375

Re: Part-time math hobbyist, I just took ODE. Any applications?

As a follow-up, you mentioned the MIT OpenCourseWare material. Here's the URL for the introductory Game Theory course: http://ocw.mit.edu/OcwWeb/Economics/14-12Fall-2005/CourseHome/index.htm I think this material shouldn't be too difficult, and hopefully will give you ideas for practical problems yo...
by Fluid_Dynamic
Mon Jun 22, 2009 12:32 am UTC
Forum: Mathematics
Topic: Part-time math hobbyist, I just took ODE. Any applications?
Replies: 30
Views: 3375

Re: Part-time math hobbyist, I just took ODE. Any applications?

If you're interested in doing econ / finance, I would suggest looking in to Statistics / Probability for starters. If you don't know that stuff, you're pretty much screwed. Combinatorics plays nicely with Probability, and can be fun math. Once you understand that well, look into SDEs (basically PDEs...
by Fluid_Dynamic
Fri May 29, 2009 3:54 am UTC
Forum: Mathematics
Topic: Trouble with Improper Integrals
Replies: 3
Views: 974

Re: Trouble with Improper Integrals

Hint : Have you worked with polar coordinate integration in 2D problems before?
It still works in 3D, it's just given the name cylindrical coordinates.
Whenever I see x^2 + y^2, I immediately think of redoing the problem in polar coordinates.
by Fluid_Dynamic
Wed May 27, 2009 11:37 pm UTC
Forum: Mathematics
Topic: A question about random walks
Replies: 33
Views: 3027

Re: A question about random walks

Ah, here's a question. Let n = number of times you return to 0, p_n = probability of n We now see p_0, so the obviously problem then becomes find p_n, E[p_n], and V[p_n]. I think this is much simpler, as after that I think p_n = P^n for some P where p_0 + p_1 + ... = 1. Then there's the problem of e...
by Fluid_Dynamic
Wed May 27, 2009 9:38 pm UTC
Forum: Mathematics
Topic: Finding a neat distribution
Replies: 12
Views: 1466

Re: Finding a neat distribution

Sorry, but why can't you use a two-dimensional normal distribution? It seems like the most natural here. The mean is wherever you are aiming, and the variance can be based on the skill of the archer and distance to the target. Given that the initial post suggested using a uniform distribution, I'm ...
by Fluid_Dynamic
Wed May 27, 2009 9:05 pm UTC
Forum: Mathematics
Topic: A question about random walks
Replies: 33
Views: 3027

Re: A question about random walks

@Ended : Ahhhh. OK, now I get it. Yeah, we use the same principle to count the paths (you use the special case of the ballot problem solution, while I sum over the general cases), though you count paths that go back to 0 while I do the opposite. Two sides of the same coin, basically. Problem solved....
by Fluid_Dynamic
Wed May 27, 2009 7:52 pm UTC
Forum: Mathematics
Topic: A question about random walks
Replies: 33
Views: 3027

Re: A question about random walks

@Fluid_Dynamic: that was basically my method (except I restricted to n=m, which you can do if you condition on the first step). Unless I'm mistaken, your formulation solves for the probability that, after 2n steps, you have returned to 0. (We can call that P_2n) I am assuming the question is what's...
by Fluid_Dynamic
Wed May 27, 2009 7:38 pm UTC
Forum: Mathematics
Topic: A question about random walks
Replies: 33
Views: 3027

Re: A question about random walks

Sigh. Ok, I was just alluding to it, but I'll be more definitive. Choose N = n + m = total number of steps = steps to the right + steps to the left. Assume n >= m >= 0, otherwise you would certainly step to the left and reach the zero mark. How many path are there that take n steps to the right, m s...
by Fluid_Dynamic
Wed May 27, 2009 7:10 am UTC
Forum: Mathematics
Topic: Finding a neat distribution
Replies: 12
Views: 1466

Re: Finding a neat distribution

Might I suggest the Beta distribution? (Basically, a generalization of your 1 - x^2)
by Fluid_Dynamic
Wed May 27, 2009 6:53 am UTC
Forum: Mathematics
Topic: A question about random walks
Replies: 33
Views: 3027

Re: A question about random walks

Here's one possible way to do the problem. On the first step, it goes either left or right. Let's assume right (or flip the universe if he went left). After that, count the number of paths after n steps where the path subtotal never goes negative. Now you're just thinking of the Ballot problem. http...
by Fluid_Dynamic
Wed May 20, 2009 12:49 am UTC
Forum: Mathematics
Topic: ITT: Why Math Is Awesome.
Replies: 51
Views: 6396

Re: ITT: Why Math Is Awesome.

Though my reasons changed with time, in high school it was far more pragmatic. No matter how much the teacher hated me, 1 + 1 = 2, and they had to give me the A. Related Note : One problem on a trigonometry test I got in high school was as follows: [My name] is pushed off a cliff by [a fellow classm...
by Fluid_Dynamic
Sun Apr 05, 2009 2:25 am UTC
Forum: Mathematics
Topic: Help with a tricky Fourier series, perhaps?
Replies: 8
Views: 1283

Re: Help with a tricky Fourier series, perhaps?

Did you consider f(0) = 0?

I dunno, just seems a lot quicker, and you don't have to deal with jump discontinuity issues.
Just sayin'.

P.S. Extra credit : using this result, find the value of

[math]\sum_{n=1}^\infty \frac{1}{n^2}[/math]
by Fluid_Dynamic
Mon Dec 29, 2008 6:05 pm UTC
Forum: Mathematics
Topic: Intriguing Impressions of an Improper Integral
Replies: 5
Views: 1538

Re: Intriguing Impressions of an Improper Integral

1. Change of variables x=u^(\frac{2}{n}) , dx= \frac{2}{n}u^(\frac{2}{n}-1) 2. Decomposition of the integrand into partial fractions, \frac{A}{u+i} + \frac{B}{u-i} , which gives A=-\frac{1}{n}exp(-\frac{\pi i}{n}) and B=-\frac{1}{n}exp(\frac{\pi i}{n}) . -------------...
by Fluid_Dynamic
Mon Dec 29, 2008 4:39 am UTC
Forum: Mathematics
Topic: Milkshakes
Replies: 5
Views: 1361

Re: Milkshakes

As a point of note, you mention dV/dt = C < 0 a constant for the rate on consumption. Obviously, some people drink milkshakes faster than others, and furthermore increasing the (absolute) value of C will obviously decrease the amount of time the milkshake has to thaw before being consumed, leading t...
by Fluid_Dynamic
Fri Nov 28, 2008 2:23 am UTC
Forum: Mathematics
Topic: mail googles
Replies: 11
Views: 1502

Re: mail googles

heyitsguay wrote:Also, [imath]tan^{-1}\left(\frac{\pi}{2}\right)[/imath] is undefined.


I think that is defined.
I'd put it at a value between [imath]\frac{\pi}{4}[/imath] and [imath]\frac{\pi}{2}[/imath], though closer to [imath]\frac{\pi}{4}[/imath].
by Fluid_Dynamic
Fri Nov 28, 2008 2:02 am UTC
Forum: Mathematics
Topic: A calculus problem I came up with
Replies: 9
Views: 1932

Re: A calculus problem I came up with

Please correct me if I misunderstood your problem. Let L = length of PQ. You want to see the pdf f(L) = probability density function for the length L. I thought of a way to obtain F(L) = the cumulative distribution function (from which you can derive f(L) = F'(L) ). Assume you have chosen the point ...
by Fluid_Dynamic
Mon Nov 10, 2008 7:20 am UTC
Forum: Science
Topic: You might be a physics major if...
Replies: 540
Views: 64751

Re: You might be a physics major if...

you can solve the wave equation, but you can't add up your bill. To extend on that one... When the bill comes at a restaurant, you'll spend 15 minutes dividing cost, recalculating the tax and tip, and debating what proportion of the shared appetizer should be paid by whom instead of either laying d...

Go to advanced search