## Search found 69 matches

- Wed Dec 02, 2015 3:58 pm UTC
- Forum: Mathematics
- Topic: Game-tree complexity of Connect Four
- Replies:
**7** - Views:
**2866**

### Re: Game-tree complexity of Connect Four

Quite quickly you have columns you cannot play because it means an immediate loss, and columns you have to play because not playing gives an immediate loss. Maybe 5 would be a better estimate, but it definately has to be less then 7

- Fri Nov 27, 2015 7:28 pm UTC
- Forum: Mathematics
- Topic: Integer Factorization of large semiprimes
- Replies:
**6** - Views:
**3505**

### Re: Integer Factorization of large semiprimes

Jopus wrote: It's pretty arcane stuff.

I assure you it is not. It is a really well studied subject. If you are really interested you should check out the general numberfield sieve. It is dauntingly complex, but the best we have at the moment. For a more gentle method you could look at Pollard's p-1 algorithm

- Fri Nov 27, 2015 6:28 pm UTC
- Forum: Mathematics
- Topic: Record High/Low
- Replies:
**3** - Views:
**1281**

### Re: Record High/Low

can we calculate what the odds are that the nth year would be a record high (or low) measurement? Yes. The probability of finding a current maximum the nth year is 1/n. If we assume all draws are independent and identically distributed, then the probability of a specific one out of n being the maxi...

- Tue Oct 20, 2015 4:11 am UTC
- Forum: Coding
- Topic: Coding: Fleeting Thoughts
- Replies:
**9708** - Views:
**1447595**

### Re: Coding: Fleeting Thoughts

That is a very nice talk! I like your analogy with radio active waste and will use it when trying to explain my liking of online privacy.

Did the audience like it as well?

- Tue Oct 20, 2015 12:20 am UTC
- Forum: Mathematics
- Topic: Little conjecture
- Replies:
**6** - Views:
**1681**

### Re: Little conjecture

>-) wrote:the probability that each of your 2p-2k-1 is composite is about the same: (1-2/(ln(2)*p)) ~= (1-2.885/p)

That's neat: so the probability that all of them are composite (i.e. no primes) is about (1-2/(ln(2)*p))^p, which converges to exp(-2/ln(2)) which is about 5%

- Sun Oct 11, 2015 4:55 pm UTC
- Forum: Mathematics
- Topic: Axioms and multiplication?
- Replies:
**18** - Views:
**2459**

### Re: Axioms and multiplication?

So what's your metric on the rational functions? ie what's a Cauchy sequence and what isn't. Constructing the reals from the rationals via Cauchy sequences is very similar to completing other metric spaces, but as you have noticed, because the theory of metric spaces uses real numbers pervasively, ...

- Thu Apr 09, 2015 5:40 pm UTC
- Forum: Mathematics
- Topic: Closed infinite intersection of open sets
- Replies:
**11** - Views:
**2443**

### Re: Closed infinite intersection of open sets

{0} as a subset of ℤ is closed and open Depends on the topology on ℤ. While ℝ has a "default" topology, on ℤ several are sensible. Offhand, one might consider ℤ as a subspace of ℝ, this leads to the discrete topology and is probably what you intend. On the other hand, one can also conside...

- Sat Mar 14, 2015 11:43 pm UTC
- Forum: Mathematics
- Topic: Happy Super Pi Day, Everyone!
- Replies:
**37** - Views:
**3466**

### Re: Happy Super Pi Day, Everyone!

Flumble wrote:(I wanted to add a word for "anti-socialistic", but I couldn't find the right one. Any help?)

McArthyist?

- Thu Mar 05, 2015 11:38 pm UTC
- Forum: Coding
- Topic: genetic go bot
- Replies:
**6** - Views:
**2799**

### Re: genetic go bot

The standard way to code them is as minimax algorithms, which should be easy to look up information and tutorials for. The non-trivial bit that you have to supply is the board evaluation function - given a particular board state and a particular player, how "good" is that board for that p...

- Thu Mar 05, 2015 7:00 am UTC
- Forum: Mathematics
- Topic: Correlation for Sine Model?
- Replies:
**3** - Views:
**1281**

### Re: Correlation for Sine Model?

Typically one wants to find the maximum likelihood estimators. If your errors are Normal distributed then this is equivalent to finding those parameters that minimize the squared error. This suggests the root-mean-square error as a reasonable measure.

- Sat Feb 28, 2015 9:21 am UTC
- Forum: Mathematics
- Topic: Polynomials : Multiplicity of roots Homework problem
- Replies:
**11** - Views:
**2501**

### Re: Polynomials : Multiplicity of roots Homework problem

Paradoxica wrote:Turns out the question was incorrectly stated. r = -1

Presumably you now managed to find the answer?

- Mon Jan 05, 2015 1:35 am UTC
- Forum: School
- Topic: Does anyone feel like previous levels don't prepare you?
- Replies:
**19** - Views:
**12467**

### Re: Does anyone feel like previous levels don't prepare you?

Many people come out of high school without even a basic understanding of algebra, but some have a good grasp of calculus. Wha..? I'm curious; how are you defining algebra? How is this confusing? He's saying that some people get out of high school knowing more math than other people, not that some ...

- Fri Oct 17, 2014 3:09 pm UTC
- Forum: Mathematics
- Topic: Non-contractible, simply connected subsets of R^n
- Replies:
**4** - Views:
**1912**

### Non-contractible, simply connected subsets of R^n

(This problem was suggested to me by a friend who told me the first two observations) The first observation one can make, is that S^2 is non-contractible and simply connected (trivial fundamental group), yielding that for n>=3 such subsets exist. Secondly, for n=0,1 all connected subsets are immedia...

- Wed Jul 09, 2014 7:07 pm UTC
- Forum: Mathematics
- Topic: Probability of a string of consecutive successes
- Replies:
**12** - Views:
**2710**

### Re: Probability of a string of consecutive successes

Well that is where the markov chain method really shines!, You could consider the process with the following matrix P 1/2 1/2 0 0 0 1/3 0 2/3 0 0 1/4 0 0 3/4 0 1/5 0 0 0 4/5 0 0 0 0 1 You then calculate P 100 , and then you can read the answer of from the left-bottom corner. (in general with a start...

- Mon Dec 09, 2013 2:25 am UTC
- Forum: Mathematics
- Topic: Question about differential equations!
- Replies:
**5** - Views:
**1813**

### Re: Question about differential equations!

I agree that as posed you're heading in the right direction, but independent of the constants, your limit already is 0 instead of 5/6, so the problem as it stands is ill posed. This does assume real (and not complex) x, but I think that is a safe assumption. Taking the limit x to 0 seems sane, are y...

- Sun Dec 08, 2013 5:31 pm UTC
- Forum: Coding
- Topic: Making self-deleting files
- Replies:
**17** - Views:
**17555**

### Re: Making self-deleting files

Because circumvention is basically trivial?

- Sun Dec 08, 2013 4:30 pm UTC
- Forum: Mathematics
- Topic: Question about differential equations!
- Replies:
**5** - Views:
**1813**

### Re: Question about differential equations!

You probably made a slight mistake in posing the problem, because as it stands, lim

You might've swapped the -4y' and 4y' or u and v

_{x->oo}v=0 and lim_{x->oo}u=oo which means that automatically lim_{x->oo}v^{4}/u=0You might've swapped the -4y' and 4y' or u and v

- Thu Dec 05, 2013 10:59 pm UTC
- Forum: Coding
- Topic: Making self-deleting files
- Replies:
**17** - Views:
**17555**

### Re: Making self-deleting files

Yes the "attaching the kill code" is the entire problem, Halo. You haven't brought anything new to this thread, which, by the way, was dead for almost four years, before you had to chime in. As the other posters have already mentioned, attaching such a switch is, because of the possible mi...

- Mon Dec 02, 2013 3:25 pm UTC
- Forum: Science
- Topic: What is the smallest object that has gravity?
- Replies:
**65** - Views:
**15233**

### Re: What is the smallest object that has gravity?

Cool story! I wouldn't have expected that to work, because of the (assumedly) large distance, but apparantely it does...

- Mon Dec 02, 2013 3:23 pm UTC
- Forum: Mathematics
- Topic: Limit exponential/power function
- Replies:
**3** - Views:
**2285**

### Re: Limit exponential/power function

and of course ln/exp is continuous so the answer translates.

- Mon Dec 02, 2013 3:21 pm UTC
- Forum: Mathematics
- Topic: Jordan exchange-Independence
- Replies:
**2** - Views:
**1571**

### Re: Jordan exchange-Independence

mathmari wrote:Are the results at both cases equal??

Yes. Your matrix only has rank 3 so your solution set is an entire line.

- Mon Nov 25, 2013 5:33 pm UTC
- Forum: Mathematics
- Topic: Measure-theory-ish thingamajig
- Replies:
**38** - Views:
**5588**

### Re: Measure-theory-ish thingamajig

Let's consider the following intervals I n =[0,1/n). The quantity of such an interval should be q(I n )=1/n R 1 . Now, in the limit(intersection over all n) I n is [0,0] or the single point 0, which has a quantity of 1, whilst the limit of the quantities is 0, assuming limits are linear over R 1 . I...

- Wed Nov 13, 2013 8:21 pm UTC
- Forum: Mathematics
- Topic: Integrating the Gaussian pdf over a half-space
- Replies:
**14** - Views:
**2023**

### Re: Integrating the Gaussian pdf over a half-space

Okay If you have a "generalized" volume integral in R^n (the subset over which we integrate contains a non-empty open subset of R^n) and we want to change basis from variables x to variables x' via x'=Ax with A a matrix. Then your "volume" element changes as dx'=\det A \cdot dx. ...

- Tue Nov 12, 2013 6:20 am UTC
- Forum: Mathematics
- Topic: Integrating the Gaussian pdf over a half-space
- Replies:
**14** - Views:
**2023**

### Re: Integrating the Gaussian pdf over a half-space

I am pretty sure that the problem is not solvable if \mu doesn't lie in H though, because e^{-x^2} doesn't have a primitive. Big hint: Its solvable in terms of the Gaussian. Have a look at the pic on the top right here. http://en.wikipedia.org/wiki/Multivariate_normal_distribution The 1 dimensional...

- Sun Nov 10, 2013 11:08 pm UTC
- Forum: Mathematics
- Topic: Integrating the Gaussian pdf over a half-space
- Replies:
**14** - Views:
**2023**

### Re: Integrating the Gaussian pdf over a half-space

Hi all, Someone could observe that if the bias term, b , is equal to zero, i.e., the hyperplane passes through the origin, then - by symmetry - the integral should be equal to 1/2 (am I wrong?). This is only true if \mu=0 ie. the chance is actually only 1/2 if \mu^t w=-b I am pretty sure that the p...

- Thu Nov 07, 2013 8:02 pm UTC
- Forum: Mathematics
- Topic: Dogma in Math
- Replies:
**98** - Views:
**9319**

### Re: Dogma in Math

frog, that brick bussiness is very rude. On topic, 0! is the empty product and can be defined unambiguously as 1. It is very much a logical choice. (and yes there is exactly one function from the empty set to another set. The empty map that is.) Also compare with the empty sum. Google these terms(em...

- Mon Oct 28, 2013 2:44 pm UTC
- Forum: Logic Puzzles
- Topic: Prisoners disguised as guards
- Replies:
**29** - Views:
**7618**

### Re: Prisoners disguised as guards

Given that there are 2^60 configurations, half of them with more than half of the people guards,st least 59 questions are necessary.

- Sat Oct 26, 2013 4:15 pm UTC
- Forum: News & Articles
- Topic: In other news... (humorous news items)
- Replies:
**13758** - Views:
**1719849**

### Re: In other news... (humorous news items, etc)

Not that it will ever make it into a headline, but the chance of an impact is estimated at 1 in 63 000 , which is better than winning the lottery but I'm still not overly concerned by. Now one in 11,000 chance of impact. How're those dams and dykes looking now, Diadem? living less than 10 miles fro...

- Sat Sep 28, 2013 11:31 pm UTC
- Forum: Language/Linguistics
- Topic: Spreek Nederlands en Praat Afrikaans (Dutch & Afrikaans)
- Replies:
**418** - Views:
**121510**

### Re: Spreek Nederlands en Praat Afrikaans (Dutch & Afrikaans)

Given how fond many Germanic groups were of using Roman coins, I'd be quite surprised if a word that similar were independently developed rather than simply being borrowed from the nearby powerful culture with whom they were trading. Both google and my dictionary confirm that consto, litterally &qu...

- Sat Sep 28, 2013 8:21 pm UTC
- Forum: Mathematics
- Topic: I want to compare the random numbers generated from many RNG
- Replies:
**12** - Views:
**3007**

### Re: I want to compare the random numbers generated from many

Relatively common used is linear congruential. (see wikipedia) Also, you could try using something fourier-transform (esque?) to look for repetitions. At least I remember reading this suggestion a few years ago, when I did some research on this topic with a reference to Knuth's Taocp. I didn't know ...

- Wed Sep 18, 2013 11:21 pm UTC
- Forum: Mathematics
- Topic: mean of geometric distribution: *intuitive* reason
- Replies:
**14** - Views:
**3927**

### Re: mean of geometric distribution: *intuitive* reason

And your friends have more friends than average (they have you)

- Wed Sep 18, 2013 11:15 pm UTC
- Forum: Mathematics
- Topic: Justifying L'Hopital to an ambitious undergrad
- Replies:
**8** - Views:
**3237**

### Re: Justifying L'Hopital to an ambitious undergrad

Taylor the function:

lim x->a f(x)/g(x)

=lim x->a (f(a)+(x-a)f'(a)) / (g(a)+(x-a)g'(a))

given that f(a)=g(a)=0:

=lim x->a ((x-a)f'(a)) / ((x-a)g'(a))

=lim x->a (f'(a)) / (g'(a))

Taylor is super useful, also in numerical analysis.

lim x->a f(x)/g(x)

=lim x->a (f(a)+(x-a)f'(a)) / (g(a)+(x-a)g'(a))

given that f(a)=g(a)=0:

=lim x->a ((x-a)f'(a)) / ((x-a)g'(a))

=lim x->a (f'(a)) / (g'(a))

Taylor is super useful, also in numerical analysis.

- Fri Sep 13, 2013 2:01 pm UTC
- Forum: Science
- Topic: Solid Expansion
- Replies:
**9** - Views:
**1695**

### Re: Solid Expansion

That's cool and a very useful property for tires, or is that effect to small to be useful?

- Wed Sep 11, 2013 3:31 pm UTC
- Forum: Mathematics
- Topic: Normal way to show Q(cube root of 2) is a subfield of R?
- Replies:
**7** - Views:
**3132**

### Re: Normal way to show Q(cube root of 2) is a subfield of R?

You can probably prove this by showing that (x^3-2) is a prime ideal in Q[x] then your thing must be afield.

- Tue Sep 10, 2013 9:04 pm UTC
- Forum: Mathematics
- Topic: Normal way to show Q(cube root of 2) is a subfield of R?
- Replies:
**7** - Views:
**3132**

### Re: Normal way to show Q(cube root of 2) is a subfield of R?

So I shouldn't write posts in a hurry.. AACtually multiplicative inverses are relatively easy: (a+b*e)(a-b*e)/(a^2+b^2)=1 for any extension element e. This easily extends to multiple extensions. (Remember C is just R[i] ) What? (a^2-b^2 e^2)/(a^2 + b^2) = 1 for all a, b and e? [..] I think you are m...

- Tue Sep 10, 2013 1:37 pm UTC
- Forum: Mathematics
- Topic: Normal way to show Q(cube root of 2) is a subfield of R?
- Replies:
**7** - Views:
**3132**

### Re: Normal way to show Q(cube root of 2) is a subfield of R?

AACtually multiplicative inverses are relatively easy: (a+b*e)(a-b*e)/(a^2+b^2)=1 for any extension element e. This easily extends to multiple extensions. (Remember C is just R[i] )

- Sun Sep 01, 2013 4:27 pm UTC
- Forum: Science
- Topic: Two beams of light affecting each other
- Replies:
**9** - Views:
**2179**

### Re: Two beams of light affecting each other

Tass wrote:If they are not parallel, then there is also a gravitational effect, albeit very small.

Why are there no gravitational effects if they are paralel?

- Thu Aug 29, 2013 11:03 pm UTC
- Forum: Science
- Topic: What happens to a photon after you see it?
- Replies:
**8** - Views:
**3303**

### Re: What happens to a photon after you see it?

When you see it, it is absorbed. Once it hits something it is absorbed. We can see stars in all directions because space is ridiculously empty. There is an effect in wich a molecule first absorbs a photon and shortly after releases a photon with the same energy and momentum. Others can probably expl...

- Sun Aug 25, 2013 3:49 pm UTC
- Forum: Mathematics
- Topic: Throwing a random die
- Replies:
**20** - Views:
**4375**

### Re: Throwing a random die

That basically was my first try at a solution, but it probably isn't very good.

For example, some of the surfaces might be shaped such that the center of gravity doesn't lie over it, making it impossible that the die will end on that surface.

For example, some of the surfaces might be shaped such that the center of gravity doesn't lie over it, making it impossible that the die will end on that surface.

- Fri Aug 16, 2013 9:58 pm UTC
- Forum: Science
- Topic: Trapping Particals in magnetic feild.
- Replies:
**3** - Views:
**1420**

### Re: Trapping Particals in magnetic feild.

Given arbitrary instruments to create the magnetic field: yes*. only using the sphere: I doubt it. However, binding it electrostatically might be easier, just put the opposite charge in the sphere. By the way, if your particle isn't charged, like a neutron, then the answer is no. *: constant magnett...