Math thread! Come in and have some pi...

[John L]

lambda is (3*(10^8)/(2.4*10^9))

The G's are 1, it tells you this

I got about 0.4*10^(-8)

i also have no idea what the second part is asking

Great, I got that answer for the first part as well. I have absolutely no idea what I have to do for lambda or the G's in the second part.

[juiceboxx03]

Great, I got that answer for the first part as well. I have absolutely no idea what I have to do for lambda or the G's in the second part.

I would use the same value for lambda and gains for the cell phone part, if they didnt give you anything else. Make sure you convert d to meters as well

[GaryOatz]

anybody know, what the H means? It's not explained in the book and I don't know how to google it. pls

[tfwnogfsrs]

LaTeX problem!

I want to type that:

cos^{2}(1/n) - 2cos(1/n) + 1 <=> (cos(1/n)-1)*(cos(1/n)-1) <=> (cos(1/n)-1)^{2}

and that

cos^{3}(1/n) - cos^{2}(1/n) - cos(1/n) + 1 <=> (cos(1/n)-1)*(cos(1/n)-1)*(cos(1/n)+1) <=> (cos(1/n)-1)^{2}*(cos(1/n)+1)

in LaTeX in a nice way, but it fukks up when I do it (not aligned etc). I barely know anything about this program, feels bad man. Could anyone show me how?

I use \usepackage{amsmath} if that helps lulz

[juiceboxx03]

anybody know, what the H means? It's not explained in the book and I don't know how to google it. pls

Sobolev space

[GaryOatz]

thanks m8

[tfwnogfsrs]

\begin{align*}
\cos^3\left(\dfrac{1}{n}\right) - \cos^2\left(\dfrac{1}{n}\right) - \cos\left(\dfrac{1}{n}\right) + 1 
&= \left(\cos\left(\dfrac{1}{n}\right)-1\right)\left(\cos\left(\dfrac{1}{n}\right)-1\right)\left(\cos\left(\dfrac{1}{n}\right)+1\right)\\
&= \left(\cos\left(\dfrac{1}{n}\right)-1\right)^{2}\left(\cos\left(\dfrac{1}{n}\right)+1\right)
\end{align*}

edit: had to add [code..] tags because the forum inserts spaces

hhnnngggg

thanks brah

[SCAR-H]

Maybe someone here can help with this.

I'm transcribing audio and looking for key phrases that must be grouped.

For instance, I tell it to look for "in the end", but instead of looking for the whole string it looks for "in", "the", "end" and returns all instances of the words.

I figured I could use their start and end times to rule out any extra occurrences.

It looks like this
even 0.45 0.65
even 4.92 5.25
doesn't 4.51 4.92
it 3.16 3.45
it 4.36 4.51

http://puu.sh/n6OMy.png

Any clever way to find the closest n points? In this case it would be the closest three.

As you can see, the three closest points are what I actually want.

atm just thinking of getting rid of the y coordinate, iterating through the inner points, and comparing their difference.

Should return the smallest distance and keep those three points.

[Chesssbrah]

Maybe someone here can help with this.

I'm transcribing audio and looking for key phrases that must be grouped.

For instance, I tell it to look for "in the end", but instead of looking for the whole string it looks for "in", "the", "end" and returns all instances of the words.

I figured I could use their start and end times to rule out any extra occurrences.

It looks like this
even 0.45 0.65
even 4.92 5.25
doesn't 4.51 4.92
it 3.16 3.45
it 4.36 4.51

http://puu.sh/n6OMy.png

Any clever way to find the closest n points? In this case it would be the closest three.

As you can see, the three closest points are what I actually want.

atm just thinking of getting rid of the y coordinate, iterating through the inner points, and comparing their difference.

Should return the smallest distance and keep those three points.

If I'm understanding correctly, given a point P, you are trying to find the closest n points to P, i.e. the famous https://en.wikipedia.org/wiki/K-near...bors_algorithm ?

If so, there are many solutions available online, a quick Google search yields http://stackoverflow.com/questions/2...ensional-plane

[SCAR-H]

If I'm understanding correctly, given a point P, you are trying to find the closest n points to P, i.e. the famous https://en.wikipedia.org/wiki/K-near...bors_algorithm ?

If so, there are many solutions available online, a quick Google search yields http://stackoverflow.com/questions/2...ensional-plane

I came across that but thought it was too complex for what I am doing. I don't think I'll ever have more than ten data points.

'Find the n nearest points to each other' and not to a specific point

{a, b, c, d, e, f}

I'm not trying to find the n closest points to a, or b, c, d, etc. I'm trying to find just the n (in this case three) closest points to each other.

Might be {a, b, c} or {b,c,d}, but it will never be {a,c,f} etc.

Currently working but might be really slow

[MoviePy] Writing audio in TEMPsound.wav
[MoviePy] Done.
current distance 0.65, min distance 0.65
current distance 1.92, min distance 0.65
[[u'it', 0.44, 0.69], [u'starts', 0.69, 1.09], [u'with', 1.09, 1.2]]
[MoviePy] Writing audio in TEMPsound.wav
[MoviePy] Done.
[[u'one', 0.98, 1.18], [u'thing', 1.18, 1.42]]
[MoviePy] Writing audio in TEMPsound.wav
[MoviePy] Done.
[MoviePy] Writing audio in TEMPsound.wav
[MoviePy] Done.
[[u'why', 0.96, 1.24]]
[MoviePy] Writing audio in TEMPsound.wav
[MoviePy] Done.
current distance 3.91, min distance 3.91
current distance 1.35, min distance 3.91
current distance 0.56, min distance 1.35
[[u'it', 4.36, 4.51], [u"doesn't", 4.51, 4.92], [u'even', 4.92, 5.25]]
[MoviePy] Writing audio in TEMPsound.wav
[MoviePy] Done.
[[u'matter', 2.03, 2.29], [u'how', 2.29, 2.51]]
[MoviePy] Writing audio in TEMPsound.wav
[MoviePy] Done.
[]
[MoviePy] Writing audio in TEMPsound.wav
[MoviePy] Done.
current distance 0.37, min distance 0.37
[[u'keep', 1.23, 1.43], [u'that', 1.43, 1.6], [u'in', 1.6, 1.69]]
[MoviePy] Writing audio in TEMPsound.wav
[MoviePy] Done.
[[u'mind', 0.36, 0.56], [u'I', 0.56, 0.59]]
[MoviePy] Writing audio in TEMPsound.wav
[MoviePy] Done.
[]
[MoviePy] >>>> Building video Final/clip_0.mp4
[MoviePy] Writing audio in clip_0TEMP_MPY_wvf_snd.mp3

[Chesssbrah]

I came across that but thought it was too complex for what I am doing. I don't think I'll ever have more than ten data points.

'Find the n nearest points to each other' and not to a specific point

{a, b, c, d, e, f}

I'm not trying to find the n closest points to a, or b, c, d, etc. I'm trying to find just the n (in this case three) closest points to each other.

Might be {a, b, c} or {b,c,d}, but it will never be {a,c,f} etc.

Currently working but might be really slow

Ah I see now. I would conjecture that a triplet of points p1,p2,p3 among a set of points P are closest to one another if and only if the triangle formed by the vertices p1,p2, and p3 has the smallest area. So exploiting this idea coupled with Heron's Formula (https://people.richland.edu/james/le...lications.html) it seems like you can easily find the closest 3 points in linear time.

General pseudo-code could look like this:

minArea = infinity
startIndex = 0
for index i = 0 ... N - 2
  p1 = points[i]
  p2 = points[i + 1]
  p3 = points[i + 2]
  area = HeronsFormula(p1,p2,p3)
  if area < minArea
    startIndex = i
    minArea = area

After completion, points[startIndex,...,startIndex+2] would contain the closest 3 points.

I haven't tested this yet though give me a sec and I'll see whether it works

[SCAR-H]

Ah I see now. I would conjecture that a triplet of points p1,p2,p3 among a set of points P are closest to one another if and only if the area formed by the vertices p1,p2, and p3 has the smallest area. So exploiting this idea coupled with Heron's Formula (https://people.richland.edu/james/le...lications.html) it seems like you can easily find the closest 3 points in linear time.

I haven't tested this yet though give me a sec and I'll see whether it works

That's exactly what I was thinking but I went about it more programatically.

Data looks like [ [word, start_time, end_time], ... ]

#this gets you the distance between start_time and end_time for each list
minDistance = elm[size(elm)-1][2] - elm[0][1]
for element in dataset:
    distance = elm[size(elm)-1][2] - elm[0][1]
    if distance <= minDistance:
        minDistance = distance

I'll definitely be changing it.

I can make it 1 dimensional since the data is already ordered, and that's sort of what I did above

Need to buy more RAM for this :'(

EDIT: saw your psuedo code. We're essentially doing the same thing just in different dimensions. looks good.

[Chesssbrah]

That's exactly what I was thinking but I went about it more programatically.

Data looks like [ [word, start_time, end_time], ... ]

#this gets you the distance between start_time and end_time for each list
minDistance = elm[size(elm)-1][2] - elm[0][1]
for element in dataset:
    distance = elm[size(elm)-1][2] - elm[0][1]
    if distance <= minDistance:
        minDistance = distance

I'll definitely be changing it.

I can make it 1 dimensional since the data is already ordered, and that's sort of what I did above

Need to buy more RAM for this :'(

EDIT: saw your psuedo code. We're essentially doing the same thing just in different dimensions. looks good.

Yeah I think you can take advantage of the fact that the points are all ordered that way... although I wonder if you could do this in logarithmic time... Is linear time too slow for your application? I was going to say you can get rid of expressions like sqrt when computing norms/areas which make a difference in practice, but it seems like your code doesn't have any of those as it is.

[SCAR-H]

Yeah I think you can take advantage of the fact that the points are all ordered that way... although I wonder if you could do this in logarithmic time... Is linear time too slow for your application? I was going to say you can get rid of expressions like sqrt when computing norms/areas which make a difference in practice, but it seems like your code doesn't have any of those as it is.

There's a lot I still need to do to make this more efficient.

Product: https://streamable.com/qjly

Using Bluemix speech recognition doesn't match all keywords, so the clips that are too long had no matches.

Hundreds of non-matches

[John L]

I would use the same value for lambda and gains for the cell phone part, if they didnt give you anything else. Make sure you convert d to meters as well

Thanks brah, I'll probably just do that. Any ideas on what the significance of the problem giving that random ass info of cell towers operating on 0.75 to 1 watt of power? That part's really throwing me for a loop

[juiceboxx03]

Thanks brah, I'll probably just do that. Any ideas on what the significance of the problem giving that random ass info of cell towers operating on 0.75 to 1 watt of power? That part's really throwing me for a loop

I'm not sure why they would give you information on car phones, then talk exclusively about cell phones/cell towers. That's what threw me off, and I kept re-reading the problem. The only thing I can think of is (provided they didn't give you any other information) is they want you to look up the frequency? And then assume the gains are 1, not 100% sure

[ctownballer04]

Okay so I'm a little confused w/ stats, so I feel like I have an answer, but we haven't covered confidence intervals in this class and it's been forever since I took the first part of this sequence so let me just run something by this thread real quick:

"Suppose that the waiting time for a bus, in minutes, has the uniform in (0,10) distribution. In five months a person catches the bus 120 times. Find an approximation to the 95th percentile of the total waiting time. "

There's no way to do this other than w/ standard confidence intervals right? This is in a chapter where I'm not seeing anything like this so I'm a little confused, but on a surface level I think I'm fine, this just happens to be a problem w/o an answer in the back.

Isn't it just a 95% CI?
So xi~U(0,10)
Let T= x1+x2+...+x120
By CLT, T~N(600,1000)

CI = 600 +/- 1.96*sqrt(1000)

I feel this a dumb question, but this is what they want right?


EDIT:
Actually I think they want a single number, is that what they're looking for?

P(T<x)=.95
P[z<((x-600)/sqrt(1000))]=.95
Say phi(y)=.95 => y=1.645

1.645=(x-600)/sqrt(1000) => x=652.02

[ctownballer04]

One last question if someone has a sec, I tried going to the stats tutoring in the math lab but the person could only tutor the 200 level intro course.

"Components that are critical for the operation of electrical systems are replaced immediately upon failure. Suppose that the life time of a certain such component has mean and standard deviation of 100 and 30 time units, respectively. How many of these components must be in stock to ensure a probability of at least 0.95 for the system to be in continuous operation for at least the next 3000 time units? (Hint: If T= x1+x2+...+xn is the combined duration of n components, we want P(T>3000)=0.95. This means that 3000 is the 5th percentile of T. Using the CLT to approximate the 5th percentile of T leads to a quadratic equation for the square root of n, that is, an equation of the form ax^2+bx+c=0, with x being the square root of n."

Now this is what I have:
T~N(100n,900n)
P(T>3000)=.95 => [1-P(T<3000)]=.95
[1-P(z<(3000-100n)/sqrt(900n))] =.95

[1-Phi(y)]=.95 => -1.645
-1.645= (3000-100n)/sqrt(900n)

Which gives me 32.83, but the answer says just 33. Is this just rounding or am I actually wrong?

[ctownballer04]

^ im only able to help with elementary stats myself, but am not so sure about the bus stop thing. do you have a link for the CLT stating that a sum of uniform RVs is normal? i have only found this: https://en.wikipedia.org/wiki/Irwin%...l_distribution

i understand that the sampling distribution for the means of uniform rvs is approximately normal for large n

edit: ah, maybe its similar to the previous thing.

sum(xi) = 120*(sum(xi)/120) = 120*xbar

so mu'= E(sum(xi)) = 120*E(xbar) = 120*mu = 600

i think what you did is correct, but this is only supposed to be an approximation, to the estimation, of the mean? i think stats has gone too far

I'm in a four hour finance lecture atm, so don't have my book, but doesn't the central limit theorem essentially say that the sum and arithmetic average of a large number of iid random variables is approximately normal regardless of the underlying distribution?

Yeah just estimation. I think I'm okay, I just figured I'd run it by this thread in case anyone had any insight. Thanks man.

[Hardcore_D00d]

Holy fuking chit gravitational waves detected! Einstein himself thought they would never be found. sucks that I'm gonna die before we can practically utilize this technology.

[Plyoz]

Do you guys have any resources for learning Linear Algebra besides Khan Academy? I just don't get this **** like I do Calculus. I don't know if it's the terminology or that every problem is just a box of numbers or what. Really struggling.

[ctownballer04]

maybe, the CLT we have in our elementary text only applies to the means of samples of distributions. yours may be a more general version

Just to follow up w/ my books definition, it just says the following:

CLT: Let X1, X2, ... , Xn be iid w/ mean mu and finite variance sigma^2= s^2. Then, for large enough n

1) xbar has approximately a normal distribution w/ mean mu and variance s^2/n

2) T= X1 + X2 +...+ Xn has approximately a normal distribution with mean n*mu and variance n*s^2.

[killakms]

I checked calculated online answer and its suppose to be right?

[ctownballer04]

I checked calculated online answer and its suppose to be right?

There is no value given for h, so how did you get rid of it?

The idea is to show that the something of the form (a^x)^y=a^x*y where something of the form a^x*a^y=a^(x+y)


So you using these properties you have (2h)^6*(2h)^72=(2h)^78

[killakms]

Reps on Recharge.

Also i'm having a problem with this. I even tried the ^ after six after and still didnt work???



only got one shot left...

[ctownballer04]

Mathematician, m8, what you teaching these days? You get a full time teaching gig or whats new mayn?

Reps on Recharge.

Also i'm having a problem with this. I even tried the ^ after six after and still didnt???

You tried 1/(64*w^6)?? If that didn't work, you got some problems m8.

[killakms]

Mathematician, m8, what you teaching these days? You get a full time teaching gig or whats new mayn?




You tried 1/(64*w^6)?? If that didn't work, you got some problems m8.

yea i put dat carrot after w wtf. not the brackets you have tho. Will use as my last shot. oh well..

[ctownballer04]

yea i put dat carrot after w wtf. oh well..

Make sure there are parenthesis too. The way the computer interprets it is that you're in the numerator unless there are parenthesis in the denominator. Going off your picture, that's interpreted by the computer as (1/64)*w6. So even if you put a carot in there in that format, it's still wrong. (1/64)*(w^6) wouldn't be correct, you need the w^6 in the denominator.

[killakms]

Make sure there are parenthesis too. The way the computer interprets it is that you're in the numerator unless there are parenthesis in the denominator. Going off your picture, that's interpreted by the computer as (1/64)*w6. So even if you put a carot in there in that format, it's still wrong. (1/64)*(w^6) wouldn't be correct, you need the w^6 in the denominator.

Thanks baller. The brackets work! Would rep so hard but out from all the repping i did with earlier math problems...

[ctownballer04]

Thanks baller. The brackets work! Would rep so hard but out from all the repping i did with earlier math problems...

Glad you got it figured out, don't worry about it dude, I'm not concerned about the reps lol.