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Everything posted by cosine

  1. Yeah, there's another meaning of Hypothesis when you are doing statistics.
  2. Mr. Skeptic brings up a good point... Mary, are your 1000 numbers an ordered sequence?
  3. Oh I see, k in the p equation is the 'really k' from later on! Sorry CalleighMay! Um... are you still working on this problem?
  4. It can be intuitively difficult to imagine such a function because when we draw something it tends to be smooth (a.e. -for technicality's sake). But continuous Brownian Motion is an example of a function that is continuous everywhere but nowhere differentiable. (Note: Brownian Motion is also referred to as a Weiner Process.) Merged post follows: Consecutive posts merged hey insane_alien, I know what you mean by the bean machine, that is the sort of image I have in mind! Actually, what I want to see is that as the balls and spaces get smaller and more plentiful, the end result of the bean machine approximates a bell curve. I just want to see that in math language (aka by passing to the limit).
  5. I see why you might say that, but no it is not like that. You can only take Reimann integrals over continuous domains, but because your theta goes from (-pi, pi), you're not allowed to jump from pi to -pi! If you could do the reimann sum as you were saying, then you would necessarily have: [math] \int^{-\pi+\epsilon}_{\pi-\epsilon} d\theta = -\int^{\pi-\epsilon}_{-\pi+\epsilon} d\theta [/math] However, all is not lost because the region you highlighted is just: [math] \int^{-\pi+\epsilon}_{-\pi} d\theta + \int^{\pi}_{\pi-\epsilon} d\theta [/math]
  6. You can actually do this naïvely with brute force. there are 32 choices for a and 32 choices for c, so you only have 934 possibilities. So take any two numbers next two each other in the sequence and use it as a check for all the possible values of a and c. Store the ones that work for this pair, and then try these out on another pair in the sequence. Do it until needed. This should be O(n).
  7. Hey guys, long time no post! In the past few years I wound up getting a BA in math and then accidently wound up going to grad school. I'm giving an informal presentation in a few days where I will introduce Brownian motion to some colleagues (no laxitive jokes, please!). Anyway, for the presentation I want to pass from discrete Brownian motion to continuous Brownian motion, but I need some help connecting the dots! I'll put what I have so far here and then maybe you can point the way. Thanks! Here we go: Here is a diagram of the simplest Brownian motion: 1 / 0 \ -1 Where each possible outcome (either 1 or -1) has a probability of 1/2. Let's say this happens over the discrete time period /\s. Now let's look at two time steps: 2 / 1 / \ 0 0 \ / -1 | \ | -2 | | [u]/\[/u]s, 2[u]/\[/u]s Now we can define p(t, x), a probability density function, where t is the time, and x is the position on the vertical axis. There is a counting arguement where you define n, the number of time steps that have passed, as t//\s, that allows you to define this function explicitly. I won't go into the arguement here, but instead just show that: p(t, x) = {n}CHOOSE{(n+x)/2} / 2^n Ok, so this part has been straight forward. What I want to do is find the limit of p(t, x) as /\s -> 0. Actually, it will be that p(t, x) is a normal distribution in x, where t is the squareroot of the variance, and 0 is the mean. Any ideas on how to show this though by letting /\s -> 0? Thanks again for the help guys!
  8. your p is very strange as it is the sum of a vector and a scalar value. i j and k are vectors. how they work is like this: you could write the point (1, 2, 3) as 1i + 2j + 3k also this p is weird because density is a scalar value, not a vector value, so there should be no i's j's or k's that don't cancel out in its formula. when you have this figured out the straight forward way to look at this would be to use cylindrical co-ordinates. the cross-section of the object at any given z is a circle of radius 2. thats because cos t i + sin t j is the parametrization of a circle in a single variable. maybe when you come back with more details on p we can help you out more
  9. Philosophy should be a good course for presidential candidates. I seriously think that people who have something to gain by winning the presidency should not be president.
  10. Step 1. Write a research proposal that requires the calculation of factorials. Step 2. Budget for a program that already calculates factorials. Step 3. Get research grant. Step 4. Purchase and install program. 4 lines of code, easy!
  11. As an aside, I believe this method is part of a larger curriculum called Vedic mathematics, which claims to have roots in the Hindu Vedas, and has some following in Indian education.
  12. I think you're meaning that that doesn't only apply to mathematics, in which case I totally agree. I'm just trying to dispell the illusions that most mathematicians lock themselves up alone in offices and out pops formulae
  13. Well I would argue that it is a social discipline because you the social mathematician is infinitely better than the unsocial one. First off, explaining your thoughts is a very social skill. I appeal to authority now when I agree with the Feynmann/Einstein quote (depending on your source) that "If you can't explain it to a 6 year old [or an interested undergraduate], then you don't understand it enough yourself." And secondly the development of mathematics is much richer and quicker when you're bouncing ideas with a partner instead of only on your own path. I think of it much like this, If you consider a person as a vector, His ideas can span the space with the basis of one vector, aka a 1-dimensional space. Then add another person as a vector into the thought process, and the thoughts spanned by the two are 2-dimensional instead of 1!
  14. I beg to differ! Mathematician A: Let's assume Fermat's Last Theorem to be true... Mathematician B: No. Mathematician A: Please? Mathematician B: No. Mathematician A: Pretty please? It will simplify the proof... Mathematician B: Well, okay then. Mathematician A: Well if we assume Fermat's Last Theorem, then my proof of it follows from our assumption! Haha I win! Mathematician C: B got pwned! Mathematician A: Thanks C.
  15. I'm stumped, what is the trick behind this one? Edit: Is it order of operations? PEMDAS here in America, BEDMANS in Canada, I don't know other countries' convention names. But anyway before you do the exponent of 1/2 on both sides (aka take the square root) you have to complete the division first! Because you're taking the squareroot of each side in its entirety, you have to perform the operation of each side first.
  16. Well there are several types of infinities we talked about. (cf: http://www.scienceforums.net/forum/showpost.php?p=343622&postcount=10) But the sense in which you are talking about is infinity as a limiting concept. (cf: http://en.wikipedia.org/wiki/Limit_%28mathematics%29)
  17. Oh I see the joke now... lolz
  18. Hmm, I looked for examples of probability distributions on wikipedia denoted with an R, I found so far: http://en.wikipedia.org/wiki/Rayleigh_distribution http://en.wikipedia.org/wiki/Rice_distribution But I haven't any real idea what these are or are commonly used for
  19. Ah you beat me to it Also I'm sure The Teaching Company has some resources you might like, as I'm thoroughly enjoyed every other product of theirs that I've used. They're audio and video lectures. Edit: Also along similar lines, http://en.wikiversity.org/wiki/Portal:Mathematics
  20. Could someone please explain what [math]X =^{d} R(0,\theta)[/math] means? What is an equals sign superscripted with a d mean? and is R some well-known probability distribution?
  21. I think it should be classified that most of these posts are all dealing with different things referred to as infinity. Ecoli is talking about the infinity of calculus which technically exists only as a limit. w=f[z] is talking about the infinities which are transfinite cardinalities. KLB is talking about To Infinity, and Beyond! And geoguy and dave are talking about "the point at infinity" which exists in some non-euclidean geometries, most notably (as was said) Reimann geometry, which is a geometry on a sphere.
  22. When you say Algebra... do you mean what is more colloquially called "highschool algebra" or "college algebra" that has to do with variables and polynomials or are you referring to what's more often called "abstract algebra" with groups and rings?
  23. cosine


    Excuse me for nitpicking, but there is a technical other consideration. Any nonzero number divided by zero is undefined (unless working in some non-euclidean planes, then they are "the point at infinity"). As for [math]\frac{0}{0}[/math] is sometimes an exception if it is the limit of a function. If it is the limit of a function then it is called an indeterminate form and you need to use calculus to see if it has a value or not. (Cf: L'hopital's rule)
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