Recent content by ptolema

I do have some bio classes (1 year of general biology) and a summer internship involving genetics and computational bio. I've also picked up some bio from sitting in on classes and video lectures. Is there a particular area/course that they prefer?

I'm getting ready to apply to grad schools, and I'm having a hard time choosing schools to apply to. I'm an applied math major, and I'm really interested in mathematical/computational biology. I don't necessarily want to study math in grad school, but I'm open to math programs with a more...

Homework Statement The independent random variables X_1, ..., X_n have the common probability density function f(x|\alpha, \beta)=\frac{\alpha}{\beta^{\alpha}}x^{\alpha-1} for 0\leq x\leq \beta. Find the maximum likelihood estimators of \alpha and \beta. Homework Equations log...

Homework Statement Find the general solution: 2xy \frac{dy}{dx} = y + x^4Homework Equations The Attempt at a Solution I have tried to solve this as a linear first order equation, a Bernoulli equation, and an exact equation. I'm not sure how to approach this, any ideas?

Homework Statement Let z be a complex number such that z^n=(z+1)^n=1. Show that n|6 (n divides 6) and that z^3=1. Homework Equations n|6 → n=1,2,3,6 The Attempt at a Solution The z+1, I think, is what throws me off. Considering z^n=1 by itself, for even n, z=±1 and for odd n...

I see now. So 5, 17, and 101 are the factors of 8585. 5=2^2 + 1^2, 17=4^2 + 1^2, and 101=10^2 + 1^2. Using the Brahmagupta-Fibonacci identity yields the results shown.

Homework Statement Find integers A and B such that A2 +B2 = 8585 Homework Equations The Attempt at a Solution So in this case, I already know the answer: Sum of 2 squares: 8585 = 67^2 + 64^2 = 76^2 + 53^2 = 88^2 + 29^2 = 92^2 + 11^2. I started off looking at the graph of the...

I actually just tried it a different way. I used your suggestion, ehild, of drawing out the path. [PLAIN]http://www.privateline.com/Cellbasics/sevencellcluster.gif So the tourist travels in a path that traces the outside of this hexagon cluster. At least, this is how I ended up coming up...

Yes, I understand that now. My problem is that although I can figure out the angle of the tourist after a given number of stages, I'm stuck on how to find the distance between the starting and ending points. When I do it graphically, I get a path that looks like partial traces of hexagons. The...

Homework Statement A tourist takes a tour through a city in stages. Each stage consists of 3 segments of length 100 feet, separated by right turns of 60°. Between the last segment of one stage and the first segment of the next stage, the tourist makes a left turn of 60°. At what distance...

A(-x) = a0 - a1x + a2x2 - a3x3 + ... I see now. So when I add A(x)+A(-x), I get 2*E(x). Similarly, A(-x)-A(x) = -2*O(x). Thanks, your hint was a huge help!

Homework Statement Let A(x) = a0 + a1x + a2x2 + a3x3 + ... = Ʃanxn. Express E(x) = a0 + a2x2 + a4x4 + ... = Ʃa2nx2n. Do the same for O(x) = a1x + a3x3 + a5x5 + ... Homework Equations A(x) = a0 + a1x + a2x2 + a3x3 + ... = Ʃanxn The Attempt at a Solution So I tried using A(x2)...

So you're saying that n integers have been partitioned into (k+1) element groups, just to be clear? Would it be nCk+1, then? Or rather, since the sets are ordered, nPk+1? Is it assumed that the set {a1, a2, ..., ak, n} may not have all distinct elements?

Homework Statement Let k and n be positive integers. In how many ways are there integers a1≤ a2≤ ... ≤ ak≤ n. Homework Equations The Attempt at a Solution I don't really know where to begin. Simply using permutations doesn't seem to work. I know that for a1, there are n integers...

Homework Statement If a and theta are real numbers such that x + 1/x = 2cos(theta), then: x^n +1/x^n = 2cos(n*theta) Homework Equations x + 1/x = 2cos(theta) The Attempt at a Solution So I was able to show that the statement was true for n=1, but I'm stuck on how to even start...