Recent content by muzak

Homework Statement |z| = 2, \oint\frac{1}{z^3} Homework Equations Cauchy's Integral Formula http://en.wikipedia.org/wiki/Cauchy%27s_integral_formula The Attempt at a Solution Seems like a simple application of the general formula on the wiki page with n = 2, a = 0, and f(z) = 1...

Alright, thanks. Messed up the title of this thread but think I corrected it. Guess I can't fix the thread title, ah well. Criterion of Abel looks promising maybe: The criterion of Abel Let ∑+∞n=0an be a (real or complex) convergent series . Let (vn)n be a bounded sequence of real numbers...

Invented. Just curious if there exists any such condition to give convergence. I don't know anything about techniques to deal with divergent series, so I'd be satisfied with any specific reference material in lieu of some answer.

Convergence of Divergent Series Whose Sequence Has a Limit Homework Statement Suppose ∑a_{n} is a series with lim a_{n} = L ≠ 0. Obviously this diverges since L ≠ 0. Suppose we make the new series, ∑(a_{n} - L). My question is this: is there some sufficient condition we could put solely...

Hello, I will be applying to graduate school soon and have no real idea of where to apply. I was wondering if any of you know of any schools geared towards the pure end of mathematics, primarily real analysis and functional analysis and/or variations of the two, etc. I've looked into a few...

This is likely going to be a stupid question given that I am not in com sci, have very little com sci knowledge with regards to information storage/algorithms. I was wondering, if this question has any meaning, what are the costs of scanning for something vs carrying out some integer...

This might seem like a stupid question but would the null space of a matrix and its, say Gaussian elimination transforms, have the same null space. I guess, I am asking if this is valid: Let x be in N(A). Let A_{m} be some iteration of A through elimination matrices, i.e. A_{m} =...

Homework Statement Ax ≤ b, assuming A is nxn and solution exists Homework Equations The Attempt at a Solution I don't know of any concrete methods offhand. A grad student suggested rearranging it to: Ax - b ≤ 0, zero vector Then I don't know where to go from here. I was...

Homework Statement x_{n+1} = (x_{n} + 2)/(x_{n}+3), x_{0}= 3/4Homework Equations The Attempt at a Solution I've worked out a few of the numbers and got 3/4, 11/15, 41/56, 153/209, ... It seems to be monotone and bounded below indicating it does converge I think. I need help figuring out what...

Homework Statement I am given a set S consisting of the union of line segments from the point (0,1) to points (x,0) x-values are rationals from [0,1]. I want to show that this is path connected. Homework Equations Finding a continuous function f:[0,1] -> S such that f(0) = a and f(1) =...

On a related question, are there books on optimization that you guys could recommend, specifically something related to linear algebra and more on the problem solving side? I've taken the advanced linear algebra courses where we covered most of the topics in the Friedberg book. Perhaps...

Exactly what the title says. The prompt is this: Chose an actual example of scientific explanation, and use it to evaluate Hempel's and Ruben's accounts of explanation. I am not understanding the second part, how I am supposed to use an example to evaluate Hempel's and Ruben's accounts of...

Homework Statement Consider the polynomials: f(x) = x^{6} + x^{3} +1 and g(x) = x^{2} + x + 1 Denote the roots of f(x) = 0 by x_{1}, ... , x_{6}. Show that \sumg(x_{k}) = 6 , 1\leqk\leq6Homework Equations Vieta relations. The Attempt at a Solution Please correct any initial...

Any class that teaches differential geometry I think. Ask your advisor.

Homework Statement Let S = {(x,y): x^{2}+y^{2}<1}. Prove that \overline{S} is (that formula for the unit circle) \leq 1 and the boundary to be x^{2}+y^{2}=1. Homework Equations Boundary of S is denoted as the intersection of the closure of S and the closure of S complement. p \epsilon...