Recent content by lol_nl

I am doing Part III of the Mathematical Tripos in Cambridge and am focussing mostly on theoretical physics. The trouble is that I have no idea what to do next and so far do not have any PhD offers. Before this I completed a bachelor's degree in mathematics and physics elsewhere in Europe. In...

Hi, First of all, congratulations with being accepted to two great programmes! I am not necessarily more knowledgeable than you about the programmes or the cities, but since I was applying for masters abroad last year I know a little how it is to be in such a position. Here are some things...

In a nutshell, I am trying to see how to derive the conditions of coexistence between a solid and a liquid from a phase diagram. The situation is as follows: Consider a mixture of hard spheres of diameter σ. The potential energy for a hard sphere system is given by \beta U(r) = 0 (r > \sigma)...

In 2 dimensions the answer seems to be 2: with the length of all three sides determined, any two such triangles must be congruent, and also share the side ab. In three dimensions, there is an entire circle. However, letting |x-a| vary over all positive values, one gets a curve in two...

It's a circle. My intuition tells that the set that satisfies the first equation is a hyperbola: the difference of two distances is a constant (namely 0). Only the factor two seems misleading...

Homework Statement Suppose a \in R^{k},b \in R^{k}. Find c \in R^{k} and r > 0 such that |x-a| = 2|x-b| if and only if |x-c| = r. Homework Equations Solution: 3c = 4b - a, 3r = 2|b-a| The Attempt at a Solution Technically, I can't seem to find any way to express |x-c| in terms of |x-a|...

Working through A Book of Abstract Algebra, I encountered several exercises on roots of polynomials in Z_{n} I was just wondering whether there exists something like a quadratic equation for polynomials of degree 2. If the solutions of the usual quadratic formula happen to be integers, can one...

I am an undergraduate and used my iPad for study quite extensively in the past year. I have mixed feelings about it, but on the whole it is not at all a bad idea. So what books could you store on an iPad? I didn't use my iPad for all my courses, but just a few. If a course has digital course...

Recently, I bought a number of cheap Dover textbooks on (mathematical) topics I am going to study coming semester, including Abstract Algebra, Differential Geometry and Functional Analysis. I found some of the books remarkably clear and well-written, but as I was reading through them and looked...

I want to start a graduate program on theoretical physics after I finish. Which courses would be most important? I heard differential geometry (and geometry in general) is used quite extensively in theoretical physics.

I am an undergraduate student in mathematics and physics starting on my third and final year in the Netherlands. The system here appears to be quite different from the US system from what I read on other pages. Basically, my impression is that we have to (or choose to) do more courses in a...

Reading through my electrodynamics textbook, I frequently get confused with the use of the del (nabla) operator. There is a whole list of vector identities with the del operator, but in some specific cases I cannot figure out what how the operation is exactly defined. Most of the problems...

You can compare the two series since they are polynomials in x, and what you are interested in is only one of the terms of the polynomial. f^(2000) occurs exactly in the term of x^(2005), so you can ignore all other terms and compare the coefficients of x^2005 on both sides.

Let me write it out more explicitly: |f(x) + K| < K means -K < f(x) + K < K. (compare with the first reply). Now substract K from all three terms to get: -2K < f(x) < 0 . Hence the 2 is simply the result of the calculation.

This should be a^x = (e^{ln(a)})^{x} = e^{(ln(a)) x}. Now taking the derivate with respect to x should bring you directly to your answer (remember that ln(a) is a constant).