Michael Moody, former HMC Math Chair, DiesProf. Moody was one of those unusually influential and inspirational people. And he stood out as such among Harvey Mudd professors, who can generally be described that way ( Read more... )

For work and for fun, I've started thinking hard about statistics in non-Euclidean spaces. For example, how do you average angles or find the MLE of a point in SE(3)n given a collection of relative rigid-body transformations or a generalized median of several homographiesI've found some interesting papers, but no great references... do you have any ( Read more... )

Dear Lazyweb,
It appears that Maple cannot integrate a vector-valued function. For example:

> int([x, 2*x], x=0..1);
Error, (in int) wrong number (or type) of arguments
> [int(x,x=0..1), int(2*x,x=0..1)];
[1/2, 1]

This seems completely broken. Is there a workaround for this?
Update: Answer

Here's the solution:

> with( ( Read more... )

I've been looking into optimization algorithms recently. That is, given f(x), find x to minimize f(x) where x may be multidimensional (or even infinite-dimensional). It turns out that surprisingly many useful problems can be cast as an optimization problem. For example, solving the equation Ax=b (where A is a symmetric matrix) can be thought of as ( Read more... )

I recently got an answer to something that's been bugging me for quite a while.

When you first learned about vectors, the teacher probably drew an arrow and said this arrow, x, represents a displacement!, or something similar. Then the teacher probably said something like
Suppose we are at some point x [draws arrow from an origin to some point] ( Read more... )

From negatendo:

( Read more... )

On my way home I was walking down a flight of outdoor steps while on the phone with mew0422. I noticed a garter snake on a step in front of me. My attempts at SoaP jokes failed until mew0422 pointed out that it was actually a snake on a plane - a snake on R2.

In case it wasn't already clear, mew0422 is awesome.

Hmm... what about snakes on a real projective plane?

( Read more... )

Most of you know that dy/dx means limΔx→0 (y(x+Δx)−y(x))/Δx . Similarly most of you know ∂y/∂x means the same thing (at least in one variable). But what does dy mean on its own? We use it all the time in an integral, but is there some limit for which it can be substituted? What about ∂y?

Extra credit for differential geometry folks: Suppose V is a ( Read more... )

As posted by Jamin Philip Gray on planet.gnome.org:


( Read more... )

On a series of car trips this past week with mew0422, she taught me some stats. This, along with Wikipedia, has cleared up some important things that I hadn't understood before.

The first big concept is the difference between Bayesian probability and Frequentist probability. As I understand it, Bayesian statistics applies probabilities to any statement, ( Read more... )