## Group Theory (lecture 2) by Robert de Mello Koch

As promised in the previous post, here is the second lecture by Prof Robert de Mello Koch on Group Theory. Please comment if you have thoughts or questions from this video.

## Group Theory (lecture 1) by Robert de Mello Koch

Some ten (and change) years ago, the African Summer Theory Institute (ASTI) took place in Cape Town at UCT. This was a course designed for students to give them a taste of a number of topics related to theoretical physics. These lectures were all recorded, and I watched them at [...]

## “Integration sounds like interrogation and that scares me”

I recently received a message from a friend and the heading of the post perfectly describes what was said to me. Thereafter, an interesting integration question was sent to me. It read as follows: I must admit, it does look quiet scary. My immediate thought was that some [...]

## The least preferred, but maybe the most understandable way of approximating π

Why $latex \pi$? I assume this is the question on everyone's mind. (Whether you're a Math lover or not) The simple answer would be that we all love pie, now don't we? Before I begin discussing any technicalities, I'd like to acknowledge that it is possible for some of us [...]

## Maxwell’s Equations

Essentially, the entire theory of electromagnetism can be found in the following four equations: \begin{aligned}\mathbf{\nabla \cdot E} &= \frac{\rho}{\epsilon_{0}} \\ \mathbf{\nabla \times E} &= - \frac{\partial{\mathbf{B}}}{\partial{t}}\\ \mathbf{\nabla \cdot B} &= 0\phantom{\frac{1}{2}}\\ \mathbf{\nabla \times B} &= \mu_{0} \mathbf{j}+\mu_{0} \epsilon_{0} \frac{\partial{\mathbf{E}}}{\partial{t}} \end{aligned} These are Maxwell's Equations in differential form, not in [...]

## Faith, Fashion and Fantasy in the New Physics of the Universe, by Roger Penrose – a review

Cover page taken from http://press.princeton.edu/titles/10664.html Roger Penrose is unquestionably a giant of 20th century theoretical physics. He has been enormously influential in diverse areas of both mathematics and physics, from the nature of spacetime to twistor theory, to geometrical structures and beyond. His famous, but perhaps less [...]

## A Linear algebra problem

I have this linear algebra problem in the context of quantum mechanics. Let $latex \mathbf{f}_\lambda$ be a family of linear operators so to each $latex \lambda \in \mathbf{R}$ we have a linear operator $latex \mathbf{f}_\lambda : \mathcal{H} \to \mathcal{H}$ where $latex \mathcal{H}$ is a complex vector space if one is [...]

## Dependent Types

This blog post will carry on from the previous one, and introduce dependent types. So what is a dependent type? To motivate the idea let's talk about equality. Remember that we interpret propositions as types, so if we have $latex x, y : A$ then the statement "$latex x$ is [...]

## Checking direction fields

I was recently asked about how to spot which direction field corresponds to which differential equation. I hope that by working through a few examples here we will get a reasonable intuition as to how to do this. Remember that a direction field is a method for getting the general [...]