Welcome to Scholar. This is an experiment in putting lecture notes online. It's a work in progress and material is being added and improved all the time.
News: posts on Scholar
Threads weave a path through the collection of articles. They correspond to a course or part of a course.
Exploration of the role of probability in various areas of physics
A course on quantum theory, concentrating on the structure of quantum mechanics as a basis of physical theory rather than the quantum physics of particular systems. We take a Hilbert space approach.
Exploration of the role of symmetry in physics. Covering topics from the principle of stationary action, Lagrangians, Hamiltonians and Noether's theorem.
The physics and mathematics of rotating systems.
The classical theory for oscillations and waves at a second year university level.
Communication through memory-less static channels will be examined, and in particular using repetition codes to counteract the errors introduced by the channel.
The relative entropy, or Kullback-Leibler divergence is a measure of the difference of two distributions
The joint entropy and its properties
Quick introduction to convex sets, convex functions and Jensen's inequality
We examine the problem of optimally encoding a set of symbols in some alphabet to reduce the average length of the code.
A definition of information is introduced which leads to yet another connection with entropy.
A factorisation of the joint probability distribution can be represented in a graph known as a Bayesian Network. These networks codify independencies between variables and information flow as variables are measured.
When we have several variables, the joint probability distribution over all the variables has all the information we need to calculate any simpler probability distribution. The joint probability distribution can be expressed efficiently if there are independence relationships between variables.