This page, which will be updated occasionally, summarises important results and useful formulae for the Part IB Quantum Mechanics course.

Vector spaces, inner products and duality

Let $V$ be an inner product space over $\mathbb{C}$.

We use ket notation for vectors: $|\psi\rangle \in V$

The inner product between …

This is the second article about how working with temporal information in computer systems. The first article was about contained some definitions about astronomical time and timezones.

This article describes options for storing temporal values in your programs, and their limitations. In particular, it describes two pitfalls that can happen …

Here are some notes for my Fluid Dynamics II students about vectors, pseudovectors and how they transform under reflections.

Let n be a unit vector and consider the reflection R in the plane perpendicular to n.

Quantities such as the position r and velocity v are regular vectors and transform …

Many cultural and religious traditions place a lot of importance in names, and hold that names have power. There is something magical about them.

In Classical Greek tradition, Hades was feared and his name was not spoken. The Bible supposes that the name of God is to be used for …

One reason why Python is such a popular and powerful language is that it is straightforward to learn and make good progress. Learners can quickly become comfortable with many aspects of the language, such as control flow and functions.

The first obstacle that many learners come across is when they …

This is a collection of notes about time and related concepts. A future post will talk about the problems of representing time in computer systems, especially distributed systems. These notes will be occasionally updated.

Introduction

Time is taken to be a primitive concept that cannot be defined in terms of …

I was a volunteer and organiser for codebar for several years and was heavily involved in outreach activities during my time at Cambridge. In the face of cuts to DEI initiatives, I believe that the lack of diversity at all levels of the tech sector seriously harms the sector.

Besides …

I have been reading – at a very shallow level – about category theory (wiki), and thinking about its applicability to software and system design for data engineering. This post is a loose collection of thoughts on the subject, and a manifesto for employing a more rigorous language when building such systems …

Emergency services, GPs, hospitals, transportation systems and the like are funded, at least in part, by public money. When their computer systems go down, the public is badly affected and people can get hurt, and lives can be put at risk. So what regulations and quality controls are there on …

Having reliable, detailed but searchable logs is an essential part of any application, especially of long-running services that need to be debugged and monitored for uptime and stability. As one of the oldest modules in the Python standard library, the logging module provides a very powerful set of tools for …