On the Mathematics of the Berry Phase

I tried to upload this to my wordpress however it wasn’t working. So here is a link to a pdf file of some notes and observations I wrote over the course of a few years on the Geometric Phase. Mathematics of the Geometric Phase by no means is this original, and there are many excellent… Continue reading On the Mathematics of the Berry Phase

STEM Education Interview: Robert Talbert

I’m excited to put up my first ever interview. I’m working on a project for an organisation and this is an interview as part of my research. Robert Talbert is a Mathematics professor at Grand Valley State University, who researches Cryptography but has also spent a lot of time recently experimenting in the field of… Continue reading STEM Education Interview: Robert Talbert

An Introduction to Coalgebras

I’ve just dumped this here, I wrote it for a project in Luxembourg a few months ago. Its not well edited, and there are errors. I may fix these in the future. However it may be of benefit to someone. Introduction to various classical notions of algebras. Coalgebras are defined and introduced, as are various… Continue reading An Introduction to Coalgebras

Geometric Phases

I wrote this article as part of extending my undergraduate thesis. Its certainly not original but should be of benefit to someone. 1. Introduction A considerable understanding of the formal description of quantum mechanics has been achieved after Berrys discovery{BerryPhase} of a geometric feature related to the motion of a quantum system. He showed that… Continue reading Geometric Phases

Commutative Algebra

These notes are based on a lecture on Commutative Algebra at the University of Luxembourg. A variety of sources including Eisenbud, the Princeton Companion to Mathematics and a Classic ‘Algebra’ text by MacLane and Birkhoff have been used to compile these notes. Hopefully it will be of benefit to those studying this course. 1. Lecture… Continue reading Commutative Algebra

Twitter co-founder on Computational Thinking

I’ve long been a fan of Jack Dorsey, and I came across this excellent article about an interview on Charlie Rose. Gary Stager a school reformer and Educational reformer speaks very well about Jack Dorsey. When we speak of using Computing in education, we often forget that in the words of Mitch Reznick ‘the computer… Continue reading Twitter co-founder on Computational Thinking

Training students for the 21st Century

Education is a hugely politically loaded issue. I want to write today briefly about education. I’ve two years of experience as a tutor and Teaching Assistant in a Northern Ireland Grammar School, and continue to tutor a range of ages while I undergo my Masters studies in Mathematics. I definitely will focus on STEM subjects,… Continue reading Training students for the 21st Century

Control theory in Financial Markets

I unfortunately know very little about Control Theory however what I do understand about it, is that in some sense it deals with feedback in complex systems. Since the financial markets are complex systems, and very difficult for human beings to regulate. Not to mention the huge explosion of Algorithmic Trading. Certainly it doesn’t seem… Continue reading Control theory in Financial Markets

He who refuses to do arithmetic is doomed to talk nonsense

The above slogan came to my attention once again from the excellent Cosma Shalizi comments on Krugmans book ‘Pop Internationalism’. In the book review The great Computer Scientist has a slogan which Shalizi extends from merely arithmetic to algebra. This short essay will be looking at this issue. It is often said by politicians for… Continue reading He who refuses to do arithmetic is doomed to talk nonsense