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

Programming as an essential skill

In discussions about jobs and the future. We sometimes make references to skills. In educational communities people speak of ‘transferable skills’ and ‘critical thinking’. Recently its become fashionable to discuss STEM. On this blog I’ve written some things about this. The following articles re-inspired my interest On Reviews in Depth: Why everyone should learn to… Continue reading Programming as an essential skill

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

Learning as Debugging

Recently in Luxembourg there was a talk on ‘Mathematics Education’. As always being interested in STEM and the cultivation of learning and thinking, I found this fascinating. I came across on Robert Talbert’s excellent blog, the following: Yes! As somebody once said, true learning consists in the debugging process. And that’s where the fun in… Continue reading Learning as Debugging

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

Procepts in Mathematics education

Todays blog post is a bit different to some of my views on politics, or current affairs. Its back closer to my student life as a Mathematics Masters student. Inevitably when one enjoy mathematics and physics one gets involved in giving tutorial classes or helping friends and family. Mathematics is something that we all agree… Continue reading Procepts in Mathematics education