The beautiful language of tensors

by | Aug 22, 2018 | Physics, Pure Maths

You’ve probably heard the word ‘tensor’ before, but if you’re like me, you’ve gone through your entire physics degree without knowing what they are. So today, I’m going to express the relativistic wave equation in the language of...

Real Projective Space and Quotient Spaces

by | May 28, 2018 | Pure Maths

So these spaces are really interesting, but super duper hard to get your head around. So in this blog, I hope to make there equivalent definitions a little bit easier to understand. I’m going to present 3 equivalent definitions of the n-dimensional real projective...

A voyage through space(s) (Part IV)

by | Nov 28, 2017 | Pure Maths

We have alas reached the final leg of our journey, we will continue with the idea of a normed vector space and then we will describe Banach spaces and Hilbert spaces. Associated with the norm on our vector space , is the metric     So is endowed with a...

A voyage through space(s) (Part III)

by | Oct 2, 2017 | Pure Maths

As promised, we begin our quest today in understanding what a normed vector space is. We will begin with a vector space , and we would like to give it some structure similar to our metric spaces. Now we could of course give any metric to , but we already have two...

A voyage through space(s) (Part II)

by | Sep 30, 2017 | Pure Maths

We left the last post on a cliff hanger, namely that in any given metric space, Cauchy sequences need not converge. Now if you’re reading this, you have chosen to take the red pill, and I’m here to show you just how the deep the rabbit hole goes. We shall...

A voyage through space(s) (Part I)

by | Sep 27, 2017 | Pure Maths

So in the last post I talked about wave functions being vectors that live in Hilbert space. In this post, I would like to describe the mathematics of Hilbert space, but before we do that we have to go on a journey, a journey through space(s)! The first type of space...