by Anthony Salib | 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...
by Anthony Salib | Apr 22, 2018 | Physics
Energy of a System The energy of a system will be the total worked required to assemble it. For example, if you wanted to make a system of two protons separated by a distance of 5cm (assuming you bring them in from infinity) the energy of the system will be the amount...
by Anthony Salib | Apr 1, 2018 | Physics
So, if you ever want to undertake a physics major at Monash University, you will probably want to take theoretical physics. Most of the course deals with Maxwells Equations and then applying them to matter, so that’s where we begin, after which we will then move...
by Anthony Salib | Dec 12, 2017 | Uncategorized
In a direct proof we deal with If P then Q types of statements, more formally known as conditionals. An example of a conditional, is “If n is an odd integer, then n^2 is odd.” However, it might not be worded like this, it could have been, “The square...
by Anthony Salib | 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...
by Anthony Salib | 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...
by Anthony Salib | 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...
by Anthony Salib | 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...
by Anthony Salib | Aug 15, 2017 | Physics
In quantum mechanics, we cannot speak of the exact location of a particle, but rather, we talk about the probability of a particle being in a certain region of space. Mathematically, we describe this using a probability density function, known as the wave function,...
by Anthony Salib | Aug 3, 2017 | Pure Maths
Firstly, let’s consider what it means to have a sequence of functions by looking closely at All this is saying is that our sequence is going of to infinity. But this is just boring though, what we want to know is what happens when I go to infinity?...
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