Analysis Tricks Part 1

I recently learnt a really neat trick when it comes to proving two quantities are equivalent. It started of with my supervisor claiming that for some and , (1)   is obvious. To me, it was not obvious at all, and may not be so obvious to you either. But what my...

Putnam 2017 A2

EDIT: So I started the blogging marathon, “One a day”, in the original post a bit too soon. I’ll keep you posted on when it will actually begin. I am currently in China doing a lot of nice work on the wave equation, can’t wait to tell you all...

The Cauchy Problem in General Relativity

So last week, I presented a talk on the Cauchy Problem in General relativity, at the science student research showcase run by my university. Today I wanted to do a brief overview of the problem and the developments made in it since Einstein published his theory of...

The beautiful language of tensors

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

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...

Casba Wars: The Csaba Strikes back

A not so long time ago in a classroom not too far away, we arrived eagerly for our 9am, (in fact me and my friend Ivan, check him out at ivanbegic.wordpress.com, got there at 6am, back to the story), we arrived eagerly for our next encounter with the one and only...

Csaba Wars: A new hope

So, if you ever want to undertake a physics major at Monash University, you will probably want to learn some theoretical physics. Although, the title will lure you, you will enviably have to face the one and only Csaba Balazs, figure 1 below. Now, the man is a bit of...

Logic and direct proofs

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...

A voyage through space(s) (Part IV)

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...
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