A Year in Hiatus!

This year has been rather crazy for me and so haven’t had much time to blog. The reason being that I completed my honours year in Australia in 6 months instead of the full year (they thought it was impossible, but I did it!) which required a lot of time and...

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

I am currently in China doing a lot of nice work on the wave equation, can’t wait to tell you all about it! But here is a nice problem I did for fun. Today we will look at a Putnam Problem, here is the question, (screenshot from the problem sheet that can be...

On the definition of a Topological Manifold

EDIT 7/1/2019: The proof for each finite subset of a Hausdorff space is closed is corrected. Before I begin, as stated in my articles section, I said I am going to start writing about all the neat maths I’ve learnt throughout my final year project in physics, in...

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...
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