by Anthony Salib | Aug 23, 2020 | Uncategorized

So last week we talked about the Baire Category Theorem, and this important tool will give us three equivalent theorems about the qualitative properties of operators on Banach spaces. Today we will begin with the first theorem, uniform boundedness. The proof of this...
by Anthony Salib | Aug 23, 2020 | Problem Solving, Pure Maths

This one is simple! Why is called...
by Anthony Salib | Aug 16, 2020 | Problem Solving

So this problem is in line with the post of this week, Baire’s Lemma. Have a go and let me know your thoughts in the comments! Let be unbounded and open. Then let the set Prove that is dense in...
by Anthony Salib | Aug 13, 2020 | Uncategorized

So today I am starting a new series on the Principles of Functional Analysis to give you all an appreciation for the power that these simple truths hold. We will start today with Baire’s Lemma , which will require some definitions, hopefully, all familiar. (If...
by Anthony Salib | Nov 12, 2019 | Uncategorized

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...
by Anthony Salib | Dec 28, 2018 | Problem Solving, Pure Maths

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...
by Anthony Salib | Dec 16, 2018 | Problem Solving

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...
by Anthony Salib | Dec 6, 2018 | Pure Maths

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...
by Anthony Salib | Oct 12, 2018 | Physics

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...
by Anthony Salib | 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...
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