Problem of the Week 1

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...

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...