Ever found yourself doing the same proof over and over again?
You know the drill: you are studying something, and to really understand it, you sit down and work through a few exercises or proofs. Then, weeks or months later, you need that exact result again โ and of course, you have completely forgotten how you did it! So you redo all the steps from scratch. Again. For the hundredth timeโฆ
Happens to me all the time! I have probably rederived the Chernoff bound more times than Iโd like to admit โ starting from Markovโs inequality and going through all the usual steps, until that exponential tail finally shows up.
Every time I need it, I end up repeating the same reasoning from scratch.
So I have decided to use this page to write down those little proofs and exercises I work out while studying (the ones that are a pain to redo but super useful to have on hand).