Probability with martingales
by Williams, David · first published 1991
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On the probability front I recommend: - Probability and Random Processes by Grimmett - Probability with Martingales by David Williams Grimmett is probably a better bet to start with since it doesn't expect quite as much prior math knowledge and covers a lot more topics. The Williams book is shorter, denser and doesn't…
on “A Cheat Sheet on Probability” ↗…available. I don't maintain a collection of these, but I can probably recommend * Stephen Abbott, Understanding Analysis, for mathematical analysis and a little bit of real analysis * David Williams, Probability with Martingales, for advanced probability * Dym and McKean, Fourier Series and Integrals Alternatively if you have a more cursory interest, you can probably check out Metacademy [1] which provides roadmaps to learning…
on “Ask HN: Is there a website specialized in mathematics courses?” ↗David Williams’ Probability with Martingales is a personal favourite. And I’m not the only one.
on “Ask HN: Math books you recommend just for the way they are written?” ↗…style). It helps to read a few different books on the same topic simultaneously, anyway. - Two books on measure-theoretic probability theory that are more readable than many of the usual suspects are "Probability with Martingales" by Williams and "A User's Guide to Measure-Theoretic Probability" by Pollard. There is also a nice book called "Probability through Problems" that develops the theory through a series of exercises.
on “Ask HN: Learning advanced math” ↗…which is much better than his analysis book, but it's hefty. Good problems though. For a book on Probability, we read A Probability Path at my university. I wasn't fond of it. Someone referred me to Probability with Martingales, and though I didn't read it, it looked very good.
on “Ask HN: Learning advanced math” ↗