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Dr_Manhattan comments on The Best Textbooks on Every Subject - Less Wrong

167 Post author: lukeprog 16 January 2011 08:30AM

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Comment author: [deleted] 27 January 2011 07:30:47PM *  6 points [-]

Feller comes in two volumes, and goes from extremely introductory to measure theory in the second volume. It's a classic and Feller is famous for his writing style, and so this is probably the best book. I remember finding it confusing once upon a time, but that was probably because I was too young and not because of the book.

Ross is elementary, and isn't a measure-theoretic approach, and has lots of applications (e.g. to queuing theory and operations). It's handy as a "gimme the facts" kind of book -- if you want to look up common distributions and formulae you'll find them in Ross faster than anywhere else -- but it doesn't have all the mathematical foundations you might want.

Koralov and Sinai is a measure-theory based probability course. The second half of the book has stochastic processes, martingales, etc. If you don't know any probability at all (let's say... haven't seen the Bernoulli distribution derived) or if you haven't seen measure theory, it's probably not intuitive enough to be your first textbook. I had no complaints with the presentation; it was all straightforward enough.

Basically, I'd split the difference between elementary and advanced by using Feller; he includes EVERYTHING so you can safely skip what you know and read what you don't.

Comment author: Dr_Manhattan 27 January 2011 09:21:42PM 1 point [-]

Feller is very good, though I haven't even finished vol1. I also like Tijms for real beginners - easy and fun, good examples. http://www.amazon.com/Understanding-Probability-Chance-Rules-Everyday/dp/0521701724/ref=sr_1_1?ie=UTF8&qid=1296163232&sr=8-1