Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

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

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

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (327)

Sort By: Popular

You are viewing a single comment's thread.

Comment author: lukeprog 19 January 2011 08:26:31PM *  1 point [-]

I would like to request a book recommendation on probability theory.

Following the rules if possible.

Comment author: Vlad 29 April 2011 12:18:52PM 1 point [-]

The best introductory book I've read is Chance in Biology: Using Probability to Explore Nature by Mark Denny and Steven Gaines. While most introductory books have mainly examples from games of chance, this book uses examples from physics, chemistry and biology. It's very accessible and it takes you very fast from the basic rules of probability theory to useful examples.

I would also recommend Jaynes' lectures. They're more informal than the book (and also free :D). These I think are the best for quickly understanding the "subjectivist" approach to probability theory.

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

Comment author: lukeprog 27 January 2011 10:05:52PM 0 points [-]

Awesome, thanks!

Comment author: Matt_Simpson 21 January 2011 02:29:07PM *  1 point [-]

I was just about to ask the same question, specifically for a measure theoretic treatment of probability theory. I've only read/still am reading Measure Theory and Probability Theory by Athreya and Lahiri for the second of a two course sequence and am not too impressed. For one, there are many typos that decrease the readability unless you're already familiar with measure theory and functional analysis (I was not). I haven't read any other texts of this nature, so I can't make any comparisons.