A good book for probability theory? Any recommendations?

[fleazo]

Hi all. I am searching for a good textbook on probability theory. I finished my B.S. in mathematics last fall and have covered real analysis and abstract algebra so I want a book that goes into actual mathematical theory and not just a basic book about probability like you would learn in discrete mathematics. But not one that is TOO advanced as my studies of theoretical mathematics have been limited to what I mentioned above and then 1 graduate course (functional analysis) which ended up more about application then theory anyway...

I am doing research in multiagent systems and I have come into the problem of needing to prove convergence in certain systems and right now I just can't grasp it... I always think, no but there's this 0.00000000001% chance (in reality so many more 0s than that lol) but then my prof will say, no you can't think like that because we are talking about the probability and all this... I trust him of course but I can't wrap my mind around it. I want to see some good theory and proofs. I never studied probability in all my college actually outside of discrete math but it was just so basic I need more!

So any recommendations would help! I really want to be able to contribute more in my research! I always would feel back in real analysis, the prof would say something and I would think "no way, how is it like that??" you know that crazy lingering doubt even though I would know he's obviously right but I just need to convince myself lol but then once I would see a proof you know i just felt satisfied and comfortable and I need that feeling for certain things in probability it makes me crazy when I can't just see a proof for something!

 

[bpet]

Hi all. I am searching for a good textbook on probability theory. I finished my B.S. in mathematics last fall and have covered real analysis and abstract algebra so I want a book that goes into actual mathematical theory and not just a basic book about probability like you would learn in discrete mathematics. But not one that is TOO advanced as my studies of theoretical mathematics have been limited to what I mentioned above and then 1 graduate course (functional analysis) which ended up more about application then theory anyway...

My personal favourite is the two volume set by Feller which nicely balances theory and application, and is concise yet rigorous and comprehensive. If that one seems too much like drinking from a firehose, another one you might like is by Grimmett & Stirzaker.

Other authors I haven't read but are frequently recommended, at various levels: Ross, Shiryaev, Billingsley, Chung.

HTH

 

[mtaboga]

You might want to have a look at a digital textbook on the fundamentals of probability theory at http://www.statlect.com/fndprb.htm (intermediate level). If you prefer a more mathematically sophisticated introduction have a look at the Probability tutorials by Noel Vaillant (http://www.probability.net).