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I'm undergraduate student in probability theory (and its applications). There are lots of different and definitely good text on standard, functional analysis-based approach, but I'm interested in alternative approaches - maybe, some more algebraic variants. Could you name some ideas/papers/texts about this? I'm especially interested in the ones those can be used in applied problems (such as financial mathematics or something). I've surely saw some approaches in Wikipedia, but I have absolutely no idea of using them in practical problems.

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Perhaps you could give an example of the kinds of text you are not after - e.g. "this is a good book, but I want something which approaches this part differently" –  Yemon Choi May 21 '11 at 8:07
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If you just want to get some probabilistic intuition, then something like Grimmett and Stirzaker might be worth a look. –  Yemon Choi May 21 '11 at 8:08
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It's possible to base a theory of probability on Von Neumann algebras. This construction is known as free probability, and has applications to quantum mechanics. See Terry Tao's book on random matrices. There's a free preprint on his website. –  Simon Lyons May 21 '11 at 11:45
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@Simon: as someone who's dabbled in both, I am not sure that starting with free probability is a good way to learn about classical probability. –  Yemon Choi May 21 '11 at 18:45
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@Yemon: thank you for all books offered; I just wanna note that I'm not starting learning probability (I hope that I already know something about classical one). I'll take a look at all of them. –  Jury Razumau May 23 '11 at 4:33
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Yuri, you may have a look at the introductory probability book by Henk Tijms, Understanding Probability. An excellent book having the nice feature that simulation is used throughout to develop probabilistic intuition.

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