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I work as a professional composer, and I also program most of my own software. I failed every year of math in high school.

I am studying Bayesian Probabilities in reference to music, and while I understand most of what is being said I can't help but feel progress would be greatly enhanced by a stronger foundation in the basics.

Similarly I have also been studying deep learning, restricted boltzmann machines and such.

What books are well regarded for concisely covering the foundations that lead to these disciplines?

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I think a beautiful source is Gian-Carlo Rota's and Kenneth Baclawski's Introduction to Probability and Random Processes. (Made available online by David Ellerman with the permission of Professor Baclawski.) Rota was a brilliant combinatorialist and his writing combines a friendly, clear style with a deep, well-developed organization.

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Thank you, that looks extremely helpful (the grubby look is also particularly appealing). What I am searching for though is a more remedial book to bring me up to speed on the basic tools. Sum and product over a set being an examples that I had to figure out recently, simple but I just had no exposure to them -- I don't know what I don't know. I imagine, for this crowd, such a book is superfluous as these skills have been honed over the years -- I'm looking for a jump start of sorts. –  Casey James Basichis Jun 21 '12 at 19:27
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