Good books on random numbers & info theory?
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Giuseppe Verde
2004-10-18 02:07:13 UTC
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Hello all!

I'm interested in random numbers (including and especially creating
random numbers in a specific statistical distribution) and information
theory (e.g. Shannon Entropy). What books and articles would you
recommend reading to begin to get up to speed on these topics? [I like
math and have a modicum of experience with some higher maths, so it need
not be for the layperson. In fact, a rigorous theoretical/mathematical
treatment is what I'm hoping to get in the end.]

Thank you very much for your assistance.

Joseph (aka Giuseppe Verde)
Mohamed Alimi
2004-10-22 04:59:20 UTC
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Joseph, I recommend you to check the following books:
(*) For 'Shannon' information theory: "Elements of Information Theory" by
Thomas Cover et al. http://www-isl.stanford.edu/~jat/eit2/index.shtml.
(*) For 'algorithmic' information theory aka 'Kolmogorov' information
theory: "An Introduction to Kolmogorov Complexity and Its Applications" by
Paul Vitanyi et al. http://homepages.cwi.nl/~paulv/kolmogorov.html. This
would require notions of computability theory.
(*) For (pseudo-)randomness in computational complexity and its use in
cryptography: "The Foundations of Cryptography" by Oded Goldreich
http://www.wisdom.weizmann.ac.il/~oded/foc.html. This would require notions
in computability theory and computational complexity theory.
(*) Great definitions of random binary sequences are defined using
Kolmogorov complexity and computable analysis. "Introduction to Computable
Analysis" by Klaus Weihrauch, and "Information and Randomness: an
Algorithmic Perspective" by Cristian Calude are also good books for this.

Good luck,