Prerequisites for

Exploring Randomness
Chaitin, Gregory J. 2001. 164 pages.
Categories: Mathematics
Algorithmic Information Theory (AIT) is what you get when you mix Turing's computation theory with Shannon's information theory. AIT demonstrates that randomness arises naturally in pure mathematics, and can be equated with incompressibility. You'll recall that long ago, Russell and Whitehead attempted to develop all of mathematics from a few clearly stated axioms and rules of inference in pure logic. But AIT claims that "The classical logical effort to concentrate axioms into a minimal irredundant set was an attempt to achieve incompressibility and therefore randomness".
Instead of using self referential mathematics (like Gödel), the author uses LISP. One of the interesting results of AIT is that you can prove that you can never determine the lower bound of a computer program size complexity.
Annoying parts of the book include the author's insistence that he should be credited with formulating what is known to everyone else as Kolmogrov complexity. Additionally, the author would like AIT to impress beyond it's abilities with statements like "AIT will lead to the major breakthrough of 21st century mathematics, which will be information-theoretic and complexity based characterizations and analyses of what is life, what is mind, what is intelligence, what is consciousness, of why life has to appear spontaneously and then to evolve."

Recommended prerequisite books:
Either of these books:   
       
(Read review)
       
(Read review)
Suggested mathematical background in:

-  Computational Complexity
-  Probability and Statistics
Suggested computer language experience:

-  LISP