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(Categorizing under Category:Theoretical foundations)
(General: G.J. Chaitin: ``The Unknowable''. Copying link from Combinatory logic#Self-replication, quines, reflective programming)
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Paul Taylor: Practical Foundations of Mathematics. Free online book on mathematics, huge areas of mathematics are described thoroughly, many of them closely related to computer science and functional programming (relational algebra, category theory, Curry-Howard isomorphism).
 
Paul Taylor: Practical Foundations of Mathematics. Free online book on mathematics, huge areas of mathematics are described thoroughly, many of them closely related to computer science and functional programming (relational algebra, category theory, Curry-Howard isomorphism).
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[http://www.cs.auckland.ac.nz/CDMTCS/chaitin/ G.J. Chaitin] especially his [http://www.cs.auckland.ac.nz/CDMTCS/chaitin/italy.html Understandable Papers on Incompleteness], especially [http://www.cs.auckland.ac.nz/CDMTCS/chaitin/unknowable/index.html The Unknowable] (the book ''is'' available on this page, just roll the page bellow that big colored photos).
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The book begins with the limits of mathematics: Gödel's undecidable, Turing's uncompatiblity, Chaitin's randomness); ''but'' (or exactly ''that's why''?) it ends with writing on the future and beuty of science.
   
 
== Topics ==
 
== Topics ==

Revision as of 10:44, 7 June 2006

Contents


1 General

Paul Taylor: Practical Foundations of Mathematics. Free online book on mathematics, huge areas of mathematics are described thoroughly, many of them closely related to computer science and functional programming (relational algebra, category theory, Curry-Howard isomorphism).

G.J. Chaitin especially his Understandable Papers on Incompleteness, especially The Unknowable (the book is available on this page, just roll the page bellow that big colored photos). The book begins with the limits of mathematics: Gödel's undecidable, Turing's uncompatiblity, Chaitin's randomness); but (or exactly that's why?) it ends with writing on the future and beuty of science.

2 Topics