Omega and why maths has no TOEs December 2005 Over the millennia, many mathematicians have hoped that mathematics would one day produce a Theory of Everything (TOE); a finite set of axioms and rules from which every mathematical truth could be derived. But in 1931 this hope received a serious blow: Kurt Gödel published his famous Incompleteness Theorem, which states that in every mathematical theory, no matter how extensive, there will always be statements which can't be proven to be true or false. Gregory Chaitin has been fascinated by this theorem ever since he was a child, and now, in time for the centenary of Gödel's birth in 2006, he has published his own book, called Meta Math! Kurt Gödel Splattered ink My story begins with Leibniz in 1686, the year before Newton published his Principia. In sections V and VI of the Discours de métaphysique, Leibniz discusses the crucial question of how we can distinguish a world which can be explained by science from one that cannot. What is complexity? Gottfried von Leibniz
Introduction to Automata Theory, Languages, and Computation Free Course in Automata Theory I have prepared a course in automata theory (finite automata, context-free grammars, decidability, and intractability), and it begins April 23, 2012. You can learn more about the course at www.coursera.org/course/automata. Several other courses will start at the same time, including Alex Aiken on Compilers, Mike Genesereth's Logic course, Nick Parlante on computing for everyman/woman, and a repeat of ANdrew Ng's Machine-Learning class. You can learn about each of these courses at www.coursera.org/ Gradiance News The Gradiance contract with Pearson (Addison-Wesley + Prentice-Hall) has terminated, and we have decided to turn Gradiance into a FREE service. Then, email your chosen login, with the book whose materials you want, to support@gradiance.com We'll enable you to create a class using those materials. Index Table of Contents The Table of Contents for the new book. Solutions to Starred Exercises Here are the Solutions to starred exercises. Errata