Mathematics eBooks Page 9

God not only plays dice in quantum mechanics, but even with the whole numbers! The discovery of randomness in arithmetic is presented in my book Algorithmic Information Theory published by Cambridge University Press. There I show that to decide if an algebraic equation in integers has finitely or infinitely many solutions is in some cases absolutely intractable. I exhibit an infinite series of such arithmetical assertions that are random arithmetical facts, and for which it is essentially the case that the only way to prove them is to assume them as axioms. This extreme form of Gdel incompleteness theorem shows that some arithmetical truths are totally...

This book offers a well-balanced presentation on designing algorithms, complexity analysis of algorithms, and computational complexity that is accessible to mainstream computer science students who have a background in college algebra and discrete structures....

Formal languages, automata, computability, and related matters form the major part of the theory of computation. This textbook is designed for an introductory course for computer science and computer engineering majors who have knowledge of some higher-level programming language....

With a dynamic learn-by-doing focus, this laboratory manual encourages students to explore data structures by implementing them, a process through which students discover how data structures work and how they can be applied....