Exploring RANDOMNESS


Book Description

This essential companion to Chaitin's successful books The Unknowable and The Limits of Mathematics, presents the technical core of his theory of program-size complexity. The two previous volumes are more concerned with applications to meta-mathematics. LISP is used to present the key algorithms and to enable computer users to interact with the authors proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter. "No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. This book tells you everything hes seen. Don miss it." John Casti, Santa Fe Institute, Author of Goedel: A Life of Logic.'




People & Ideas in Theoretical Computer Science


Book Description

Theory and theoreticians have played a major role in computer science. Many insights into the nature of efficient computations were gained and theory was crucial for some of the most celebrated engineering triumphs of computer science (e.g., in compiler design, databases, multitask operating systems, to name just a few). Theoretical computer science (TCS) functions as a communication bridge between computer science and other subjects, notably, mathematics, linguistics, biology; it is a champion in developing unconventional models of computation (DNA, quantum). This book collects personal accounts and reflections of fourteen eminent scientists who have dedicated themselves to the craft of TCS. Contributions focus on authors specific interests, experiences, and reminiscences. The emerging picture, which is just one among other possible ones, should be a catalyst for further developments and continuations. Was most interested to learn about the project, which should be a worthwhile one." N. Chomsky, MIT. "The human story of creativity is inspiring and documents a very noble activity - the creation of knowledge in its most beautiful and useful form - the creation of a science. Supplying the technical and intellectual tools to probe some of the most fascinating questions about the nature of thought and intelligence, theoretical computer science is trying to grasp the limits of rational thought, the limits of knowable. This book will contribute to the understanding of the creation of a magnificent science." J. Hartmanis, NSF. "This is obviously an extremely worthwhile project." D. E. Knuth, Stanford University.




Relations and Graphs


Book Description

Relational methods can be found at various places in computer science, notably in data base theory, relational semantics of concurrency, relationaltype theory, analysis of rewriting systems, and modern programming language design. In addition, they appear in algorithms analysis and in the bulk of discrete mathematics taught to computer scientists. This book is devoted to the background of these methods. It explains how to use relational and graph-theoretic methods systematically in computer science. A powerful formal framework of relational algebra is developed with respect to applications to a diverse range of problem areas. Results are first motivated by practical examples, often visualized by both Boolean 0-1-matrices and graphs, and then derived algebraically.




Physics and Theoretical Computer Science


Book Description

Aims to reinforce the interface between physical sciences, theoretical computer science, and discrete mathematics. This book assembles theoretical physicists and specialists of theoretical informatics and discrete mathematics in order to learn about developments in cryptography, algorithmics, and more.




Connecting Discrete Mathematics and Computer Science


Book Description

Computer science majors taking a non-programming-based course like discrete mathematics might ask 'Why do I need to learn this?' Written with these students in mind, this text introduces the mathematical foundations of computer science by providing a comprehensive treatment of standard technical topics while simultaneously illustrating some of the broad-ranging applications of that material throughout the field. Chapters on core topics from discrete structures – like logic, proofs, number theory, counting, probability, graphs – are augmented with around 60 'computer science connections' pages introducing their applications: for example, game trees (logic), triangulation of scenes in computer graphics (induction), the Enigma machine (counting), algorithmic bias (relations), differential privacy (probability), and paired kidney transplants (graphs). Pedagogical features include 'Why You Might Care' sections, quick-reference chapter guides and key terms and results summaries, problem-solving and writing tips, 'Taking it Further' asides with more technical details, and around 1700 exercises, 435 worked examples, and 480 figures.




Discrete Mathematics in the Schools


Book Description

A collection of articles written by experienced primary, secondary, and collegiate educators. It explains why discrete mathematics should be taught in K-12 classrooms and offers guidance on how to do so. It offers school and district curriculum leaders material that addresses how discrete mathematics can be introduced into their curricula.




Quantum Logic


Book Description

Quantum Logic deals with the foundations of quantum mechanics and, related to it, the behaviour of finite, discrete deterministic systems. The quantum logical approach is particulalry suitable for the investigation and exclusion of certain hidden parameter models of quantum mechanics. Conversely, it can be used to embed quantum universes into classical ones. It is also highly relevant for the characterization of finite automation. This book has been written with a broad readership in mind. Great care has been given to the motivation of the concepts and to the explicit and detailed discussions of examples.




Discrete Mathematics for Computer Science


Book Description

Master the fundamentals of discrete mathematics with DISCRETE MATHEMATICS FOR COMPUTER SCIENCE with Student Solutions Manual CD-ROM! An increasing number of computer scientists from diverse areas are using discrete mathematical structures to explain concepts and problems and this mathematics text shows you how to express precise ideas in clear mathematical language. Through a wealth of exercises and examples, you will learn how mastering discrete mathematics will help you develop important reasoning skills that will continue to be useful throughout your career.