This book introduces QPLEX, a powerful computational framework designed for modeling and analyzing nonstationary stochastic systems with large state spaces. The methodology excels at rapidly and accurately generating approximate distributions of system performance over time, offering a robust tool for understanding the dynamics of such systems. QPLEX circumvents the curse of dimensionality by imposing conditional independence, which may be represented via a probabilistic graphical model, a...

Recent years have seen the development of powerful tools for verifying hardware and software systems, as companies worldwide realise the need for improved means of validating their products. There is increasing demand for training in basic methods in formal reasoning so that students can gain proficiency in logic-based verification methods. The second edition of this successful textbook addresses both those requirements, by continuing to provide a clear introduction to formal reasoning whi...

Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of ...

1 + 1 = 1 An Introduction to Boolean Algebra and Switching Circuits was originally published by Williamsville Publishing Company as part of their popular Tape 'n Text Computer Math Series. It has been expanded and republished as Volume 4 in this new series. The paperback and e-book editions are intended for classroom teachers, students and as a reference for libraries.In elementary algebra 1 + 1 equals 2. In Boolean algebra 1 + 1 equals 1. Boolean algebra is not isomorphic (similar)...

The focus of this book is the P versus NP Question and the theory of NP-completeness. It also provides adequate preliminaries regarding computational problems and computational models. The P versus NP Question asks whether or not finding solutions is harder than checking the correctness of solutions. An alternative formulation asks whether or not discovering proofs is harder than verifying their correctness. It is widely believed that the answer to these equivalent formulations is positive...

An accessible introduction to philosophical logic, suitable for undergraduate courses and above.Rigorous yet accessible, Logical Methods introduces logical tools used in philosophy—including proofs, models, modal logics, meta-theory, two-dimensional logics, and quantification—for philosophy students at the undergraduate level and above. The approach developed by Greg Restall and Shawn Standefer is distinct from other texts because it presents proof constru...

Greatly expanded, this new edition requires only an elementary background in discrete mathematics and offers a comprehensive introduction to the role of randomization and probabilistic techniques in modern computer science. Newly added chapters and sections cover topics including normal distributions, sample complexity, VC dimension, Rademacher complexity, power laws and related distributions, cuckoo hashing, and the Lovasz Local Lemma. Material relevant to machine learning and big data an...

Mathematics plays a key role in computer science, some researchers would consider computers as nothing but the physical embodiment of mathematical systems. And whether you are designing a digital circuit, a computer program or a new programming language, you need mathematics to be able to reason about the design -- its correctness, robustness and dependability. This book covers the foundational mathematics necessary for courses in computer science.The common approach to presenting ...

Shimon Even's Graph Algorithms, published in 1979, was a seminal introductory book on algorithms read by everyone engaged in the field. This thoroughly revised second edition, with a foreword by Richard M. Karp and notes by Andrew V. Goldberg, continues the exceptional presentation from the first edition and explains algorithms in a formal but simple language with a direct and intuitive presentation. The book begins by covering basic material, including graphs and shortest paths, trees, de...

This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer character...

"Introduction to Mathematical Logic" is tailored for undergraduate students seeking a comprehensive introduction to this essential field of mathematics. We provide an accessible yet rigorous exploration of the principles, methods, and applications of mathematical logic.From the foundations of propositional and predicate logic to advanced topics like Gödel's incompleteness theorems and computability theory, we cover a broad range of concepts central to the study of logic. Through cle...

This textbook is aimed at transitioning high-school students who have already developed proficiency in mathematical problem solving from numerical-answer problems to proof-based mathematics. It serves to guide students on how to write and understand mathematical proofs. It covers proof techniques that are commonly used in several areas of mathematics, especially number theory, combinatorics, and analysis. In addition to just teaching the mechanics of proofs, this book showcases key materia...