Mathematics of Discrete Structures for Computer Science

Although computation and the science of physical systems would appear to be unrelated, there are a number of ways in which computational and physical concepts can be brought together in ways that illuminate both. This volume examines fundamental questions which connect scholars from both disciplines: is the universe a computer? Can a universal computing machine simulate every physical process? What is the source of the computational power of quantum computers? Are computational approaches to solving physical problems and paradoxes always fruitful? Contributors from multiple perspectives reflecting the diversity of thought regarding these interconnections address many of the most important developments and debates within this exciting area of research. Both a reference to the state of the art and a valuable and accessible entry to interdisciplinary work, the volume will interest researchers and students working in physics, computer science, and philosophy of science and mathematics.

Although computation and the science of physical systems would appear to be unrelated, there are a number of ways in which computational and physical concepts can be brought together in ways that illuminate both. This volume examines fundamental questions which connect scholars from both disciplines: is the universe a computer? Can a universal computing machine simulate every physical process? What is the source of the computational power of quantum computers? Are computational approaches to solving physical problems and paradoxes always fruitful? Contributors from multiple perspectives reflecting the diversity of thought regarding these interconnections address many of the most important developments and debates within this exciting area of research. Both a reference to the state of the art and a valuable and accessible entry to interdisciplinary work, the volume will interest researchers and students working in physics, computer science, and philosophy of science and mathematics.

This is the first comprehensive introduction to the theory of word-representable graphs, a generalization of several classical classes of graphs, and a new topic in discrete mathematics. After ex

More scientists now use C than any other programming language. This book contains practical, computer-ready algorithms for many standard methods of numerical mathematics. It describes the principles o

Once upon a time students of mathematics and students of science or engineering took the same courses in mathematical analysis beyond calculus. Now it is common to separate" advanced mathematics for s

Assuming only an elementary background in discrete mathematics, this textbook is an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algori

The IRIS series consists of computer science, computer networks, and telecommunication books intended for students in higher education (first year university to postgraduate degree level, preparation

For graduate-level neural network courses offered in the departments of Computer Engineering, Electrical Engineering, and Computer Science. Neural Networks and Learning Machines, Third Edition i

Triangular arrays are a unifying thread throughout various areas of discrete mathematics such as number theory and combinatorics. They can be used to sharpen a variety of mathematical skills and too

Designed for a first Computer Science (CS1) Java course, JAVA PROGRAMMING: FROM PROBLEM ANALYSIS TO PROGRAM DESIGN 5e will motivate readers while building a cornerstone for the Computer Science curric

This textbook is devoted to Combinatorics and Graph Theory, which are cornerstones of Discrete Mathematics. Every section begins with simple model problems. Following their detailed analysis, the read

The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. This volume covers many areas of contemporary logic: model theory, proof theory, set theory, and computer science, as well as philosophical logic, including tutorials on cardinal arithmetic, on Pillay's conjecture, and on automatic structures. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.

This traditional treatment of abstract algebra is designed for the particular needs of the mathematics teacher. Readers must have access to a Computer Algebra System (C. A. S.) such as Maple, or at mi

The new and revised version of this comprehensive pocket reference guide is ideal for anyone who deals with physics, chemistry, mathematics, finance, and computer systems and needs to review or quickl

The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer scien

The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer scienc

Combining different perspectives from materials science, engineering, and computer science, this reference provides a unified view of the various aspects necessary for the successful realization of in

Recent applications to biomolecular science and DNA computing have created a new audience for automata theory and formal languages. This is the only introductory book to cover such applications. It begins with a clear and readily understood exposition of the fundamentals that assumes only a background in discrete mathematics. The first five chapters give a gentle but rigorous coverage of basic ideas as well as topics not found in other texts at this level, including codes, retracts and semiretracts. Chapter 6 introduces combinatorics on words and uses it to describe a visually inspired approach to languages. The final chapter explains recently-developed language theory coming from developments in bioscience and DNA computing. With over 350 exercises (for which solutions are available), many examples and illustrations, this text will make an ideal contemporary introduction for students; others, new to the field, will welcome it for self-learning.

Recent applications to biomolecular science and DNA computing have created a new audience for automata theory and formal languages. This is the only introductory book to cover such applications. It begins with a clear and readily understood exposition of the fundamentals that assumes only a background in discrete mathematics. The first five chapters give a gentle but rigorous coverage of basic ideas as well as topics not found in other texts at this level, including codes, retracts and semiretracts. Chapter 6 introduces combinatorics on words and uses it to describe a visually inspired approach to languages. The final chapter explains recently-developed language theory coming from developments in bioscience and DNA computing. With over 350 exercises (for which solutions are available), many examples and illustrations, this text will make an ideal contemporary introduction for students; others, new to the field, will welcome it for self-learning.

In 1736, the mathematician Euler invented graph theory while solving the Konigsberg seven-bridge problem. Over 200 years later, graph theory remains the skeleton content of discrete mathematics, which

Accessible even to readers with only a basic knowledge of discrete mathematics, this treatment develops the underlying algebra gently but rigorously, and nearly 200 exercises reinforce the concepts. W

UNIX & Shell Programming is specially designed as a textbook for undergraduate and postgraduate students of Computer Science, Information Technology, and Computer Applications. The book seeks to i

?For undergraduate students in Computer Science and Computer Programming courses or beginning programmers A solid foundation in the basics of C++ programming will allow readers to create efficien

This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the second publication in the Lecture Notes in Logic series, is the proceedings of the Association for Symbolic Logic meeting held in Helsinki, Finland, in July 1990. It contains eighteen papers by leading researchers, covering all fields of mathematical logic from the philosophy of mathematics, through model theory, proof theory, recursion theory, and set theory, to the connections of logic to computer science. The articles published here are still widely cited and continue to provide ideas for ongoing research projects.

This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used

Cryptography plays a crucial role in many aspects of today's world, from internet banking and ecommerce to email and web-based business processes. Understanding the principles on which it is based is an important topic that requires a knowledge of both computational complexity and a range of topics in pure mathematics. This book provides that knowledge, combining an informal style with rigorous proofs of the key results to give an accessible introduction. It comes with plenty of examples and exercises (many with hints and solutions), and is based on a highly successful course developed and taught over many years to undergraduate and graduate students in mathematics and computer science.

Undergraduate Topics in Computer Science (UTiCS) delivers high-quality instructional content for undergraduates studying in all areas of computing and information science. From core foundational and

Fourier transform theory is of central importance in a vast range of applications in physical science, engineering and applied mathematics. Providing a concise introduction to the theory and practice of Fourier transforms, this book is invaluable to students of physics, electrical and electronic engineering, and computer science. After a brief description of the basic ideas and theorems, the power of the technique is illustrated through applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of Computer Axial Tomography (CAT scanning). The book concludes by discussing digital methods, with particular attention to the Fast Fourier Transform and its implementation. This new edition has been revised to include new and interesting material, such as convolution with a sinusoid, coherence, the Michelson stellar interferometer and the van Cittert–Zernike theorem,

Integrates research by cognitive psychologists and mathematics educators to show its relevance to the debate about reform of mathematics education. Discusses different knowledge structures representin

McGregor (computer science, Clemson University) and Sykes (computer science, Furman University) discuss real-world issues that arise in planning and implementing effective testing for object-oriented

Planetary rings are among the most intriguing structures of our solar system and have fascinated generations of astronomers. Collating emerging knowledge in the field, this volume reviews our current understanding of ring systems with reference to the rings of Saturn, Uranus, Neptune, and more. Written by leading experts, the history of ring research and the basics of ring–particle orbits is followed by a review of the known planetary ring systems. All aspects of ring system science are described in detail, including specific dynamical processes, types of structures, thermal properties and their origins, and investigations using computer simulations and laboratory experiments. The concluding chapters discuss the prospects of future missions to planetary rings, the ways in which ring science informs and is informed by the study of other astrophysical disks, and a perspective on the field's future. Researchers of all levels will benefit from this thorough and engaging presentation.

The emerging science of bionanotechnology refers to the harnessing of the vast diversity of self-assembling building blocks and processes for the assembly of nano-scaled structures for the manufacture

The skills, knowledge and understanding of the subjects involved in STEM (science, technology, engineering and mathematics) are vital for all young people in an increasingly science and technology dri

The skills, knowledge and understanding of the subjects involved in STEM (science, technology, engineering and mathematics) are vital for all young people in an increasingly science and technology dri

Recursion theory – now a well-established branch of pure mathematics, having grown rapidly over the last 35 years – deals with the general (abstract) theory of those operations which we conceive as being `computable' by idealized machines. The theory grew out of, and is usually still regarded, as a branch of mathematical logic. This book is a collection of advanced research/survey papers by eminent research workers in the field, based on their lectures given at the Leeds Logic Colloquium 1979. As such it provides an up-to-date view of current ideas and developments in the field of recursion theory as a whole. The individual contributions fit together naturally so as to provide an overview of all the main areas of research in the field. It will therefore be an important and invaluable source for advanced researchers and research students in mathematics and computer science (particularly in Europe, USA and USSR).

Oriented matroids are a very natural mathematical concept which presents itself in many different guises and which has connections and applications to many different areas. These include discrete and computational geometry, combinatorics, convexity, topology, algebraic geometry, operations research, computer science and theoretical chemistry. This is the second edition of the first comprehensive, accessible account of the subject. It is intended for a diverse audience: graduate students who wish to learn the subject from scratch; researchers in the various fields of application who want to concentrate on certain aspects of the theory; specialists who need a thorough reference work; and others at academic points in between. A list of exercises and open problems ends each chapter. For the second edition, the authors have expanded the bibliography greatly to ensure that it remains comprehensive and up-to-date, and they have also added an appendix surveying research since the work was firs

This textbook is designed as a first book on concurrent programming for computer science undergraduates, and provides a comprehensive introduction to the problems of concurrency. Concurrency is of vital importance in many areas of computer science, particularly in operating systems. It is also increasingly being taught in undergraduate courses. The book builds on the student's familiarity with sequential programming in a high level language, which will make it very accessible to computer science students. The book is concerned mainly with the high level aspects of concurrency, which will be equally applicable to traditional time sliced or more recent truly parallel systems.

Chan (mathematics, University of California) and Shen (mathematics, University of Minnesota) develop the mathematical foundations of modern image processing and low-level computer vision. They first i

In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic (intuitionistic type theories) is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificia