Mathematics of Discrete Structures for Computer Science

This 2003 book provides an analysis of combinatorial games - games not involving chance or hidden information. It contains a fascinating collection of articles by some well-known names in the field, such as Elwyn Berlekamp and John Conway, plus other researchers in mathematics and computer science, together with some top game players. The articles run the gamut from theoretical approaches (infinite games, generalizations of game values, 2-player cellular automata, Alpha-Beta pruning under partial orders) to other games (Amazons, Chomp, Dot-and-Boxes, Go, Chess, Hex). Many of these advances reflect the interplay of the computer science and the mathematics. The book ends with a bibliography by A. Fraenkel and a list of combinatorial game theory problems by R. K. Guy. Like its predecessor, Games of No Chance, this should be on the shelf of all serious combinatorial games enthusiasts.

How the cerebellum accomplishes its highly complex feats of coordination has been the subject of much inquiry; one of the pre-eminent theories places adaptive control at the forefront. This book reinforces the view that the cerebellum functions as an adaptive control system; that is, it automatically adjusts its output as needed for such eventualities as temporary or lasting weakness of muscle. It is the first text to synthesize the substantial body of literature on the subject, combining the neuroscience of the cerebellum with the science of control theory common to electrical and computer engineers. Organized in four parts, the book examines cerebellar anatomy and physiology; cerebellar function; models and theories; and ends with a summary and conclusions. The author's clinical perspective offers a broader view of cerebellar function beyond the basic neuroscience. An appendix demonstrates evidence supporting the adaptive control model from a detailed comparison of the cerebellum wit

This is an advanced 2001 textbook on modal logic, a field which caught the attention of computer scientists in the late 1970s. Researchers in areas ranging from economics to computational linguistics have since realised its worth. The book is for novices and for more experienced readers, with two distinct tracks clearly signposted at the start of each chapter. The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects, and applications to issues in logic and computer science such as completeness, computability and complexity are considered. Three appendices supply basic background information and numerous exercises are provided. Ideal for anyone wanting to learn modern modal logic.

Engineering is the application of science and mathematics to achieve useful objectives for the benefit of society. Typically, the goal of an engineering education is to effectively pass on to students

A broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. The text emphasises applications,

High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular attention given to enforcement of incompressibility. Advanced discretizations, implementation issues, and parallel and vector performance are considered in the closing sections. Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual app

Finance provides a dramatic example of the successful application of advanced mathematical techniques to the practical problem of pricing financial derivatives. This self-contained 2002 text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus: proofs in the continuous-time world follow naturally. The Black-Scholes pricing formula is first derived in the simplest financial context. The second half of the book is then devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts can be app

Finance provides a dramatic example of the successful application of advanced mathematical techniques to the practical problem of pricing financial derivatives. This self-contained 2002 text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus: proofs in the continuous-time world follow naturally. The Black-Scholes pricing formula is first derived in the simplest financial context. The second half of the book is then devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A valuable feature is the large number of exercises and examples, designed to test technique and illustrate how the methods and concepts can be app

Neurons in the brain communicate by short electrical pulses, the so-called action potentials or spikes. How can we understand the process of spike generation? How can we understand information transmission by neurons? What happens if thousands of neurons are coupled together in a seemingly random network? How does the network connectivity determine the activity patterns? And, vice versa, how does the spike activity influence the connectivity pattern? These questions are addressed in this 2002 introduction to spiking neurons aimed at those taking courses in computational neuroscience, theoretical biology, biophysics, or neural networks. The approach will suit students of physics, mathematics, or computer science; it will also be useful for biologists who are interested in mathematical modelling. The text is enhanced by many worked examples and illustrations. There are no mathematical prerequisites beyond what the audience would meet as undergraduates: more advanced techniques are introd

The Cambridge Dictionary of Scientists is an invaluable one-stop reference book for anyone wanting a brief and accurate account of the life and work of those who created science from its very beginnings to the present day. This alphabetically organized, illustrated biographical dictionary has been thoroughly revised and updated, covering over 1,500 key scientists (157 more than in the previous edition) from 40 countries. Fields represented include physics, chemistry, biology, geology, astronomy, mathematics, medicine, meteorology and technology, with special attention paid to pioneer women whose achievements and example opened the way to scientific careers for others. As well as Nobel Prizewinners, this second edition includes winners of the Fields Medal, the mathematician's equivalent of the Nobel Prize. Illustrated with around 150 portraits, diagrams, maps and tables, and with special panel features, this book is a clear and accessible guide to the world's prominent scientific perso

The Cambridge Dictionary of Scientists is an invaluable one-stop reference book for anyone wanting a brief and accurate account of the life and work of those who created science from its very beginnings to the present day. This alphabetically organized, illustrated biographical dictionary has been thoroughly revised and updated, covering over 1,500 key scientists (157 more than in the previous edition) from 40 countries. Fields represented include physics, chemistry, biology, geology, astronomy, mathematics, medicine, meteorology and technology, with special attention paid to pioneer women whose achievements and example opened the way to scientific careers for others. As well as Nobel Prizewinners, this second edition includes winners of the Fields Medal, the mathematician's equivalent of the Nobel Prize. Illustrated with around 150 portraits, diagrams, maps and tables, and with special panel features, this book is a clear and accessible guide to the world's prominent scientific perso

This book provides a thorough introduction to one of the most efficient approximation methods for the analysis and solution of problems in theoretical physics and applied mathematics. It is written with practical needs in mind and contains a discussion of 50 problems with solutions, of varying degrees of difficulty. The problems are taken from quantum mechanics, but the method has important applications in any field of science involving second order ordinary differential equations. The power of the asymptotic solution of second order differential equations is demonstrated, and in each case the authors clearly indicate which concepts and results of the general theory are needed to solve a particular problem. This book will be ideal as a manual for users of the phase-integral method, as well as a valuable reference text for experienced research workers and graduate students.

Based on a lecture course given at Chalmers University of Technology, this 2002 book is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before applying it to study a range of randomized algorithms with important applications in optimization and other problems in computing. Amongst the algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recent Propp-Wilson algorithm. This book will appeal not only to mathematicians, but also to students of statistics and computer science. The subject matter is introduced in a clear and concise fashion and the numerous exercises included will help students to deepen their understanding.

Felix Klein, one of the great nineteenth-century geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries. For a century, these images barely existed outside the imagination of mathematicians. However, in the 1980s, the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.

This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.

Combinatorics on words has arisen independently within several branches of mathematics, for instance number theory, group theory and probability, and appears frequently in problems related to theoretical computer science. The first unified treatment of the area was given in Lothaire's book Combinatorics on Words. Originally published in 2002, this book presents several more topics and provides deeper insights into subjects discussed in the previous volume. An introductory chapter provides the reader with all the necessary background material. There are numerous examples, full proofs whenever possible and a notes section discussing further developments in the area. This book is both a comprehensive introduction to the subject and a valuable reference source for researchers.

Basics of Holography is a general introduction to the subject written by a leading worker in the field. It begins with the theory of holographic imaging, the characteristics of the reconstructed image, and the various types of holograms. Practical aspects of holography are then described, including light sources, the characteristics of recording media and recording materials, as well as methods for producing different types of holograms and computer-generated holograms. Finally, important applications of holography are discussed, such as high-resolution imaging, holographic optical elements, information processing, and holographic interferometry. The book includes comprehensive reference sections and appendices summarizing some useful mathematical results. Numerical problems with their solutions are provided at the ends of chapters. This is an invaluable resource for advanced undergraduate and graduate students as well as researchers in science and engineering who would like to learn m

Basics of Holography is a general introduction to the subject written by a leading worker in the field. It begins with the theory of holographic imaging, the characteristics of the reconstructed image, and the various types of holograms. Practical aspects of holography are then described, including light sources, the characteristics of recording media and recording materials, as well as methods for producing different types of holograms and computer-generated holograms. Finally, important applications of holography are discussed, such as high-resolution imaging, holographic optical elements, information processing, and holographic interferometry. The book includes comprehensive reference sections and appendices summarizing some useful mathematical results. Numerical problems with their solutions are provided at the ends of chapters. This is an invaluable resource for advanced undergraduate and graduate students as well as researchers in science and engineering who would like to learn m

Karnes (U. of S. Mississippi) and Stephens' (Duke U.) guide will provide motivation and support for girls and young women considering careers in science, mathematics, and technology. Coverage include

Provides an innovative hands-on introduction to techniques for specifying the behaviour of software components. It is primarily intended for use as a text book for a course in the 2nd or 3rd year of Computer Science and Computer Engineering programs, but it is also suitable for self-study. Using this book will help the reader improve programming skills and gain a sound foundation and motivation for subsequent courses in advanced algorithms and data structures, software design, formal methods, compilers, programming languages, and theory. The presentation is based on numerous examples and case studies appropriate to the level of programming expertise of the intended readership. The main topics covered are techniques for using programmer-friendly assertional notations to specify, develop, and verify small but non-trivial algorithms and data representations, and the use of state diagrams, grammars, and regular expressions to specify and develop recognizers for formal languages.

Provides an innovative hands-on introduction to techniques for specifying the behaviour of software components. It is primarily intended for use as a text book for a course in the 2nd or 3rd year of Computer Science and Computer Engineering programs, but it is also suitable for self-study. Using this book will help the reader improve programming skills and gain a sound foundation and motivation for subsequent courses in advanced algorithms and data structures, software design, formal methods, compilers, programming languages, and theory. The presentation is based on numerous examples and case studies appropriate to the level of programming expertise of the intended readership. The main topics covered are techniques for using programmer-friendly assertional notations to specify, develop, and verify small but non-trivial algorithms and data representations, and the use of state diagrams, grammars, and regular expressions to specify and develop recognizers for formal languages.

The huge and growing demand for wireless communication systems has spurred a massive effort on the parts of the computer science and electrical engineering communities to formulate ever-more efficient

Supramolecular Chemistry deals with the design, synthesis and study of molecular structures held together by non-covalent interactions. Structures of this type are ubiquitous in nature and are frequently used as blueprints for the design of synthetic equivalents. This book is intended to demonstrate the seminal importance of supramolecular chemistry and self-organization in the design and synthesis of novel organic materials, inorganic materials and biomaterials. With contributions from leading workers in the field, the book shows how the bottom-up approach of supramolecular chemistry can be used to synthesize not only new materials, but function specific molecular devices as well. This book will be of interest to researchers and graduate students in chemistry, materials science and physics who need a summary of the most recent developments in the field.

The 17th century was a time of transition for the study of science and mathematics. The technological achievements of this time directly impacted both society and the future of science. This referenc

Corporate loggers have damaged much of the tropical forest throughout the Asia-Pacific over the last four decades. Despite a steady rise in global and local concern, few firms have changed their practices. Loggers and Degradation in the Asia-Pacific examines why and how loggers have resisted and ignored calls for environmental reforms. Concentrating on the period after 1990, the book explains what is happening on the ground and highlights the structures within which firms and governments operate. Within this broader context the author considers a range of factors including: the science of tropical forest management, the capacity of states to regulate and enforce rules, the relative power of environmental reformers, and the 1997–9 Asian financial crisis. This is a constructive, insightful approach to a depressing, yet urgent, problem. It will be accessible to academic and student readers as well as those in corporations, government and NGOs.

Corporate loggers have damaged much of the tropical forest throughout the Asia-Pacific over the last four decades. Despite a steady rise in global and local concern, few firms have changed their practices. Loggers and Degradation in the Asia-Pacific examines why and how loggers have resisted and ignored calls for environmental reforms. Concentrating on the period after 1990, the book explains what is happening on the ground and highlights the structures within which firms and governments operate. Within this broader context the author considers a range of factors including: the science of tropical forest management, the capacity of states to regulate and enforce rules, the relative power of environmental reformers, and the 1997–9 Asian financial crisis. This is a constructive, insightful approach to a depressing, yet urgent, problem. It will be accessible to academic and student readers as well as those in corporations, government and NGOs.

Luminescence is presently, and will continue to be, a challenging field of research in materials science, solid-state physics and chemistry. Recent progress in optoelectronic and display technology continues to drive this field in the search for new luminescent materials. Demands on new procedures for synthesis, and understanding underlying luminescence processes in these materials, will create new opportunities for both fundamental and applied research. This book is a compilation of papers, both invited and solicted, from around the world that focus on luminescence and luminescent materials - from theory and modeling, characterization of luminescent materials, and systems with confined structures such as nanocrystallites and quantum wells and dots, to synthesis and device applications.

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selecte

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selecte

This volume investigates the nature of constitutional democratic government in the United States and elsewhere. The editors introduce a basic conceptual framework which the contributors clarify and develop in eleven essays organized into three separate sections. The first section deals with constitutional founding and the founders' use of cultural symbols and traditions to facilitate acceptance of a new regime. The second discusses alternative constitutional structures and their effects on political outcomes. The third focuses on processes of constitutional change and on why founders might choose to make formal amendments relatively difficult or easy to achieve. The book is distinctive because it provides comprehensive tools for analyzing and comparing different forms of constitutional democracy. These tools are discussed in ways that will be of interest to students and readers in political science, law, history and political philosophy.

Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.

In this second edition of the now classic text, the already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents a comprehensive account of random graph theory. The theory (founded by Erdös and Rényi in the late fifties) aims to estimate the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self-contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study.

In this second edition of the now classic text, the already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents a comprehensive account of random graph theory. The theory (founded by Erdös and Rényi in the late fifties) aims to estimate the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self-contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study.

This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily at logisticians in mathematics, philosophy, computer science and

Linear Algebra: An Introduction Using MAPLE is a text for a first undergraduate course in linear algebra. All students majoring in mathematics, computer science, engineering, physics, chemistry, econo

Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, it is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for the book will be students and professionals in philosophy, computer science, and AI. Among the special features of the book are a chapter on evidential probability, which has not received a basic exposition before; chapters on nonmonotonic reasoning and theory replacement, matters rarely addressed in standard philosophical texts; and chapters on Mill's methods and statistical inference that cover material sorely lacking in the usual treatments of AI and computer science.

One of the motivating questions in materials research today is, how can elements be combined to produce a solid with specified properties? This book is intended to acquaint the reader with established principles of crystallography and cohesive forces that are needed to address the fundamental relationship between the composition, structure and bonding. Starting with an introduction to periodic trends, the book discusses crystal structures and the various primary and secondary bonding types, and finishes by describing a number of models for predicting phase stability and structure. Containing a large number of worked examples, exercises, and detailed descriptions of numerous crystal structures, this book is primarily intended as an advanced undergraduate or graduate level textbook for students of materials science. It will also be useful to scientists and engineers who work with solid materials.

Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.

Dynamic pricing and on-line auctions are emerging as the preferred models for e-business. This multi-disciplinary 2001 book presents a framework of negotiation protocols for electronic markets. It was the first book to combine economics with computer science and the first to describe multidimensional auction mechanisms - i.e. automated negotiations on multiple attributes and/or multiple units of a product. In addition it summarises the introductory economics needed to understand electronic markets, and surveys the literature on negotiation and auction theory. Case studies include the trading of financial derivatives. For use in the design, implementation and upgrade of electronic markets, for researchers in: economics, information systems and operations management, computer science and all students of the e-commerce phenomenon.