Mathematics of Discrete Structures for Computer Science

Ainslie argues that our responses to the threat of our own inconsistency determine the basic fabric of human culture. He suggests that individuals are more like populations of bargaining agents than like the hierarchical command structures envisaged by cognitive psychologists. The forces that create and constrain these populations help us understand so much that is puzzling in human action and interaction: from addictions and other self-defeating behaviors to the experience of willfulness, from pathological over-control and self-deception to subtler forms of behavior such as altruism, sadism, gambling, and the 'social construction' of belief. This book integrates approaches from experimental psychology, philosophy of mind, microeconomics, and decision science to present one of the most profound and expert accounts of human irrationality available. It will be of great interest to philosophers and an important resource for professionals and students in psychology, economics and political

Ainslie argues that our responses to the threat of our own inconsistency determine the basic fabric of human culture. He suggests that individuals are more like populations of bargaining agents than like the hierarchical command structures envisaged by cognitive psychologists. The forces that create and constrain these populations help us understand so much that is puzzling in human action and interaction: from addictions and other self-defeating behaviors to the experience of willfulness, from pathological over-control and self-deception to subtler forms of behavior such as altruism, sadism, gambling, and the 'social construction' of belief. This book integrates approaches from experimental psychology, philosophy of mind, microeconomics, and decision science to present one of the most profound and expert accounts of human irrationality available. It will be of great interest to philosophers and an important resource for professionals and students in psychology, economics and political

A textbook for a course of two semesters or three quarters in a general education or core program, primarily for non-science majors whose background in mathematics extends up to but not including calc

Computerized data acquisition systems are often the principle method of recording experimental results. This book takes the reader step-by-step through the process of data acquisition and analysis, explaining how to set up the systems and then obtain useful information from the data recorded. In an easy-to-read style, it guides researchers through the basics of data acquisition systems, explains the important underlying concepts, and gives numerous examples of how to analyze the recorded information. While aimed at researchers in the life sciences, the topics covered are general and will be valuable to anyone interested in learning to use data acquisition systems. The principles can be applied to the collection of data from respiratory apparatus to behavioral science experiments, and a host of other situations. Many illustrations and worked examples accompany the text, and the mathematics are kept simple. This book is an invaluable tool for the non-engineer who is collecting and analyz

Proceedings of a high-level conference on discrete mathematics, focusing on group actions in the areas of pure mathematics, applied mathematics, computer science, physics, and chemistry. A useful tool

Computerized data acquisition systems are often the principle method of recording experimental results. This book takes the reader step-by-step through the process of data acquisition and analysis, explaining how to set up the systems and then obtain useful information from the data recorded. In an easy-to-read style, it guides researchers through the basics of data acquisition systems, explains the important underlying concepts, and gives numerous examples of how to analyze the recorded information. While aimed at researchers in the life sciences, the topics covered are general and will be valuable to anyone interested in learning to use data acquisition systems. The principles can be applied to the collection of data from respiratory apparatus to behavioral science experiments, and a host of other situations. Many illustrations and worked examples accompany the text, and the mathematics are kept simple. This book is an invaluable tool for the non-engineer who is collecting and analyz

This is a major synthesis of the knowledge and practice of early modern English medicine in its social and cultural contexts. The book vividly maps out some central areas: remedies (and how they were made credible), notions of disease, advice on preventive medicine and on healthy living, and how surgeons worked upon the body and their understanding of what they were doing. The structures of practice and knowledge examined in the first part of the book came to be challenged in the later seventeenth century, when the 'new science' began to overturn the foundation of established knowledge. However, as the second part of the book shows, traditional medical practice was so well entrenched in English culture that much of it continued into the eighteenth century. Various changes did however occur, which set the agenda for later medical treatment and which are discussed in the final chapter.

This is a major synthesis of the knowledge and practice of early modern English medicine in its social and cultural contexts. The book vividly maps out some central areas: remedies (and how they were made credible), notions of disease, advice on preventive medicine and on healthy living, and how surgeons worked upon the body and their understanding of what they were doing. The structures of practice and knowledge examined in the first part of the book came to be challenged in the later seventeenth century, when the 'new science' began to overturn the foundation of established knowledge. However, as the second part of the book shows, traditional medical practice was so well entrenched in English culture that much of it continued into the eighteenth century. Various changes did however occur, which set the agenda for later medical treatment and which are discussed in the final chapter.

Carlis (computer science, U. of Minnesota) and Maguire a program manager for Microsoft, explain to information systems analysts and database developers how to become a successful data modeler. Using t

This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.

The applications of topological techniques for understanding molecular structures have become increasingly important over the past thirty years. In this topology text, the reader will learn about knot theory, 3-dimensional manifolds, and the topology of embedded graphs, while learning the role these play in understanding molecular structures. Most of the results that are described in the text are motivated by questions asked by chemists or molecular biologists, though the results themselves often go beyond answering the original question asked. There is no specific mathematical or chemical prerequisite; all the relevant background is provided. The text is enhanced by nearly 200 illustrations and more than 100 exercises. Reading this fascinating book, undergraduate mathematics students can escape the world of pure abstract theory and enter that of real molecules, while chemists and biologists will find simple, clear but rigorous definitions of mathematical concepts they handle intuitive

This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to sel

This revised and updated second edition of a highly successful book is the only text at this level to embrace a universal approach to three major developments in classical physics; namely nonlinear waves, solitons and chaos. The authors now include new material on biology and laser theory, and go on to discuss important recent developments such as soliton metamorphosis. A comprehensive treatment of basic plasma and fluid configurations and instabilities is followed by a study of the relevant nonlinear structures. Each chapter concludes with a set of problems. This text will be particularly valuable for students taking courses in nonlinear aspects of physics. In general, it will be of value to final year undergraduates and beginning graduate students studying fluid dynamics, plasma physics and applied mathematics.

Computer simulations provide a powerful tool for understanding ecological and evolutionary systems. Simulating Ecological and Evolutionary Systems in C models a diverse range of biological processes and systems, including competition, foraging, predation, mating systems, and life-history optimization, by simulating large collections of interacting individuals. Using the widely available computer programming language C, the book starts with elementary programs modeling stochastic birth-death processes, slowly increasing programming complexity as the chapters progress. All the important features of C are covered, including arrays, files, pointers, and structures, within biologically motivated simulations. Although computer simulations of extremely complicated biological processes are released from rigid mathematical constraints, each of the simulations is also placed in the context of a mathematical formulation examined either analytically or numerically. Procedures covered include testi

This collection of essays addresses the issues that have arisen in the development and implementation of national and state standards in science, mathematics, history, economics, and the English lang

Semiotics, the science of signs, has long been recognised as an important discipline for understanding information and communications. Moreover it has found wide application in other areas of computer science, as it offers an effective insight into organisations and the computer systems that support them. An organisation may be viewed as a system of information and communication in which human actors, with the assistance of information technology, are able to process, represent, store and consume information. Computer systems that fit into an organisation and that support and enhance its performance and competitiveness, can be better delivered if semiotic principles are understood and applied. In this book, first published in 2000, semiotic methods are introduced and illustrated through three major case studies, which demonstrate how information systems can be developed to meet business requirements and support business objectives. It will appeal to academics, systems developers and an

Du (computer science, City U. of Hong Kong) and Hwant (applied mathematics, National Chiao Tung U., Taiwan) assemble the theories and applications of a technique for testing blood on a large scale eco

Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic guide to a large part of the modern theory of Probability, whilst retaining its vitality. The authors' aim is to present the subject of Brownian motion not as a dry part of mathematical analysis, but to convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively and readable account of the theory of Markov processes. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.

This collection of articles by well-known experts was originally published in 2000 and is intended for researchers in computer science, practitioners of formal methods, and computer programmers working in safety-critical applications or in the technology of component-based systems. The work brings together several elements of this area that were fast becoming the focus of much research and practice in computing. The introduction by Clemens Szyperski gives a snapshot of research in the field. About half the articles deal with theoretical frameworks, models, and systems of notation; the rest of the book concentrates on case studies by researchers who have built prototype systems and present findings on architectures verification. The emphasis is on advances in the technological infrastructure of component-based systems; how to design and specify reusable components; and how to reason about, verify, and validate systems from components. Thus the book shows how theory might move into pract

The authors (professors of computer science and technology at the U. of Bologna, Italy) describe design techniques for data warehousing for database designers, companies, and institutions interested i

This book, first published in 2000, is a comprehensive introduction to holomorphic dynamics, that is the dynamics induced by the iteration of various analytic maps in complex number spaces. This has been the focus of much attention in recent years, with, for example, the discovery of the Mandelbrot set, and work on chaotic behaviour of quadratic maps. The treatment is mathematically unified, emphasizing the substantial role played by classical complex analysis in understanding holomorphic dynamics as well as giving an up-to-date coverage of the modern theory. The authors cover entire functions, Kleinian groups and polynomial automorphisms of several complex variables such as complex Henon maps, as well as the case of rational functions. The book will be welcomed by graduate students and professionals in pure mathematics and science who seek a reasonably self-contained introduction to this exciting area.

Ideal for those in science and industry, this state-of-the-art guide to using MATLAB introduces readers to a wide range of numerical algorithms implemented by this modern and powerful computer softwar

This is the first volume of the second edition of the standard text on design theory. It is suitable for advanced courses and as a reference work, not only for researchers in discrete mathematics or f

This is the concluding volume of the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten to reflect this. In particular the growing importance of discrete mathematics to many parts of engineering and science have made designs a useful tool for applications, and this fact has been acknowledged here with the inclusion of an additional chapter on applications. It is suitable for advanced courses and as a reference work, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. Exercises are included throughout, and the book concludes with an extensive and updated bibliography of well over 1800 items.

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

The theme of this book is the study of the distribution of integer powers modulo a prime number. It provides numerous new, sometimes quite unexpected, links between number theory and computer science as well as to other areas of mathematics. Possible applications include (but are not limited to) complexity theory, random number generation, cryptography, and coding theory. The main method discussed is based on bounds of exponential sums. Accordingly, the book contains many estimates of such sums, including new estimates of classical Gaussian sums. It also contains many open questions and proposals for further research.

Quantum Heterostructures provides a detailed description of the key physical and engineering principles of quantum semiconductor heterostructures. Blending important concepts from physics, materials science, and electrical engineering, it also explains clearly the behaviour and operating features of modern microelectronic and optoelectronic devices. The authors begin by outlining the trends that have driven development in this field, most importantly the need for high-performance devices in computer, information, and communications technologies. They then describe the basics of quantum nanoelectronics, including various transport mechanisms. In the latter part of the book, they cover novel microelectronic devices, and optical devices based on quantum heterostructures. The book contains many homework problems and is suitable as a textbook for undergraduate and graduate courses in electrical engineering, physics, or materials science. It will also be of great interest to those involved i

In the past few years elliptic curve cryptography has moved from a fringe activity to a major challenger to the dominant RSA/DSA systems. Elliptic curves offer major advances on older systems such as increased speed, less memory and smaller key sizes. As digital signatures become more and more important in the commercial world the use of elliptic curve-based signatures will become all pervasive. This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.

Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincare wh

This book gives a friendly introduction to Fourier analysis on finite groups, both commutative and non-commutative. Aimed at students in mathematics, engineering and the physical sciences, it examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research. With applications in chemistry, error-correcting codes, data analysis, graph theory, number theory and probability, the book presents a concrete approach to abstract group theory through applied examples, pictures and computer experiments. In the first part, the author parallels the development of Fourier analysis on the real line and the circle, and then moves on to analogues of higher dimensional Euclidean space. The second part emphasizes matrix groups such as the Heisenberg group of upper triangular 2x2 matrices. The book concludes with an introduction to zeta functions on finite graphs via the trace formula.

Ideas from theoretical computer science continue to have an important influence on areas of philosophy and linguistics. The papers contained in this volume by some of the most influential computer sci

This new edition of Professor Sethian's successful text provides an introduction to level set methods and fast marching methods, which are powerful numerical techniques for analyzing and computing interface motion in a host of settings. They rely on a fundamental shift in how one views moving boundaries; rethinking the natural geometric Lagrangian perspective and exchanging it for an Eulerian, initial value partial differential equation perspective. For this edition, the collection of applications provided in the text has been expanded, including examples from physics, chemistry, fluid mechanics, combustion, image processing, material science, fabrication of microelectronic components, computer vision, computer-aided design, and optimal control theory. This book will be a useful resource for mathematicians, applied scientists, practising engineers, computer graphic artists, and anyone interested in the evolution of boundaries and interfaces.

This book, published in celebration of the 35th anniversary of MIT's LCS, chronicles its history, achievements, and continued importance to computer science.

The aim of this book is to explain the shape of Greek mathematical thinking. It can be read on three levels: as a description of the practices of Greek mathematics; as a theory of the emergence of the deductive method; and as a case-study for a general view on the history of science. The starting point for the enquiry is geometry and the lettered diagram. Reviel Netz exploits the mathematicians' practices in the construction and lettering of their diagrams, and the continuing interaction between text and diagram in their proofs, to illuminate the underlying cognitive processes. A close examination of the mathematical use of language follows, especially mathematicians' use of repeated formulae. Two crucial chapters set out to show how mathematical proofs are structured and explain why Greek mathematical practice manages to be so satisfactory. A final chapter looks into the broader historical setting of Greek mathematical practice.

The use of neural networks in signal processing is becoming increasingly widespread, with applications in many areas. Applied Neural Networks for Signal Processing is the first book to provide a comprehensive introduction to this broad field. It begins by covering the basic principles and models of neural networks in signal processing. The authors then discuss a number of powerful algorithms and architectures for a range of important problems, and describe practical implementation procedures. A key feature of the book is that many carefully designed simulation examples are included to help guide the reader in the development of systems for new applications. The book will be an invaluable reference for scientists and engineers working in communications, control or any other field related to signal processing. It can also be used as a textbook for graduate courses in electrical engineering and computer science.

Originally published by Cambridge University Press in 1900, A Treatise on the Theory of Screws is the definitive reference on screw theory. It gives a very complete geometrical treatment of the problems of small movements in rigid dynamics. In recent years the theory of screws has emerged as a novel mathematical resource for addressing complex engineering problems, with important applications to robotics, multibody dynamics, mechanical design, computational kinematics, and hybrid automatic control. The author, Sir Robert Stawell Ball, was born in Dublin in 1840 and studied at Trinity College, Dublin. When the Royal College of Science was founded in Dublin in 1867, Ball became the first professor of applied mathematics and mechanism. In 1874 he was appointed Royal Astronomer of Ireland, and in 1892 he assumed the Lowndean Chair of Astronomy and Geometry and the Directorship of the University Observatory at Cambridge, where he remained until his death in 1913.

This book brings together contributions from researchers within various social science disciplines who seek to redefine the methods and topics that constitute the study of work. They investigate work activity in ways that do not reduce it to a 'psychology' of individual cognition nor to a 'sociology' of societal structures and communication. A key theme in the material is the relationship between theory and practice. This is not an abstract problem of interest merely to social scientists. Rather, it is discussed as an issue that working people address when they attempt to understand a task and communicate its demands. Mindful practices and communicative interaction are examined as situated issues at work in the reproduction of communities of practice in a variety of settings including: courts of law, computer software design, the piloting of airliners, the coordination of air traffic control, and traffic management in underground railway systems.

This book addresses a phenomenon that has been much studied in anthropology, sociology and administrative science - the social structural foundations of coordinated activity and consensus in complexly differentiated communities and organizations. Such foundations are important because social differentiation makes coordination and agreement especially hard to achieve and maintain. Friedkin focuses on the process of social influence, and on how this process, when it is played out in a network of interpersonal influence, may result in interpersonal agreements among actors who are located in different parts of a complexly differentiated organization. This work builds on structural role analysis which provides a description of the pattern of social differentiation in a population. Interpretation of the revealed social structures has long been a problem. The steps for structural analysis that are proposed in this book are addressed to the above problem. To explain the coordination of social

This is the revised and expanded 1998 edition of a popular introduction to the design and implementation of geometry algorithms arising in areas such as computer graphics, robotics, and engineering design. The basic techniques used in computational geometry are all covered: polygon triangulations, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning. The self-contained treatment presumes only an elementary knowledge of mathematics, but reaches topics on the frontier of current research, making it a useful reference for practitioners at all levels. The second edition contains material on several new topics, such as randomized algorithms for polygon triangulation, planar point location, 3D convex hull construction, intersection algorithms for ray-segment and ray-triangle, and point-in-polyhedron. The code in this edition is significantly improved from the first edition (more efficient and more robust), and four new routines are included. Java versions fo

Bipartite graphs are perhaps the most basic of objects in graph theory, both from a theoretical and practical point of view. However, sometimes they have been considered only as a special class in some wider context. This book deals solely with bipartite graphs. Together with traditional material, the reader will also find many unusual results. Essentially all proofs are given in full; many of these have been streamlined specifically for this text. Numerous exercises of all standards have also been included. The theory is illustrated with many applications especially to problems in timetabling, chemistry, communication networks and computer science. For the most part the material is accessible to any reader with a graduate understanding of mathematics. However, the book contains advanced sections requiring much more specialized knowledge, which will be of interest to specialists in combinatorics and graph theory.