Mathematics of Discrete Structures for Computer Science

Law and the Technologies of the Twenty-First Century provides a contextual account of the way in which law functions in a broader regulatory environment across different jurisdictions. It identifies and clearly structures the four key challenges that technology poses to regulatory efforts, distinguishing between technology as a regulatory target and tool, and guiding the reader through an emerging field that is subject to rapid change. By extensive use of examples and extracts from the texts and materials that form and shape the scholarly and public debates over technology regulation, it presents complex material in a stimulating and engaging manner. Co-authored by a leading scholar in the field with a scholar new to the area, it combines comprehensive knowledge of the field with a fresh approach. This is essential reading for students of law and technology, risk regulation, policy studies, and science and technology studies.

With the arrival of genomics and genome sequencing projects, biology has been transformed into an incredibly data-rich science. The vast amount of information generated has made computational analysis critical and has increased demand for skilled bioinformaticians. Designed for biologists without previous programming experience, this textbook provides a hands-on introduction to Unix, Perl and other tools used in sequence bioinformatics. Relevant biological topics are used throughout the book and are combined with practical bioinformatics examples, leading students through the process from biological problem to computational solution. All of the Perl scripts, sequence and database files used in the book are available for download at the accompanying website, allowing the reader to easily follow each example using their own computer. Programming examples are kept at an introductory level, avoiding complex mathematics that students often find daunting. The book demonstrates that even simp

With the arrival of genomics and genome sequencing projects, biology has been transformed into an incredibly data-rich science. The vast amount of information generated has made computational analysis critical and has increased demand for skilled bioinformaticians. Designed for biologists without previous programming experience, this textbook provides a hands-on introduction to Unix, Perl and other tools used in sequence bioinformatics. Relevant biological topics are used throughout the book and are combined with practical bioinformatics examples, leading students through the process from biological problem to computational solution. All of the Perl scripts, sequence and database files used in the book are available for download at the accompanying website, allowing the reader to easily follow each example using their own computer. Programming examples are kept at an introductory level, avoiding complex mathematics that students often find daunting. The book demonstrates that even simp

Game theory is concerned with strategic interaction among several decision-makers. In such strategic encounters, all players are aware of the fact that their actions affect the other players. Game theory analyzes how these strategic, interactive considerations may affect the players' decisions and influence the final outcome. This textbook focuses on applications of complete-information games in economics and management, as well as in other fields such as political science, law and biology. It guides students through the fundamentals of game theory by letting examples lead the way to the concepts needed to solve them. It provides opportunities for self-study and self-testing through an extensive pedagogical apparatus of examples, questions and answers. The book also includes more advanced material suitable as a basis for seminar papers or elective topics, including rationalizability, stability of equilibria (with discrete-time dynamics), games and evolution, equilibrium selection and g

Formal systems that describe computations over syntactic structures occur frequently in computer science. Logic programming provides a natural framework for encoding and animating such systems. However, these systems often embody variable binding, a notion that must be treated carefully at a computational level. This book aims to show that a programming language based on a simply typed version of higher-order logic provides an elegant, declarative means for providing such a treatment. Three broad topics are covered in pursuit of this goal. First, a proof-theoretic framework that supports a general view of logic programming is identified. Second, an actual language called λProlog is developed by applying this view to higher-order logic. Finally, a methodology for programming with specifications is exposed by showing how several computations over formal objects such as logical formulas, functional programs, and λ-terms and π-calculus expressions can be encoded in λProlog.

Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in electrical engineering, applied mathematics, statistics and computer science. This book provides the first detailed introduction to the subject, highlighting theoretical advances and a range of applications, as well as outlining numerous remaining research challenges. After a thorough review of the basic theory, many cutting-edge techniques are presented, including advanced signal modeling, sub-Nyquist sampling of analog signals, non-asymptotic analysis of random matrices, adaptive sensing, greedy algorithms and use of graphical models. All chapters are written by leading researchers in the field, and consistent style and notation are utilized throughout. Key background information and clear definitions make this an ideal resource for researchers, graduate students and practitioners wanting to join this exciting research area. It can also serve as a supplementary textbook for courses on compu

Contributors from technical fields such as computer science and information technology, and from social sciences such as regional planning and communications, demonstrate the effectiveness of electron

Throughout her lifetime, Margaret Bryan (fl.1795–1816) ran several schools for girls. Although science and maths were not usually considered suitable subjects for young women, Bryan was convinced that the use of one's reasoning faculties was all but a religious obligation. She taught across a huge range of topics, including optics, trigonometry and the history of astronomy. This book is a collection of ten of her lectures and was first published in 1797. Largely non-technical and written for those without a thorough knowledge of mathematics, the lectures explain contemporary science as simply as possible, using everyday experiments and clear diagrams. From astronomical predictions for the flooding of the Nile in Ancient Egypt to Newton's theory of the aether, the material covered is still readable and fascinating today, and represents a remarkable example of female scholarship long before the acceptance of the first woman into the Royal Society.

"This book examines the emerging computing paradigm of Collective Intelligence (CI) and offers the computer and information science communities as it continue to move toward a new period of fully tech

Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. Special emphasis is given to the motivation and physical intuition behind every mathematical concept. Demystifying difficult topics by using accessible language, this book has broad appeal and is ideal for graduate students and researchers from various disciplines who want to get into this new and exciting research field.

This short book, geared towards undergraduate students of computer science and mathematics, is specifically designed for a first course in mathematical logic.A proof of Godel's completeness theorem an

Contributors from computer and information science and from business and management address the problem of the shortfall in information technology professionals now that the demand for such people has

Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. As the first book to deal exclusively with finite ordered sets, this book will be welcomed by graduate students and researchers in all of these areas. Beginning with definitions of key concepts and fundamental results (Dilworth's and Sperner's theorem, interval and semiorders, Galois connection, duality with distributive lattices, coding and dimension theory), the authors then present applications of these structures in fields such as preference modelling and aggregation, operational research and management, cluster and concept analysis, and data mining. Exercises are included at the end of each chapter with helpful hints provided for some of the most difficult examples. The authors also point to further topics of ongoing research.

For undergraduate students in Computer Science and Computer Programming courses.Now in its Tenth Edition, Concepts of Programming Languages introduces students to the main constructs of contemporary p

This collection of twelve articles on engineering and computer science education and training showcases current scholarship on communications skill development for an increasingly globalized workforce

G. H. Hardy was one of this century's finest mathematical thinkers, renowned among his contemporaries as a 'real mathematician … the purest of the pure'. He was also, as C. P. Snow recounts in his Foreword, 'unorthodox, eccentric, radical, ready to talk about anything'. This 'apology', written in 1940, offers a brilliant and engaging account of mathematics as very much more than a science; when it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it was like to be a creative artist'. C. P. Snow's Foreword gives sympathetic and witty insights into Hardy's life, with its rich store of anecdotes concerning his collaboration with the brilliant Indian mathematician Ramanujan, his idiosyncrasies and his passion for cricket. This is a unique account of the fascination of mathematics and of one of its most compelling exponents in modern times.

This book gets to the heart of science by asking a fundamental question about its essence: what is the true nature of space and time? Both defy modern physics and scientists find themselves continually searching for answers. This unique volume brings together world leaders in cosmology, particle physics, quantum gravity, mathematics, philosophy and theology, to provide fresh insights into the deep structure of space and time. In an attempt to understand the question, subjects ranging from dark matter to the philosophical and theological implications of spacetime are covered, ensuring that the issue is thoroughly explored. Interesting and thought-provoking answers provide a well-rounded read.

Classical dynamics is one of the cornerstones of advanced education in physics and applied mathematics, with applications across engineering, chemistry and biology. In this book, the author uses a concise and pedagogical style to cover all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods. Readers are introduced to the impressive advances in the field during the second half of the twentieth century, including KAM theory and deterministic chaos. Essential to these developments are some exciting ideas from modern mathematics, which are introduced carefully and selectively. Core concepts and techniques are discussed, together with numerous concrete examples to illustrate key principles. A special feature of the book is the use of computer software to investigate complex dynamical systems, both analytically and numerically. This text is ideal for graduate students and advanced undergraduates who are already familiar with the Newtonian and Lagrangian

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as to computer science, to the physical, biological,

Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introdu

For sophomore-level courses in Assembly Language Programming in Computer Science, Embedded Systems Design, Real-Time Analysis, Computer Engineering, or Electrical Engineering curricula. Requires prior

So much data is being generated these days that scientists spend a lot of time on such matters as where to store it, how to access it, or how to move it to visualization or computer resources for furt

Phylogenetic combinatorics is a branch of discrete applied mathematics concerned with the combinatorial description and analysis of phylogenetic trees and related mathematical structures such as phylogenetic networks and tight spans. Based on a natural conceptual framework, the book focuses on the interrelationship between the principal options for encoding phylogenetic trees: split systems, quartet systems and metrics. Such encodings provide useful options for analyzing and manipulating phylogenetic trees and networks, and are at the basis of much of phylogenetic data processing. This book highlights how each one provides a unique perspective for viewing and perceiving the combinatorial structure of a phylogenetic tree and is, simultaneously, a rich source for combinatorial analysis and theory building. Graduate students and researchers in mathematics and computer science will enjoy exploring this fascinating new area and learn how mathematics may be used to help solve topical problem

Murry Salby's new book provides an integrated treatment of the processes controlling the Earth-atmosphere system, developed from first principles through a balance of theory and applications. This book builds on Salby's previous book, Fundamentals of Atmospheric Physics. The scope has been expanded into climate, with the presentation streamlined for undergraduates in science, mathematics and engineering. Advanced material, suitable for graduate students and as a resource for researchers, has been retained but distinguished from the basic development. The book provides a conceptual yet quantitative understanding of the controlling influences, integrated through theory and major applications. It leads readers through a methodical development of the diverse physical processes that shape weather, global energetics and climate. End-of-chapter problems of varying difficulty develop student knowledge and its quantitative application, supported by answers and detailed solutions online for inst

State-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This innovative lab book provides a unified methodology for problem-solving in structural geology using linear algebra and computation. Assuming only limited mathematical training, the book begins with classic orientation problems and progresses to more fundamental topics of stress, strain and error propagation. It introduces linear algebra methods as the foundation for understanding vectors and tensors, and demonstrates the application of geometry and kinematics in geoscience without requiring students to take a supplementary mathematics course. All algorithms are illustrated with a suite of online MATLAB functions, allowing users to modify the code to solve their own structural problems. Containing 20 worked examples and over 60 exercises, this is the ideal lab book for advanced undergraduates or beginning graduate students. It will also p

State-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This innovative lab book provides a unified methodology for problem-solving in structural geology using linear algebra and computation. Assuming only limited mathematical training, the book begins with classic orientation problems and progresses to more fundamental topics of stress, strain and error propagation. It introduces linear algebra methods as the foundation for understanding vectors and tensors, and demonstrates the application of geometry and kinematics in geoscience without requiring students to take a supplementary mathematics course. All algorithms are illustrated with a suite of online MATLAB functions, allowing users to modify the code to solve their own structural problems. Containing 20 worked examples and over 60 exercises, this is the ideal lab book for advanced undergraduates or beginning graduate students. It will also p

Computational experiments on algorithms can supplement theoretical analysis by showing what algorithms, implementations and speed-up methods work best for specific machines or problems. This book guides the reader through the nuts and bolts of the major experimental questions: What should I measure? What inputs should I test? How do I analyze the data? To answer these questions the book draws on ideas from algorithm design and analysis, computer systems, and statistics and data analysis. The wide-ranging discussion includes a tutorial on system clocks and CPU timers, a survey of strategies for tuning algorithms and data structures, a cookbook of methods for generating random combinatorial inputs, and a demonstration of variance reduction techniques. The book can be used by anyone who has taken a course or two in data structures and algorithms. A companion website, AlgLab (www.cs.amherst.edu/alglab) contains downloadable files, programs and tools for use in experimental projects.

Computational experiments on algorithms can supplement theoretical analysis by showing what algorithms, implementations and speed-up methods work best for specific machines or problems. This book guides the reader through the nuts and bolts of the major experimental questions: What should I measure? What inputs should I test? How do I analyze the data? To answer these questions the book draws on ideas from algorithm design and analysis, computer systems, and statistics and data analysis. The wide-ranging discussion includes a tutorial on system clocks and CPU timers, a survey of strategies for tuning algorithms and data structures, a cookbook of methods for generating random combinatorial inputs, and a demonstration of variance reduction techniques. The book can be used by anyone who has taken a course or two in data structures and algorithms. A companion website, AlgLab (www.cs.amherst.edu/alglab) contains downloadable files, programs and tools for use in experimental projects.

Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive descrip

Contributors mostly from technical disciplines, but also from biology, present recent studies on the convergence of computer science and mathematics with systems biology. They focus on experimental da

Machine learning methods extract value from vast data sets quickly and with modest resources. They are established tools in a wide range of industrial applications, including search engines, DNA sequencing, stock market analysis, and robot locomotion, and their use is spreading rapidly. People who know the methods have their choice of rewarding jobs. This hands-on text opens these opportunities to computer science students with modest mathematical backgrounds. It is designed for final-year undergraduates and master's students with limited background in linear algebra and calculus. Comprehensive and coherent, it develops everything from basic reasoning to advanced techniques within the framework of graphical models. Students learn more than a menu of techniques, they develop analytical and problem-solving skills that equip them for the real world. Numerous examples and exercises, both computer based and theoretical, are included in every chapter. Resources for students and instructors,

Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and conn

Developed by computer science instructors, books in the for the absolute beginner? series teach the principles of programming through simple game creation. Get the jump on computer programming and dat

This book was first published in 2006. Earth's atmosphere and oceans exhibit complex patterns of fluid motion over a vast range of space and time scales. These patterns combine to establish the climate in response to solar radiation that is inhomogeneously absorbed by the materials comprising air, water, and land. Spontaneous, energetic variability arises from instabilities in the planetary-scale circulations, appearing in many different forms such as waves, jets, vortices, boundary layers, and turbulence. Geophysical fluid dynamics (GFD) is the science of all these types of fluid motion. This textbook is a concise and accessible introduction to GFD for intermediate to advanced students of the physics, chemistry, and/or biology of Earth's fluid environment. The book was developed from the author's many years of teaching a first-year graduate course at the University of California, Los Angeles. Readers are expected to be familiar with physics and mathematics at the level of general dyna

This textbook for beginning to intermediate computer science students provides a comprehensive overview of the practices involved in modern traditional software development processes. The work provide

Fortran is one of the oldest high-level languages and remains the premier language for writing code for science and engineering applications. This book is for anyone who uses Fortran, from the novice learner to the advanced expert. It describes best practices for programmers, scientists, engineers, computer scientists and researchers who want to apply good style and incorporate rigorous usage in their own Fortran code or to establish guidelines for a team project. The presentation concentrates primarily on the characteristics of Fortran 2003, while also describing methods in Fortran 90/95 and valuable new features in Fortran 2008. The authors draw on more than a half century of experience writing production Fortran code to present clear succinct guidelines on formatting, naming, documenting, programming and packaging conventions and various programming paradigms such as parallel processing (including OpenMP, MPI and coarrays), OOP, generic programming and C language interoperability.

Fortran is one of the oldest high-level languages and remains the premier language for writing code for science and engineering applications. This book is for anyone who uses Fortran, from the novice learner to the advanced expert. It describes best practices for programmers, scientists, engineers, computer scientists and researchers who want to apply good style and incorporate rigorous usage in their own Fortran code or to establish guidelines for a team project. The presentation concentrates primarily on the characteristics of Fortran 2003, while also describing methods in Fortran 90/95 and valuable new features in Fortran 2008. The authors draw on more than a half century of experience writing production Fortran code to present clear succinct guidelines on formatting, naming, documenting, programming and packaging conventions and various programming paradigms such as parallel processing (including OpenMP, MPI and coarrays), OOP, generic programming and C language interoperability.

In this resource for new researchers and graduate students in education, computer science, and information technology, international contributors offer detailed case examples of different phases of th

For researchers, academics, students, and business-to-business e-commerce solution providers and managers, Kumar and Sareen (financial studies and computer science, U. of Delhi, India) examine trust a

Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.