Mathematics of Discrete Structures for Computer Science

Iterative error correction codes have found widespread application in cellular communications, digital video broadcasting and wireless LANs. This self-contained treatment of iterative error correction presents all the key ideas needed to understand, design, implement and analyse these powerful codes. Turbo, low-density parity-check, and repeat-accumulate codes are given equal, detailed coverage, with precise presentations of encoding and decoding procedures. Worked examples are integrated into the text to illuminate each new idea and pseudo-code is included for important algorithms to facilitate the reader's development of the techniques described. For each subject, the treatment begins with the simplest case before generalizing. There is also coverage of advanced topics such as density-evolution and EXIT charts for those readers interested in gaining a deeper understanding of the field. This text is ideal for graduate students in electrical engineering and computer science departments

This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.

This concise text, first published in 2003, is for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics, and can also serve as a quick reference for professionals. The major topics in ordinary differential equations, initial value problems, boundary value problems, and delay differential equations, are usually taught in three separate semester-long courses. This single book provides a sound treatment of all three in fewer than 300 pages. Each chapter begins with a discussion of the 'facts of life' for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used. The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understanding the codes are discussed. The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples.

Formal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use (and the uses of formalisms more generally elsewhere) actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science.

Formal languages are widely regarded as being above all mathematical objects and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use (and the uses of formalisms more generally elsewhere) actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools to use. She looks at the history and philosophy of formal languages and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology and cognitive and computer science.

In-operation vibration monitoring for complex mechanical structures and rotating machines is of key importance in many industrial areas such as aeronautics (wings and other structures subject to stren

This collection of contributions surveys the state-of-the-art in computer applications for graphics in art, animation and design. It provides an integrative view of the technological, computer-related

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.

The aim of this book is to expand and improve upon the existing knowledge on discrete-time 1-bit look-ahead sigma-delta modulation in general, and to come to a solution for the above mentioned specifi

Euclid presents the essential of mathematics in a manner which has set a high standard for more than 2000 years. This book, an explanation of the nature of mathematics from its most important early so

Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between.

Since the time of the Ancient Greeks, much has been written about the relation between mathematics and music: from harmony and number theory, to musical patterns and group theory. Benson provides a wealth of information here to enable the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the real interplay between these two ancient disciplines. The story is long as well as broad and involves physics, biology, psycho acoustics, the history of science, and digital technology as well as, of course, mathematics and music. Starting with the structure of the human ear and its relationship with Fourier analysis, the story proceeds via the mathematics of musical instruments to the ideas of consonance and dissonance, and then to scales and temperaments. This is a must-have book if you want to know about the music of the spheres or digital music and many things in between.

Alan Turing was an inspirational figure who is now recognised as a genius of modern mathematics. In addition to leading the Allied forces' code-breaking effort at Bletchley Park in World War II, he proposed the theoretical foundations of modern computing and anticipated developments in areas from information theory to computer chess. His ideas have been extraordinarily influential in modern mathematics and this book traces such developments by bringing together essays by leading experts in logic, artificial intelligence, computability theory and related areas. Together, they give insight into this fascinating man, the development of modern logic, and the history of ideas. The articles within cover a diverse selection of topics, such as the development of formal proof, differing views on the Church–Turing thesis, the development of combinatorial group theory, and Turing's work on randomness which foresaw the ideas of algorithmic randomness that would emerge many years later.

This new book for mathematics teachers helps them gain an appreciation of geometry and its importance in the history and development of mathematics. The material is presented in three parts. The firs

If you are tired of computer training books that are written in “computer” language, then this is the book for you. This book is written in plain English and explains what the computer terms mean. If

This international and interdisciplinary collection presents and discusses the many issues and educational practices that are touched on by constructivism. Drawing on perspectives from a range of different fields (ethics, mathematics education, philosophy, social psychology, science education, social studies), this book invites us to reposition ourselves in relation to the major currents that have influenced education in this century, namely pragmatism, genetic epistemology, and social interactionism. The essays call for new reflection on the questions that are central to the project of education and that, in particular, involve the validity of knowledge and types of knowledge, the compartmentalization of school subjects, the mediating role of teachers, and, above all, the ends of education. In so doing, this book relaunches the discussion on constructivism's potential for the social empowerment of groups and individuals.

This international and interdisciplinary collection presents and discusses the many issues and educational practices that are touched on by constructivism. Drawing on perspectives from a range of different fields (ethics, mathematics education, philosophy, social psychology, science education, social studies), this book invites us to reposition ourselves in relation to the major currents that have influenced education in this century, namely pragmatism, genetic epistemology, and social interactionism. The essays call for new reflection on the questions that are central to the project of education and that, in particular, involve the validity of knowledge and types of knowledge, the compartmentalization of school subjects, the mediating role of teachers, and, above all, the ends of education. In so doing, this book relaunches the discussion on constructivism's potential for the social empowerment of groups and individuals.

“Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.” From the Principles for School Mathematics of NCTM standards, copyright NCTM

The simulation of physical systems requires a simplified, hierarchical approach which models each level from the atomistic to the macroscopic scale. From quantum mechanics to fluid dynamics, this book systematically treats the broad scope of computer modeling and simulations, describing the fundamental theory behind each level of approximation. Berendsen evaluates each stage in relation to its applications giving the reader insight into the possibilities and limitations of the models. Practical guidance for applications and sample programs in Python are provided. With a strong emphasis on molecular models in chemistry and biochemistry, this 2007 book will be suitable for advanced undergraduate and graduate courses on molecular modeling and simulation within physics, biophysics, physical chemistry and materials science. It will also be a useful reference to all those working in the field. Additional resources for this title including solutions for instructors and programs are available

Mathematics can be fun for everyone, and this book shows it. It grew out of the author's popularisation of mathematics via live, call-in TV shows and widely published articles. Everyone paging through

Can you tell the difference between talking to a human and talking to a machine? Or, is it possible to create a machine which is able to converse like a human? In fact, what is it that even makes us human? Turing's Imitation Game, commonly known as the Turing Test, is fundamental to the science of artificial intelligence. Involving an interrogator conversing with hidden identities, both human and machine, the test strikes at the heart of any questions about the capacity of machines to behave as humans. While this subject area has shifted dramatically in the last few years, this book offers an up-to-date assessment of Turing's Imitation Game, its history, context and implications, all illustrated with practical Turing tests. The contemporary relevance of this topic and the strong emphasis on example transcripts makes this book an ideal companion for undergraduate courses in artificial intelligence, engineering or computer science.

Social platforms such as MySpace, Facebook and Twitter have rekindled the initial excitement of cyberspace. Text-based, computer-mediated communication has been enriched with face-to-face communication such as Skype, as users move from desktops to laptops with integrated cameras and related hardware. Age, gender and culture barriers seem to have crumbled and disappeared as the user base widens dramatically. Other than simple statistics relating to e-mail usage, chatrooms and blog subscriptions, we know surprisingly little about the rapid changes taking place. This book assembles leading researchers on nonverbal communication, emotion, cognition and computer science to summarize what we know about the processes relevant to face-to-face communication as it pertains to telecommunication, including video-conferencing. The authors take stock of what has been learned regarding how people communicate, in person or over distance, and set the foundations for solid research helping to understand

Social platforms such as MySpace, Facebook and Twitter have rekindled the initial excitement of cyberspace. Text-based, computer-mediated communication has been enriched with face-to-face communication such as Skype, as users move from desktops to laptops with integrated cameras and related hardware. Age, gender and culture barriers seem to have crumbled and disappeared as the user base widens dramatically. Other than simple statistics relating to e-mail usage, chatrooms and blog subscriptions, we know surprisingly little about the rapid changes taking place. This book assembles leading researchers on nonverbal communication, emotion, cognition and computer science to summarize what we know about the processes relevant to face-to-face communication as it pertains to telecommunication, including video-conferencing. The authors take stock of what has been learned regarding how people communicate, in person or over distance, and set the foundations for solid research helping to understand

What mechanisms are involved in enabling us to generate predictions of what will happen in the near future? Although we use associative mechanisms as the basis to predict future events, such as using cues from our surrounding environment, timing, attentional, and configural mechanisms are also needed to improve this function. Timing mechanisms allow us to determine when those events will take place. Attentional mechanisms ensure that we keep track of cues that are present when unexpected events occur and disregard cues present when everything happens according to our expectations. Configural mechanisms make it possible to combine separate cues into one signal that predicts an event different from that predicted individually by separate cues. Written for graduates and researchers in neuroscience, computer science, biomedical engineering and psychology, the author presents neural network models that incorporate these mechanisms and shows, through computer simulations, how they explain th

The study of computational processes based on the laws of quantum mechanics has led to the discovery of new algorithms, cryptographic techniques, and communication primitives. This book explores quantum computation from the perspective of the branch of theoretical computer science known as semantics, as an alternative to the more well-known studies of algorithmics, complexity theory, and information theory. It collects chapters from leading researchers in the field, discussing the theory of quantum programming languages, logics and tools for reasoning about quantum systems, and novel approaches to the foundations of quantum mechanics. This book is suitable for graduate students and researchers in quantum information and computation, as well as those in semantics, who want to learn about a new field arising from the application of semantic techniques to quantum information and computation.

Cyber Safety covers the basics of computer security useful for typical computer users, including the five components of IT Security: firewalls, anti-virus, IDS, networking, and web security. This bo

Numerical Mathematics is a unique textbook which presents rudimentary numerical mathematics in conjunction with computational laboratory assignments. No previous knowledge of calculus or linear algebra is presupposed, and thus the book is tailor-made for undergraduate students, as well as prospective mathematics teachers. The material in the book emphasises algorithmic aspects of mathematics, which are made viable through numerical assignments, in which the traditional 'chalk-and-talk' lecturer turns, in part, into a laboratory instructor. The book is not a numerical methods book, containing ready-made computational recipes. Rather, it guides the student to create the algorithm required for any given assignment - expressed in whichever programming language is used - on the basis of the underlying mathematics. The computational assignments cover iterative processes, area approximations, solution of linear systems, acceleration of series summation, interpolative approximations, and const

The thalamus is a key structure in the mammalian brain, providing a hub for communication within and across distributed forebrain networks. Research in this area has undergone a revolution in the last decade, with findings that suggest an expanded role for the thalamus in sensory processing, motor control, arousal regulation, and cognition. Moving beyond previous studies of anatomy and cell neurochemistry, scientists have expanded into investigations of cognitive function, and harness new methods and theories of neural computation. This book provides a survey of topics at the cutting edge of this field, covering basic anatomy, evolution, development, physiology and computation. It is also the first book to combine these disciplines in one place, highlighting the interdisciplinary nature of thalamus research, and will be an essential resource for students and experts in biology, medicine and computer science.

Multiagent systems combine multiple autonomous entities, each having diverging interests or different information. This overview of the field offers a computer science perspective, but also draws on ideas from game theory, economics, operations research, logic, philosophy and linguistics. It will serve as a reference for researchers in each of these fields, and be used as a text for advanced undergraduate or graduate courses. The authors emphasize foundations to create a broad and rigorous treatment of their subject, with thorough presentations of distributed problem solving, game theory, multiagent communication and learning, social choice, mechanism design, auctions, cooperative game theory, and modal logics of knowledge and belief. For each topic, basic concepts are introduced, examples are given, proofs of key results are offered, and algorithmic considerations are examined. An appendix covers background material in probability theory, classical logic, Markov decision processes and

The increasing popularity of wireless networks makes interference and cross-talk between multiple systems inevitable. This book describes techniques for quantifying this, and the effects on the performance of wireless networks operating in the unlicensed bands. It also presents a variety of system-level solutions, obviating the need for new hardware implementations. The book starts with basic concepts and wireless protocols before moving on to interference performance evaluation, interference modeling, coexistence solutions, and concluding with common misconceptions and pitfalls. The theory is illustrated by reference to real-world systems such as Bluetooth and WiFi. With a number of case studies and many illustrations, this book will be of interest to graduate students in electrical engineering and computer science, to practitioners designing new WLAN and WPAN systems or developing new techniques for interference supression, and to general users of merging wireless technologies.

Social network analysis maps relationships and transactions between people and groups. This text was the first book-length application of this method to the ancient world, using the abundant documentary evidence from sixth-century Oxyrhynchos and Aphrodito in Egypt. Professor Ruffini combines a prosopographical survey of both sites with computer analyses of the topographical and social networks in their papyri. He thereby uncovers hierarchical social structures in Oxyrhynchos not present in Aphrodito, and is able for the first time to trace the formation of the famous Apion estate. He can also use quantitative techniques to locate the central players in the Aphrodito social landscape, allowing us to see past the family of Dioskoros to discover the importance of otherwise unknown figures. He argues that the apparent social differences between Oxyrhynchos and Aphrodito in fact represent different levels of geographic scale, both present within the same social model.

Social network analysis maps relationships and transactions between people and groups. This text was the first book-length application of this method to the ancient world, using the abundant documentary evidence from sixth-century Oxyrhynchos and Aphrodito in Egypt. Professor Ruffini combines a prosopographical survey of both sites with computer analyses of the topographical and social networks in their papyri. He thereby uncovers hierarchical social structures in Oxyrhynchos not present in Aphrodito, and is able for the first time to trace the formation of the famous Apion estate. He can also use quantitative techniques to locate the central players in the Aphrodito social landscape, allowing us to see past the family of Dioskoros to discover the importance of otherwise unknown figures. He argues that the apparent social differences between Oxyrhynchos and Aphrodito in fact represent different levels of geographic scale, both present within the same social model.

Understanding viscoelasticity is pertinent to design applications as diverse as earplugs, gaskets, computer disks, satellite stability, medical diagnosis, injury prevention, vibration abatement, tire performance, sports, spacecraft explosions, and music. This book fits a one-semester graduate course on the properties, analysis, and uses of viscoelastic materials. Those familiar with the author's precursor book, Viscoelastic Solids, will see that this book contains many updates and expanded coverage of the materials science, causes of viscoelastic behavior, properties of materials of biological origin, and applications of viscoelastic materials. The theoretical presentation includes both transient and dynamic aspects, with emphasis on linear viscoelasticity to develop physical insight. Methods for the solution of stress analysis problems are developed and illustrated. Experimental methods for characterization of viscoelastic materials are explored in detail. Viscoelastic phenomena are d

Understanding viscoelasticity is pertinent to design applications as diverse as earplugs, gaskets, computer disks, satellite stability, medical diagnosis, injury prevention, vibration abatement, tire performance, sports, spacecraft explosions, and music. This book fits a one-semester graduate course on the properties, analysis, and uses of viscoelastic materials. Those familiar with the author's precursor book, Viscoelastic Solids, will see that this book contains many updates and expanded coverage of the materials science, causes of viscoelastic behavior, properties of materials of biological origin, and applications of viscoelastic materials. The theoretical presentation includes both transient and dynamic aspects, with emphasis on linear viscoelasticity to develop physical insight. Methods for the solution of stress analysis problems are developed and illustrated. Experimental methods for characterization of viscoelastic materials are explored in detail. Viscoelastic phenomena are d

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.

Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic d

The Basics of Computer Arithmetic Made Enjoyable and Accessible-with a Special Program Included for Hands-on Learning"The combination of this book and its associated virtual computer is fantastic! Exp

Vannevar Bush, the engineer who designed the world's most powerful analog computer, predicted the development of a new kind of computing machine he called Memex. For many computer and information scie

We are in the midst of a biological revolution. Molecular tools are now providing new means of critically testing hypotheses and models of microevolution in populations of wild, cultivated, weedy and feral plants. They are also offering the opportunity for significant progress in the investigation of long-term evolution of flowering plants, as part of molecular phylogenetic studies of the Tree of Life. This long-awaited fourth edition, fully revised by David Briggs, reflects new insights provided by molecular investigations and advances in computer science. Briggs considers the implications of these for our understanding of the evolution of flowering plants, as well as the potential for future advances. Numerous new sections on important topics such as the evolutionary impact of human activities, taxonomic challenges, gene flow and distribution, hybridisation, speciation and extinction, conservation and the molecular genetic basis of breeding systems will ensure that this remains a cla

The recent launch of NASA's Gamma-Ray Observatory will increase interest in gamma-ray astronomy. This is a fully up-dated new edition of the authors' earlier volume published in 1986 and covers both the background science and the current state-of-the-art in this field. The emphasis is on the astronomy and astrophysics of known sources of cosmic gamma-rays outside the solar system. The authors discuss the mechanisms for the production and absorption of gamma-rays. The gamma-ray line astronomy of the interstellar medium, galactic centre, and various discrete sources is then considered. Gamma-ray bursts are treated in considerable detail in chapter three, and the final two chapters describe medium energy and ultra-high energy gamma-rays. Relevant data from supernova SN1987A is also included in this edition. The book includes comprehensive references to the primary literature, together with many figures and tables. The concentration on phenomenology makes this book a fine introduction to g