Mathematics of Discrete Structures for Computer Science

This is an up-to-date and integrated introduction to model theory, designed to be used for graduate courses (for students who are familiar with first-order logic), and as a reference for more experienced logicians and mathematicians. Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide variety of other areas such as set theory, geometry, algebra (in particular group theory), and computer science (e.g. logic programming and specification). Professor Hodges emphasises definability and methods of construction, and introduces the reader to advanced topics such as stability. He also provides the reader with much historical information and a full bibliography, enhancing the book's use as a reference.

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 book discusses how citizens can participate more effectively in sustainability science and environmental policy debates. It discusses designs for participatory procedures, and experiences of their application to issues of global change. While the focus is on citizen participation, the involvement of specific stakeholders - including water managers and venture capitalists - is also addressed. The book describes how focus group methods were combined with the interactive use of computer models into new forms of participation, tested with six hundred citizens. The results are discussed in relation to other important topics, including greenhouse gas and water management. By combining this with an examination of issues of interactive governance and developing country participation, the book provides state-of-the-art, practical insights for students, researchers and policy makers alike.

This book discusses how citizens can participate more effectively in sustainability science and environmental policy debates. It discusses designs for participatory procedures, and experiences of their application to issues of global change. While the focus is on citizen participation, the involvement of specific stakeholders - including water managers and venture capitalists - is also addressed. The book describes how focus group methods were combined with the interactive use of computer models into new forms of participation, tested with six hundred citizens. The results are discussed in relation to other important topics, including greenhouse gas and water management. By combining this with an examination of issues of interactive governance and developing country participation, the book provides state-of-the-art, practical insights for students, researchers and policy makers alike.

The study of complex variables is beautiful from a purely mathematical point of view, and very useful for solving a wide array of problems arising in applications. This introduction to complex variables, suitable as a text for a one-semester course, has been written for undergraduate students in applied mathematics, science, and engineering. Based on the authors' extensive teaching experience, it covers topics of keen interest to these students, including ordinary differential equations, as well as Fourier and Laplace transform methods for solving partial differential equations arising in physical applications. Many worked examples, applications, and exercises are included. With this foundation, students can progress beyond the standard course and explore a range of additional topics, including generalized Cauchy theorem, Painlevé equations, computational methods, and conformal mapping with circular arcs. Advanced topics are labeled with an asterisk and can be included in the syllabus

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

Written by world-leading experts, this book focusses on the role of biomaterials in stem cell research and regenerative medicine. Emphasising basic principles and methodology, it covers stem cell interactions, fabrication technologies, design principles, physical characterisation and biological evaluation, across a broad variety of systems and biomaterials. Topics include: stem cell biology, including embryonic stem cells, IPS, HSC and progenitor cells; modern scaffold structures, including biopolymer, bioceramic, micro- and nanofiber, ECM and biohydrogel; advanced fabrication technologies, including computer-aided tissue engineering and organ printing; cutting-edge drug delivery systems and gene therapy techniques; and medical applications spanning hard and soft tissues, the cardiovascular system and organ regeneration. With a contribution by Nobel laureate Shinya Yamanaka, this is a must-have reference for anyone in the field of biomaterials, stem cell biology and engineering, tissue

Written for graduate students and advanced undergraduates in computer science, A Second Course in Formal Languages and Automata Theory treats topics in the theory of computation not usually covered in a first course. After a review of basic concepts, the book covers combinatorics on words, regular languages, context-free languages, parsing and recognition, Turing machines, and other language classes. Many topics often absent from other textbooks, such as repetitions in words, state complexity, the interchange lemma, 2DPDAs, and the incompressibility method, are covered here. The author places particular emphasis on the resources needed to represent certain languages. The book also includes a diverse collection of more than 200 exercises, suggestions for term projects, and research problems that remain open.

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.

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.

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.

An understanding of Hedgehog structures is an essential component in any chessplayer's knowledge. These structures arise when the black c-pawn is exchanged early on for the white d-pawn (as in the Sic

From the creators of Scratch comes ScratchJr, a programming language designed for young children (ages 5-7).The ScratchJr Book is the perfect addition to the free app and makes coding and computer science easy and fun for all ages!In The ScratchJr Book, kids learn by playing with programming blocks and building their own animated collages, interactive stories, and playable games.Thirty step-by-step activities help kids develop computational thinking, problem-solving, and design skills. Each chapter has several smaller activities that build on one other, culminating with a fun, final project. By the end of the book kids and parents will be ready for all sorts of new programming adventures.Each activity includes:step-by-step, easy-to-follow directionsliteracy and math connectiontips for grown ups and teachers creative challenges to explore and grow!

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

Contributors from the computer and entertainment industries describe the design and implementation of computer-based entertainment applications. Topics include the infrastructure required for new appl

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

Computer aided design (CAD) emerged in the 1960s out of the growing acceptance of the use of the computer as a design tool for complex systems. As computers have become faster and less expensive while

This book is a step by step guide on what type of stakes are needed and how to set them for a construction project. Items included are Slope Stakes, Ditches, Minor Structures, Major Structures, Water,

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.

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 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.

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

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.

The book presents some key mathematical tools for the performance analysis of communication networks and computer systems.Communication networks and computer systems have become extremely complex. The

This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review

This book shows that it is possible to provide a fully rigorous treatment of calculus for those planning a career in an area that uses mathematics regularly (e.g., statistics, mathematics, economics,

Computer simulation-based education and training is a multi-billion dollar industry. With the increased complexity of organizational decision making, projected demand for computer simulation-based dec

Develop and manage chemical information systems This text provides a comprehensive overview of analyzing chemical problems using computer-aided methods for both newcomers and advanced computer scient

Designing the User Interface: Strategies for Effective Human-Computer Interaction provides a comprehensive introduction to the dynamic field of human-computer interaction (HCI). An expanded author tea

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.

I Use Math uses a lively first-person narrative to describe the use of mathematics in everyday situations. Correlated to first grade mathematics standards, each book contains a simple math problem for

I Use Math uses a lively first-person narrative to describe the use of mathematics in everyday situations. Correlated to first grade mathematics standards, each book contains a simple math problem for

BANG! What is G-force? What is a sonic boom? Find out more about the science of fast cars and high speed.High Speed, a Level 4 Reader, is A2 in the CEFR framework and supports YLE Flyers exams. The longer text is made up of sentences with up to three clauses, more complex past and future tense structures, modal verbs and a wider variety of conjunctions.

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

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.