Mathematics of Discrete Structures for Computer Science

This textbook provides an introduction to abstract algebra for advanced undergraduate students. Based on the authors' notes at the Department of Mathematics, National Chung Cheng University, it contains material sufficient for three semesters of study. It begins with a description of the algebraic structures of the ring of integers and the field of rational numbers. Abstract groups are then introduced. Technical results such as Lagrange's theorem and Sylow's theorems follow as applications of group theory. The theory of rings and ideals forms the second part of this textbook, with the ring of integers, the polynomial rings and matrix rings as basic examples. Emphasis will be on factorization in a factorial domain. The final part of the book focuses on field extensions and Galois theory to illustrate the correspondence between Galois groups and splitting fields of separable polynomials.Three whole new chapters are added to this second edition. Group action is introduced to give a more i

There is a growing need for a more automated system of partitioning data sets into groups, or clusters. For example, digital libraries and the World Wide Web continue to grow exponentially, the ability to find useful information increasingly depends on the indexing infrastructure or search engine. Clustering techniques can be used to discover natural groups in data sets and to identify abstract structures that might reside there, without having any background knowledge of the characteristics of the data. Clustering has been used in a variety of areas, including computer vision, VLSI design, data mining, bio-informatics (gene expression analysis), and information retrieval, to name just a few. This book focuses on a few of the most important clustering algorithms, providing a detailed account of these major models in an information retrieval context. The beginning chapters introduce the classic algorithms in detail, while the later chapters describe clustering through divergences and sh

Classical logic is concerned, loosely, with the behaviour of truths. Epistemic logic similarly is about the behaviour of known or believed truths. Justification logic is a theory of reasoning that enables the tracking of evidence for statements and therefore provides a logical framework for the reliability of assertions. This book, the first in the area, is a systematic account of the subject, progressing from modal logic through to the establishment of an arithmetic interpretation of intuitionistic logic. The presentation is mathematically rigorous but in a style that will appeal to readers from a wide variety of areas to which the theory applies. These include mathematical logic, artificial intelligence, computer science, philosophical logic and epistemology, linguistics, and game theory.

Lake Governance focuses on comparative analysis of governance structures by examining policy, legal, and institutional structures of current transboundary commissions to develop a common framework for

The purpose of this book is to provide graduate students and practitioners with traditional methods and more recent results for model-based approaches in signal processing. Firstly, discrete-time line

Narrative Science examines the use of narrative in scientific research over the last two centuries. It brings together an international group of scholars who have engaged in intense collaboration to find and develop crucial cases of narrative in science. Motivated and coordinated by the Narrative Science project, funded by the European Research Council, this volume offers integrated and insightful essays examining cases that run the gamut from geology to psychology, chemistry, physics, botany, mathematics, epidemiology, and biological engineering. Taking in shipwrecks, human evolution, military intelligence, and mass extinctions, this landmark study revises our understanding of what science is, and the roles of narrative in scientists' work. This title is also available as Open Access.

In this book, first published in 1958, the social choice theorist and economist Duncan Black aims to formulate a pure science of politics. Focusing on the mathematics of committees and, accordingly, of elections, Black's writing engages with the theories of Condorcet, Borda and Laplace in order to describe the ways in which different systems of voting will yield different results. This can, as Black discusses in detail, influence whether the chosen candidate or motion is relatively agreeable to all, or only suited to the majority group of voters. Black also presents a history of the political science of elections, placing his own work within the context of earlier research and thought on this subject. Professor Black ensures that only a basic knowledge of arithmetic is needed to understand his arguments, although his methods of reasoning will be more familiar to those readers who have previously studied mathematics and economics.

Michael Powell is one of the world's foremost figures in numerical analysis. This volume, first published in 1997, is derived from invited talks given at a meeting celebrating his 60th birthday and, reflecting Powell's own achievements, focuses on innovative work in optimisation and in approximation theory. The individual papers have been written by leading authorities in their subjects and are a mix of expository articles and surveys. They have all been reviewed and edited to form a coherent volume for this important discipline within mathematics, with highly relevant applications throughout science and engineering.

Michael Powell is one of the world's foremost figures in numerical analysis. This volume, first published in 1997, is derived from invited talks given at a meeting celebrating his 60th birthday and, reflecting Powell's own achievements, focuses on innovative work in optimisation and in approximation theory. The individual papers have been written by leading authorities in their subjects and are a mix of expository articles and surveys. They have all been reviewed and edited to form a coherent volume for this important discipline within mathematics, with highly relevant applications throughout science and engineering.

Bayesian inference has become a standard method of analysis in many fields of science. Students and researchers in experimental psychology and cognitive science, however, have failed to take full advantage of the new and exciting possibilities that the Bayesian approach affords. Ideal for teaching and self study, this book demonstrates how to do Bayesian modeling. Short, to-the-point chapters offer examples, exercises, and computer code (using WinBUGS or JAGS, and supported by Matlab and R), with additional support available online. No advance knowledge of statistics is required and, from the very start, readers are encouraged to apply and adjust Bayesian analyses by themselves. The book contains a series of chapters on parameter estimation and model selection, followed by detailed case studies from cognitive science. After working through this book, readers should be able to build their own Bayesian models, apply the models to their own data, and draw their own conclusions.

Bayesian inference has become a standard method of analysis in many fields of science. Students and researchers in experimental psychology and cognitive science, however, have failed to take full advantage of the new and exciting possibilities that the Bayesian approach affords. Ideal for teaching and self study, this book demonstrates how to do Bayesian modeling. Short, to-the-point chapters offer examples, exercises, and computer code (using WinBUGS or JAGS, and supported by Matlab and R), with additional support available online. No advance knowledge of statistics is required and, from the very start, readers are encouraged to apply and adjust Bayesian analyses by themselves. The book contains a series of chapters on parameter estimation and model selection, followed by detailed case studies from cognitive science. After working through this book, readers should be able to build their own Bayesian models, apply the models to their own data, and draw their own conclusions.

The rapidly expanding area of structural graph theory uses ideas of connectivity to explore various aspects of graph theory and vice versa. It has links with other areas of mathematics, such as design theory and is increasingly used in such areas as computer networks where connectivity algorithms are an important feature. Although other books cover parts of this material, none has a similarly wide scope. Ortrud R. Oellermann (Winnipeg), internationally recognised for her substantial contributions to structural graph theory, acted as academic consultant for this volume, helping shape its coverage of key topics. The result is a collection of thirteen expository chapters, each written by acknowledged experts. These contributions have been carefully edited to enhance readability and to standardise the chapter structure, terminology and notation throughout. An introductory chapter details the background material in graph theory and network flows and each chapter concludes with an extensive

Complex Analysis with Mathematica offers a way of learning and teaching a subject that lies at the heart of many areas of pure and applied mathematics, physics, engineering and even art. This book offers teachers and students an opportunity to learn about complex numbers in a state-of-the-art computational environment. The innovative approach also offers insights into many areas too often neglected in a student treatment, including complex chaos and mathematical art. Thus readers can also use the book for self-study and for enrichment. The use of Mathematica enables the author to cover several topics that are often absent from a traditional treatment. Students are also led, optionally, into cubic or quartic equations, investigations of symmetric chaos and advanced conformal mapping. A CD is included which contains a live version of the book: in particular all the Mathematica code enables the user to run computer experiments.

Ensure a challenging mathematics experience for every learner, every day. This must-have resource offers support and encouragement for improved mathematics achievement across every grade level of your

Dimension three is an important test-bed for hypotheses in higher category theory and occupies something of a unique position in the categorical landscape. At the heart of matters is the coherence theorem, of which this book provides a definitive treatment, as well as covering related results. Along the way the author treats such material as the Gray tensor product and gives a construction of the fundamental 3-groupoid of a space. The book serves as a comprehensive introduction, covering essential material for any student of coherence and assuming only a basic understanding of higher category theory. It is also a reference point for many key concepts in the field and therefore a vital resource for researchers wishing to apply higher categories or coherence results in fields such as algebraic topology or theoretical computer science.

Deep learning on graphs has become one of the hottest topics in machine learning. The book consists of four parts to best accommodate our readers with diverse backgrounds and purposes of reading. Part 1 introduces basic concepts of graphs and deep learning; Part 2 discusses the most established methods from the basic to advanced settings; Part 3 presents the most typical applications including natural language processing, computer vision, data mining, biochemistry and healthcare; and Part 4 describes advances of methods and applications that tend to be important and promising for future research. The book is self-contained, making it accessible to a broader range of readers including (1) senior undergraduate and graduate students; (2) practitioners and project managers who want to adopt graph neural networks into their products and platforms; and (3) researchers without a computer science background who want to use graph neural networks to advance their disciplines.

This textbook is an introduction to denotational semantics and its applications to programming languages. Dr Allison emphasizes a practical approach and the student is encouraged to write and test denotational definitions. The first section is devoted to the mathematical foundations of the subject and sufficient detail is given to illustrate the fundamental problems. The remainder of the book covers the use of denotational semantics to describe sequential programming languages such as Algol, Pascal and C. Throughout, numerous exercises, usually in Pascal, will help the student practise writing definitions and carry out simple applications. The book culminates in discussing an executable semantics of the logic-programming language Prolog. Being an introduction, advanced undergraduates in computer science and graduates new to the subject will find this a readily accessible account of one of the central topics of computer science.

This book covers block pulse and related functions for the analysis and identification of continuous and discrete-time systems. It covers ‘functions related to block pulse functions’ and pulse-width m

The "Cahier" (SAM) provides support for the improvement of the student's written French through exercises that move from the discrete point, self-check variety, to the more open-ended ones, culminatin

Most texts on logic or discrete math fail to show why math and logic are fundamental tools for programmers. Program Construction illustrates the importance of math and logic to programming, providing

Technological artefacts and biological organisms 'evolve' by very similar processes of blind variation and selective retention. This analogy is explored systematically, for the first time, by a team of international experts from evolutionary biology, history and sociology of science and technology, cognitive and computer science, economics, psychology, education, cultural anthropology and research management. Do technological 'memes' play the role of genes? In what sense are novel inventions 'blind'? Does the element of design make them 'Lamarckian' rather than 'Darwinian'? Is the recombination of ideas the essence of technological creativity? Can invention be simulated computationally? What are the entities that actually evolve - artefacts, ideas or organisations? These are only some of the many questions stimulated and partially answered by this powerful metaphor. With its practical demonstration of the explanatory potential of 'evolutionary reasoning' in a well-defined context, this

Recent and ongoing developments in science and technology - such as the prevention and treatment of disease through genetics and the development of increasingly sophisticated computer systems with wide-ranging applications - hold out the promise of vastly improving the quality of human life, but they can also raise serious ethical, legal, and public policy questions. The thirteen essays in this volume address these questions and related issues from a variety of perspectives. Written by prominent philosophers, economists, and legal theorists, these essays offer valuable insights into the nature of scientific innovation and its implications for our social policies and practices.

"The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems and is an invaluable resource not only for high-school students preparing for mathematics competit

This volume brings together scholars of Mediterranean archaeology, ancient history, and complexity science to advance theoretical approaches and analytical tools for studying maritime connectivity. For the coast-hugging populations of the ancient Mediterranean, mobility and exchange depended on a distinct environment and technological parameters that created diverse challenges and opportunities, making the modeling of maritime interaction a paramount concern for understanding cultural interaction more generally. Network-inspired metaphors have long been employed in discussions of this interaction, but increasing theoretical sophistication and advances in formal network analysis now offer opportunities to refine and test the dominant paradigm of connectivity. Extending from prehistory into the Byzantine period, the case studies here reveal the potential of such network approaches. Collectively they explore the social, economic, religious, and political structures that guided Mediterrane

The new edition of a widely used introduction to game theory and its applications, with a focus on economics, business, and politics.This widely used introduction to game theory is rigorous but accessible, unique in its balance between the theoretical and the practical, with examples and applications following almost every theory-driven chapter. In recent years, game theory has become an important methodological tool for all fields of social sciences, biology and computer science. This second edition of Strategies and Games not only takes into account new game theoretical concepts and applications such as bargaining and matching, it also provides an array of chapters on game theory applied to the political arena. New examples, case studies, and applications relevant to a wide range of behavioral disciplines are now included. The authors map out alternate pathways through the book for instructors in economics, business, and political science. The book contains four parts: strategic form

Based on the author's best-selling text Aircraft Structures for Engineering Students,?this brief book covers?the basics of structural analysis as applied to aircraft structures.? Coverage of elasticit

Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematic

In online computation a computer algorithm must decide how to act on incoming items of information without any knowledge of future inputs. How should it route the next telephone call? Where in memory should it store a just-closed record? This book provides an in-depth presentation of competitive analysis, an attractive framework within which such problems can be analyzed and solved. In this framework, the quality of an algorithm is measured relative to the best possible performance of an algorithm that has complete knowledge of the future. This methodology for the analysis of online decision making has become a standard approach in computer science. Starting with the basic definitions of the competitive analysis model, the authors present most of the essential techniques through various examples, some of which are among the central problems of the field, such as list accessing, paging in a virtual memory system, routing in a communication network, metrical task systems, k-server system

This text shows how variational principles are used to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities that arise in the theory

This concise and clear text is intended for a senior undergraduate and graduate level, one-semester course on digital signal processing. Emphasis on the use of the discrete Fourier transform (the hear

This comprehensive handbook of mathematical and programming techniques for audio signal processing will be an essential reference for all computer musicians, computer scientists, engineers, and anyon

The mechanical properties of small volumes of materials such as thin films and patterned structures can be very different from the mechanical properties of those same materials in bulk. Many explanations of the mechanical behaviors of such small volumes have depended on simplified models of dislocation behavior. However, recent developments in dislocation modeling have made it possible to understand dislocation behavior in much more detail than before. A wide range of topics is presented in these proceedings, including mechanisms of plastic deformation in heteroepitaxial, multilayered and polycrystalline thin films, as well as three-dimensional mesostructures such as epitaxial islands, semiconducting devices and microcrystallites. Experimental, theoretical and numerical simulations are addressed. Topics include: dislocation and deformation mechanisms in thin metal films and multilayers; discrete dislocations - observations and simulations; dislocations and deformation mechanisms in thi

This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large deformation finite element formulation and a formulation that can efficiently solve small deformation problems that characterize very stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practising engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dy

This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large deformation finite element formulation and a formulation that can efficiently solve small deformation problems that characterize very stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practising engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dy

Quantum annealing is a new-generation tool of information technology, which helps in solving combinatorial optimization problems with high precision, based on the concepts of quantum statistical physics. Detailed discussion on quantum spin glasses and its application in solving combinatorial optimization problems is required for better understanding of quantum annealing concepts. Fulfilling this requirement, the book highlights recent development in quantum spin glasses including Nishimori line, replica method and quantum annealing methods along with the essential principles. Separate chapters on simulated annealing, quantum dynamics and classical spin models are provided for enhanced learning. Important topics including adiabatic quantum computers and quenching dynamics are discussed in detail. This text will be useful for students of quantum computation, quantum information, statistical physics and computer science.

This text introduces the basic equations of the theory of structures. Conventional presentations of these equations follow the ideas of elastic analysis, introduced nearly two hundred years ago. The book is written against the background of advances made in structural theory during the last fifty years, notably by the introduction of so-called plastic theory. The emphasis throughout is on the derivation and application of the structural equations, rather than on details of their solution (nowadays best done by computer), and the numerical examples are deliberately kept simple.

Cummings/Worley's ORGANIZATION DEVELOPMENT AND CHANGE, 12th Edition, is the most widely-used textbook in the field. It blends rigor and relevance in a comprehensive and clear presentation. The authors work from a strong evidence-based foundation to describe, in practical terms, how behavioral science knowledge can be used to help organizations develop strategies, structures and processes for superior performance, sustainability and social outcomes.

As computers proliferate and as the field of computer graphics matures, it has become increasingly important for computer scientists to understand how users perceive and interpret computer graphics. E

This book invites the reader to understand our Universe, not just marvel at it. From the clock-like motions of the planets to the catastrophic collapse of a star into a black hole, gravity controls the Universe. Gravity is central to modern physics, helping to answer the deepest questions about the nature of time, the origin of the Universe and the unification of the forces of nature. Linking key experiments and observations through careful physical reasoning, the author builds the reader's insight step-by-step from simple but profound facts about gravity on Earth to the frontiers of research. Topics covered include the nature of stars and galaxies, the mysteries of dark matter and dark energy, black holes, gravitational waves, inflation and the Big Bang. Suitable for general readers and for undergraduate courses, the treatment uses only high-school level mathematics, supplemented by optional computer programs, to explain the laws of physics governing gravity.

In this book the authors explain what computability means for data more complex than natural numbers and similar discrete data. In particular, they show how to develop a good theory of computability i