Design Structure Matrix Methods and Applications

Applied Nonparametric Regression is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable. The computer and the development of interactive graphics programs have made curve estimation possible. This volume focuses on the applications and practical problems of two central aspects of curve smoothing: the choice of smoothing parameters and the construction of confidence bounds. Härdle argues that all smoothing methods are based on a local averaging mechanism and can be seen as essentially equivalent to kernel smoothing. To simplify the exposition, kernel smoothers are introduced and discussed in great detail. Building on this exposition, various other smoothing methods (among them splines and orthogonal polynomials) are presented and their merits discussed. All the methods presented can be understood on an intuitive level; however, exercises and supplemental materials are provided for those readers desiring a deeper un

This textbook is a follow-up to the volume Principles of Engineering Physics 1 and aims for an introductory course in engineering physics. It provides a balance between theoretical concepts and their applications. Fundamental concepts of crystal structure including lattice directions and planes, atomic packing factor, diffraction by crystal, reciprocal lattics and intensity of diffracted beam are extensively discussed in the book. The book also covers topics related to superconductivity, optoelectronic devices, dielectric materials, semiconductors, electron theory of solids and energy bands in solids. The text is written in a logical and coherent manner for easy understanding by students. Emphasis has been given to an understanding of the basic concepts and their applications to a number of engineering problems. Each topic is discussed in detail both conceptually and mathematically, so that students will not face comprehension difficulties. Derivations and solved problems are provided

In a boundary-crossing and globalizing world, the personal and social positions in self and identity become increasingly dense, heterogeneous and even conflicting. In this handbook scholars of different disciplines, nations and cultures (East and West) bring together their views and applications of dialogical self theory in such a way that deeper commonalities are brought to the surface. As a 'bridging theory', dialogical self theory reveals unexpected links between a broad variety of phenomena, such as self and identity problems in education and psychotherapy, multicultural identities, child-rearing practices, adult development, consumer behaviour, the use of the internet and the value of silence. Researchers and practitioners present different methods of investigation, both qualitative and quantitative, and also highlight applications of dialogical self theory.

In a boundary-crossing and globalizing world, the personal and social positions in self and identity become increasingly dense, heterogeneous and even conflicting. In this handbook scholars of different disciplines, nations and cultures (East and West) bring together their views and applications of dialogical self theory in such a way that deeper commonalities are brought to the surface. As a 'bridging theory', dialogical self theory reveals unexpected links between a broad variety of phenomena, such as self and identity problems in education and psychotherapy, multicultural identities, child-rearing practices, adult development, consumer behaviour, the use of the internet and the value of silence. Researchers and practitioners present different methods of investigation, both qualitative and quantitative, and also highlight applications of dialogical self theory.

This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality,

Now in paperback, this book provides an overview of the physics of condensed matter systems. Assuming a familiarity with the basics of quantum mechanics and statistical mechanics, the book establishes a general framework for describing condensed phases of matter, based on symmetries and conservation laws. It explores the role of spatial dimensionality and microscopic interactions in determining the nature of phase transitions, as well as discussing the structure and properties of materials with different symmetries. Particular attention is given to critical phenomena and renormalization group methods. The properties of liquids, liquid crystals, quasicrystals, crystalline solids, magnetically ordered systems and amorphous solids are investigated in terms of their symmetry, generalised rigidity, hydrodynamics and topological defect structure. In addition to serving as a course text, this book is an essential reference for students and researchers in physics, applied physics, chemistry, m

Efficient signal processing algorithms are important for embedded and power-limited applications since, by reducing the number of computations, power consumption can be reduced significantly. Similarly, efficient algorithms are also critical to very large scale applications such as video processing and four-dimensional medical imaging. This self-contained guide, the only one of its kind, enables engineers to find the optimum fast algorithm for a specific application. It presents a broad range of computationally-efficient algorithms, describes their structure and implementation, and compares their relative strengths for given problems. All the necessary background mathematics is included and theorems are rigorously proved, so all the information needed to learn and apply the techniques is provided in one convenient guide. With this practical reference, researchers and practitioners in electrical engineering, applied mathematics, and computer science can reduce power dissipation for low-

Artificial intelligence (AI) stands out as a transformational technology of the digital age. Its practical applications are growing very rapidly. One of the chief reasons AI applications are attaining prominence, is in its design to learn continuously, from real-world use and experience, and its capability to improve its performance.It is no wonder that the applications of AI span from complex high-technology equipment manufacturing to personalized exclusive recommendations to end-users. Many deployments of AI software, given its continuous learning need, require computation platforms that are resource intense, and have sustained connectivity and perpetual power through central electrical grid. In order to harvest the benefits of AI revolution to all of humanity, traditional AI software development paradigms must be upgraded to function effectively in environments that have resource constraints, small form factor computational devices with limited power, devices with intermittent or no

This book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail. The author demonstrates how new ideas lead to significant progress in two main applications: the solution of invariant ordinary differential equations and the structure of Euler-Lagrange equations and conservation laws of variational problems. The expository language used here is primarily that of undergraduate calculus rather than differential geometry, making the topic more accessible to a student audience. More sophisticated ideas from differential topology and Lie theory are explained from scratch using illustrative examples and exercises. This book is ideal for graduate students and researchers working in differential equations, symbolic computation, applications of Lie groups and, to

This book provides a first course on quantum mechanics and describes simple applications to physical phenomena that are of immediate and everyday interest. The first five chapters introduce the fundamentals of quantum mechanics and are followed by a revision quiz with which readers may test their understanding. The remaining chapters describe applications, including the physics of lasers, molecular binding, simple properties of crystalline solids arising from their band structure, and the operation of junction transistors. This new edition (first edition entitled Simple Quantum Physics) has been expanded to include a chapter on the theory of spin and its application to magnetic resonance imaging, as well as a description of the WKB approximation and its application to alpha decay. Ideal either as a course text or a self-study text, the book contains nearly 100 exercises and hints to their solution.

There has been an explosion of interest in the study of molecular crystals, and their applications in optics and electronics. This advanced 1994 textbook describes their chemical and physical structure, their optical and electronic properties and the reactions between neighbouring molecules in crystals. The author has taken into account research areas which have undergone extremely rapid development since the first edition was published in 1987. For instance, this edition features the applications of molecular materials in high-technology devices. There is also an additional chapter on C60 and organic non-linear optic materials. The level of treatment is aimed at first-year postgraduates or workers in industrial research laboratories wishing to gain insights into organic solid state materials. Molecular Crystals is also suitable for special topics in final year undergraduate courses in chemistry, physics and electronic engineering.

There has been an explosion of interest in the study of molecular crystals, and their applications in optics and electronics. This advanced 1994 textbook describes their chemical and physical structure, their optical and electronic properties and the reactions between neighbouring molecules in crystals. The author has taken into account research areas which have undergone extremely rapid development since the first edition was published in 1987. For instance, this edition features the applications of molecular materials in high-technology devices. There is also an additional chapter on C60 and organic non-linear optic materials. The level of treatment is aimed at first-year postgraduates or workers in industrial research laboratories wishing to gain insights into organic solid state materials. Molecular Crystals is also suitable for special topics in final year undergraduate courses in chemistry, physics and electronic engineering.

On-line learning is one of the most powerful and commonly used techniques for training large layered networks and has been used successfully in many real-world applications. Traditional analytical methods have been recently complemented by ones from statistical physics and Bayesian statistics. This powerful combination of analytical methods provides more insight and deeper understanding of existing algorithms and leads to novel and principled proposals for their improvement. This book presents a coherent picture of the state-of-the-art in the theoretical analysis of on-line learning. An introduction relates the subject to other developments in neural networks and explains the overall picture. Surveys by leading experts in the field combine new and established material and enable non-experts to learn more about the techniques and methods used. This book, the first in the area, provides a comprehensive view of the subject and will be welcomed by mathematicians, scientists and engineers,

On-line learning is one of the most powerful and commonly used techniques for training large layered networks and has been used successfully in many real-world applications. Traditional analytical methods have been recently complemented by ones from statistical physics and Bayesian statistics. This powerful combination of analytical methods provides more insight and deeper understanding of existing algorithms and leads to novel and principled proposals for their improvement. This book presents a coherent picture of the state-of-the-art in the theoretical analysis of on-line learning. An introduction relates the subject to other developments in neural networks and explains the overall picture. Surveys by leading experts in the field combine new and established material and enable non-experts to learn more about the techniques and methods used. This book, the first in the area, provides a comprehensive view of the subject and will be welcomed by mathematicians, scientists and engineers,

This book is an introduction to the physics of highly excited, easily perturbed or interacting atoms. The book begins with a brief introduction to the traditional view of electron shells and their properties, and then goes on to discuss Rydberg states, quantum defect theory, atomic f-values, centrifugal barrier effects, autoionisation, inner shell and double excitation spectra, K-matrix theory, atoms in high laser fields, statistical methods, quantum chaos, and atomic effects in solids. The emphasis is throughout on radial properties, orbital collapse, many body effects, the breakdown of the independent particle approach, the emergence of chaos, and the behaviour of atoms inside clusters and solids. A very full account of autoionisation includes not only the standard treatment for isolated resonances, but also several alternative approaches. The book discusses many experimental examples and has many diagrams and a comprehensive reference list.

This introduction to dimensional analysis covers the methods, history and formalisation of the field, and provides physics and engineering applications. Covering topics from mechanics, hydro- and electrodynamics to thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis. Introducing basic physics and fluid engineering topics through the mathematical methods of dimensional analysis, this book is perfect for students in physics, engineering and mathematics. Explaining potentially unfamiliar concepts such as viscosity and diffusivity, the text includes worked examples and end-of-chapter problems with answers provided in an accompanying appendix, which help make it ideal for self-study. Long-standing methodological problems arising in popular presentations of dimensional analysis are also identified and solved, making the book a useful text for advanced students and professionals.

This introduction to dimensional analysis covers the methods, history and formalisation of the field, and provides physics and engineering applications. Covering topics from mechanics, hydro- and electrodynamics to thermal and quantum physics, it illustrates the possibilities and limitations of dimensional analysis. Introducing basic physics and fluid engineering topics through the mathematical methods of dimensional analysis, this book is perfect for students in physics, engineering and mathematics. Explaining potentially unfamiliar concepts such as viscosity and diffusivity, the text includes worked examples and end-of-chapter problems with answers provided in an accompanying appendix, which help make it ideal for self-study. Long-standing methodological problems arising in popular presentations of dimensional analysis are also identified and solved, making the book a useful text for advanced students and professionals.

How and why do languages change? This new introduction offers a guide to the types of change at all levels of linguistic structure, as well as the mechanisms behind each type. Based on data from a variety of methods and a huge array of language families, it examines general patterns of change, bringing together recent findings on sound change, analogical change, grammaticalization, the creation and change of constructions, as well as lexical change. Emphasizing crosslinguistic patterns and going well beyond traditional methods in historical linguistics, this book sees change as grounded in cognitive processes and usage factors that are rarely mentioned in other textbooks. Complete with questions for discussion, suggested readings and a useful glossary of terms, this book helps students to gain a general understanding of language as an ever-changing system.

How and why do languages change? This new introduction offers a guide to the types of change at all levels of linguistic structure, as well as the mechanisms behind each type. Based on data from a variety of methods and a huge array of language families, it examines general patterns of change, bringing together recent findings on sound change, analogical change, grammaticalization, the creation and change of constructions, as well as lexical change. Emphasizing crosslinguistic patterns and going well beyond traditional methods in historical linguistics, this book sees change as grounded in cognitive processes and usage factors that are rarely mentioned in other textbooks. Complete with questions for discussion, suggested readings and a useful glossary of terms, this book helps students to gain a general understanding of language as an ever-changing system.

In this 1987 text Professor Jech gives a unified treatment of the various forcing methods used in set theory, and presents their important applications. Product forcing, iterated forcing and proper forcing have proved powerful tools when studying the foundations of mathematics, for instance in consistency proofs. The book is based on graduate courses though some results are also included, making the book attractive to set theorists and logicians.

In this 1987 text Professor Jech gives a unified treatment of the various forcing methods used in set theory, and presents their important applications. Product forcing, iterated forcing and proper forcing have proved powerful tools when studying the foundations of mathematics, for instance in consistency proofs. The book is based on graduate courses though some results are also included, making the book attractive to set theorists and logicians.

The notion of an (∞,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many different approaches to this structure, all of them equivalent, and each with its corresponding homotopy theory. This book provides a relatively self-contained source of the definitions of the different models, the model structure (homotopy theory) of each, and the equivalences between the models. While most of the current literature focusses on how to extend category theory in this context, and centers in particular on the quasi-category model, this book offers a balanced treatment of the appropriate model structures for simplicial categories, Segal categories, complete Segal spaces, quasi-categories, and relative categories, all from a homotopy-theoretic perspective. Introductory chapters provide background in both homotopy and category theory and contain many references to the literature, thus making the book accessible to graduates and to resea

The notion of an (∞,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many different approaches to this structure, all of them equivalent, and each with its corresponding homotopy theory. This book provides a relatively self-contained source of the definitions of the different models, the model structure (homotopy theory) of each, and the equivalences between the models. While most of the current literature focusses on how to extend category theory in this context, and centers in particular on the quasi-category model, this book offers a balanced treatment of the appropriate model structures for simplicial categories, Segal categories, complete Segal spaces, quasi-categories, and relative categories, all from a homotopy-theoretic perspective. Introductory chapters provide background in both homotopy and category theory and contain many references to the literature, thus making the book accessible to graduates and to resea

This is a self-contained exposition of general relativity with emphasis given to tetrad and spinor structures and physical measurements on curved manifolds. General relativity is now essential to the understanding of modern physics, but the power of the theory cannot be fully explained without a detailed knowledge of its mathematical structure. The aim of this book is to introduce this structure, and then to use it to develop those applications that have been central to the growth of the theory. An overview of differential geometry is provided and properties of a tetrad field are then extensively analysed. These are used to introduce spinors, to describe the geometry of congruences and define the physical measurements on a curved manifold. The coupling of fields and geometry is investigated in terms of Lagrangeans and a detailed discussion of some exact solutions of the Einstein equations are provided.

This is a self-contained exposition of general relativity with emphasis given to tetrad and spinor structures and physical measurements on curved manifolds. General relativity is now essential to the understanding of modern physics, but the power of the theory cannot be fully explained without a detailed knowledge of its mathematical structure. The aim of this book is to introduce this structure, and then to use it to develop those applications that have been central to the growth of the theory. An overview of differential geometry is provided and properties of a tetrad field are then extensively analysed. These are used to introduce spinors, to describe the geometry of congruences and define the physical measurements on a curved manifold. The coupling of fields and geometry is investigated in terms of Lagrangeans and a detailed discussion of some exact solutions of the Einstein equations are provided.

Understanding the structural unit of crystalline solids is vital in determining their optical and electronic properties. However, the disordered nature of amorphous semiconductors, where no long-range order is retained, makes it difficult to determine their structure using traditional methods. This book shows how computer modelling can be used to overcome the difficulties that arise in the atomic scale identification of amorphous semiconductors. The book explains how to generate a random structure using computer modelling, providing readers with the techniques to construct realistic material structures. It shows how the optical and electronic properties are related to random structures. Readers will be able to understand the characteristic features of disordered semiconductors. The structural and electronic modifications by photon irradiation are also discussed in detail. This book is ideal for both physicists and engineers working in solid state physics, semiconductor engineering and

An increase in the use of composite materials in areas of engineering has led to a greater demand for engineers versed in the design of structures made from such materials. This book offers students and engineers tools for designing practical composite structures. Among the topics of interest to the designer are stress-strain relationships for a wide range of anisotropic materials; bending, buckling, and vibration of plates; bending, torsion, buckling, and vibration of solid as well as thin walled beams; shells; hygrothermal stresses and strains; finite element formulation; and failure criteria. More than 300 illustrations, 50 fully worked problems, and material properties data sets are included. Some knowledge of composites, differential equations, and matrix algebra is helpful but not necessary, as the book is self-contained. Graduate students, researchers, and practitioners will value it for both theory and application.

An increase in the use of composite materials in areas of engineering has led to a greater demand for engineers versed in the design of structures made from such materials. This book offers students and engineers tools for designing practical composite structures. Among the topics of interest to the designer are stress-strain relationships for a wide range of anisotropic materials; bending, buckling, and vibration of plates; bending, torsion, buckling, and vibration of solid as well as thin walled beams; shells; hygrothermal stresses and strains; finite element formulation; and failure criteria. More than 300 illustrations, 50 fully worked problems, and material properties data sets are included. Some knowledge of composites, differential equations, and matrix algebra is helpful but not necessary, as the book is self-contained. Graduate students, researchers, and practitioners will value it for both theory and application.

Input-output analysis is the main tool of applied equilibrium analysis. This textbook provides a systematic survey of the most recent developments in input-output analysis and their applications, helping us to examine questions such as: which industries are competitive? What are the multiplier effects of an investment program? How do environmental restrictions impact on prices? Linear programming and national accounting are introduced and used to resolve issues such as the choice of technique, the comparative advantage of a national economy, its efficiency and dynamic performance. Technological and environmental spillovers are analysed, both at the national level (between industries) and the international level (the measurement of globalisation effects). The book is self-contained, but assumes some familiarity with calculus, matrix algebra, and the microeconomic principle of optimizing behaviour. Exercises and review questions are included at the end of each chapter, and solutions at t

Personality is now understood to be a function of both biological and environmental influences. This revised and updated edition of Psychobiology of Personality describes what is currently known about the biological basis of the primary personality traits, including genetic, neurological, biochemical, physiological, and behavioral influences. Emphasis is placed on understanding the connections between phenomena at these levels. The research discussed makes use of animal models, based on experimental brain research, as well as human clinical and normal personality research. Chapters are devoted to temperament and personality trait structure, psychobiological methods, and each of four major personality traits: extraversion, impulsive, sensation seeking, and aggression. Recent advances in psychobiological methods, such as molecular genetics and brain imaging have enabled us to begin to unravel the genetic and neurological sources of behavior and personality. These advances are discussed i

Personality is now understood to be a function of both biological and environmental influences. This revised and updated edition of Psychobiology of Personality describes what is currently known about the biological basis of the primary personality traits, including genetic, neurological, biochemical, physiological, and behavioral influences. Emphasis is placed on understanding the connections between phenomena at these levels. The research discussed makes use of animal models, based on experimental brain research, as well as human clinical and normal personality research. Chapters are devoted to temperament and personality trait structure, psychobiological methods, and each of four major personality traits: extraversion, impulsive, sensation seeking, and aggression. Recent advances in psychobiological methods, such as molecular genetics and brain imaging have enabled us to begin to unravel the genetic and neurological sources of behavior and personality. These advances are discussed i

This 1961 book presents a concise and systematic treatment of two-dimensional subsonic, inviscid fluid motion and its aeronautical applications. Part I surveys the relevant fluid dynamics, assuming only a basic knowledge of the topic. In Part II, the methods of conformal mapping and Cauchy integrals are developed, on the assumption that the reader has only an elementary understanding of complex variable theory; this will be of interest to a wide range of applied mathematicians and engineers. In Part III, the methods are applied to several problems in fluid mechanics and aero dynamics. The text provides an extensive account of mixed boundary-value problems and treats such examples of these problems as occur in ventilated wind-tunnel theory, jet-flap theory and unsteady Hemholtz motions.

The renowned mathematician and educator Gilbert Strang presents a collection of expository papers on the theory and applications of linear algebra, accompanied by video lectures on http://ocw.mit.edu. The essays are diverse in scope and range from purely theoretical studies on deep fundamental principles of matrix algebra to discussions on the teaching of calculus and an examination of the mathematical foundations of aspects of computational engineering. One thing these essays have in common is the way that they express both the importance and the beauty of the subject, as well as the author's passion for mathematics. This text will be of practical use to students and researchers across a whole spectrum of numerate disciplines. Furthermore, this collection provides a unique perspective on mathematics and the communication thereof as a human endeavour, complemented as these essays are by commentary from the author regarding their provenance and the reaction to them.

Recent advances in dynamics, with wide applications throughout the sciences and engineering, have meant that a new approach to the subject is needed. Furthermore, the mathematical and scientific background of students has changed in recent years. In this book, the subject of dynamics is introduced at undergraduate level through the elementary qualitative theory of differential equations, the geometry of phrase curves and the theory of stability. Each subject, from the most elementary topic to some important discoveries of recent decades, is introduced through simple examples and illustrated with many diagrams. The text is supplemented with over a hundred exercises. The examples and exercises cover subjects as diverse as mechanics and population dynamics. The mathematical background required of the reader is an understanding of the elementary theory of differential equations and matrix arithmetic. The book will be of interest to second-year and third-year undergraduates at universities,

The third edition of this successful textbook is fully updated and includes important recent developments in cosmology. It begins with an introduction to cosmology and general relativity, and goes on to cover the mathematical models of standard cosmology. The physical aspects of cosmology, including primordial nucleosynthesis, the astroparticle physics of inflation, and the current ideas on structure formation are discussed. Alternative models of cosmology are reviewed, including the model of Quasi-Steady State Cosmology, which has recently been proposed as an alternative to Big Bang Cosmology. The final chapters discuss observational cosmology, and debate theory versus observational methods. The book includes 400 problems and numerous worked examples. This introductory textbook describes modern cosmology at a level suitable for advanced undergraduates and graduates who are familiar with mathematical methods and basic theoretical physics. It is intended for use on courses in theoretic

This book presents the concepts, methods and applications of kinetic theory to rarefied gas dynamics. After introducing the basic tools, problems in plane geometry are treated using approximation techniques (perturbation and numerical methods). These same techniques are later used to deal with two- and three-dimensional problems. The models include not only monatomic but also polyatomic gases, mixtures, chemical reactions. A special chapter is devoted to evaporation and condensation phenomena. Each section is accompanied by problems which are mainly intended to demonstrate the use of the material in the text and to outline additional subjects, results and equations. This will help ensure that the book can be used for a range of graduate courses in aerospace engineering or applied mathematics.

This book presents the concepts, methods and applications of kinetic theory to rarefied gas dynamics. After introducing the basic tools, problems in plane geometry are treated using approximation techniques (perturbation and numerical methods). These same techniques are later used to deal with two- and three-dimensional problems. The models include not only monatomic but also polyatomic gases, mixtures, chemical reactions. A special chapter is devoted to evaporation and condensation phenomena. Each section is accompanied by problems which are mainly intended to demonstrate the use of the material in the text and to outline additional subjects, results and equations. This will help ensure that the book can be used for a range of graduate courses in aerospace engineering or applied mathematics.

Written in an easy-to-follow approach, the text will help the readers to understand the techniques and applications of image fusion for remotely sensed multi-spectral images. It covers important multi-resolution fusion concepts along with the state-of-the-art methods including super resolution and multi stage guided filters. It includes in depth analysis on degradation estimation, Gabor Prior and Markov Random Field (MRF) Prior. Concepts such as guided filter and difference of Gaussian are discussed comprehensively. Novel techniques in multi-resolution fusion by making use of regularization are explained in detail. It also includes different quality assessment measures used in testing the quality of fusion. Real-life applications and plenty of multi-resolution images are provided in the text for enhanced learning.

Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology

Oriented matroids play the role of matrices in discrete geometry, when metrical properties, such as angles or distances, are neither required nor available. Thus they are of great use in such areas as graph theory, combinatorial optimization and convex geometry. The variety of applications corresponds to the variety of ways they can be defined. Each of these definitions corresponds to a differing data structure for an oriented matroid, and handling them requires computational support, best realised through a functional language. Haskell is used here, and, for the benefit of readers, the book includes a primer on it. The combination of concrete applications and computation, the profusion of illustrations, many in colour, and the large number of examples and exercises make this an ideal introductory text on the subject. It will also be valuable for self-study for mathematicians and computer scientists working in discrete and computational geometry.