Mathematics of Discrete Structures for Computer Science

This volume contains survey papers by the invited speakers at the Conference on Semigroup Theory and Its Applications which took place at Tulane University in April, 1994. The authors represent the leading areas of research in semigroup theory and its applications, both to other areas of mathematics and to areas outside mathematics. Included are papers by Gordon Preston surveying Clifford's work on Clifford semigroups and by John Rhodes tracing the influence of Clifford's work on current semigroup theory. Notable among the areas of application are the paper by Jean-Eric Pin on applications of other areas of mathematics to semigroup theory and the paper by the editors on an application of semigroup theory to theoretical computer science and mathematical logic. All workers in semigroup theory will find this volume invaluable.

An applied, one-semester introduction to sampling methods for non-mathematics majors that uses simple numerical illustrations to provide an intuitive understanding of concepts and confirm major results. The text describes various methods for sample selection and estimation including unequal probability sampling and the prediction approach. The accompanying disk contains data files for ten cases and two computer programs- one of which is an interactive DOS program designed to serve as a tutorial by assisting the implementation of sampling formulas. The book is intended primarily for upper-level undergraduate or graduate level students of business, government, health administration, economics, political science and other social sciences. It may also be used as a main or supplementary text in service courses on sampling offered by statistics and math departments.

The book covers elementary aspects of category theory and topos theory for graduate students in mathematics, computer science, and logic; it has few mathematical prerequisites, and uses categorical me

The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it is hoped will make this volume an invaluable resource.

This book is of interest to mathematicians and computer scientists working in finite mathematics and combinatorics. It presents a breakthrough method for analyzing complex summations. Beautifully writ

This 1996 book defends the prospects for a science of society. It argues that behind the diverse methods of the natural sciences lies a common core of scientific rationality that the social sciences can and sometimes do achieve. It also argues that good social science must be in part about large-scale social structures and processes and thus that methodological individualism is misguided. These theses are supported by a detailed discussion of actual social research, including theories of agrarian revolution, organizational ecology, social theories of depression, and supply-demand explanations in economics. Professor Kincaid provides a general picture of explanation and confirmation in the social sciences and discusses the nature of scientific rationality, functional explanation, optimality arguments, meaning and interpretation, the place of microfoundations in social explanation, the status of neo-classical economics, the role of idealizations and non-experimental evidence, and other s

This 1996 book defends the prospects for a science of society. It argues that behind the diverse methods of the natural sciences lies a common core of scientific rationality that the social sciences can and sometimes do achieve. It also argues that good social science must be in part about large-scale social structures and processes and thus that methodological individualism is misguided. These theses are supported by a detailed discussion of actual social research, including theories of agrarian revolution, organizational ecology, social theories of depression, and supply-demand explanations in economics. Professor Kincaid provides a general picture of explanation and confirmation in the social sciences and discusses the nature of scientific rationality, functional explanation, optimality arguments, meaning and interpretation, the place of microfoundations in social explanation, the status of neo-classical economics, the role of idealizations and non-experimental evidence, and other s

The Navier–Stokes equations are a set of nonlinear partial differential equations comprising the fundamental dynamical description of fluid motion. They are applied routinely to problems in engineering, geophysics, astrophysics, and atmospheric science. This book is an introductory physical and mathematical presentation of the Navier–Stokes equations, focusing on unresolved questions of the regularity of solutions in three spatial dimensions, and the relation of these issues to the physical phenomenon of turbulent fluid motion. Intended for graduate students and researchers in applied mathematics and theoretical physics, results and techniques from nonlinear functional analysis are introduced as needed with an eye toward communicating the essential ideas behind the rigorous analyses.

This book is an up-to-date introduction to the quantum theory of measurement, a fast developing field of intense current interest to scientists and engineers for its potential high technology applications. It is also a subject of importance to students for its central role in the foundations of quantum mechanics. Although the main principles of the field were elaborated in the 1930s by Bohr, Schrödinger, Heisenberg, von Neumann and Mandelstam, it was not until the 1980s that technology became sufficiently advanced to allow its application in real experiments. Quantum measurement is now central to many ultra-high technology developments, such as squeezed light, single atom traps, and searches for gravitational radiation. It is also considered to have great promise for computer science and engineering, particularly for its applications in information processing and transfer. The book contains a pedagogical introduction to the relevant theory written at a level accessible to those with on

This book aims to introduce the reader to the behaviour of electrons in solids, starting with the simplest possible model, and introducing higher-level models only when the simple model is inadequate. Unlike other solid state physics texts, this book does not begin with complex crystallography, but instead builds up from the simplest possible model of a free electron in a box. The approach is to introduce the subject through its historical development, and to show how quantum mechanics is necessary for an understanding of the properties of electrons in solids. It does not treat the dynamics of the crystal lattice, but proceeds to examine the consequences of collective behaviour in the phenomena of magnetism and superconductivity. Throughout the mathematics is straightforward and uses standard notation. This text is suitable for a second or third year undergraduate course in physics, and would also be suitable for an introductory solid state course in materials science or materials chem

This book aims to introduce the reader to the behaviour of electrons in solids, starting with the simplest possible model, and introducing higher-level models only when the simple model is inadequate. Unlike other solid state physics texts, this book does not begin with complex crystallography, but instead builds up from the simplest possible model of a free electron in a box. The approach is to introduce the subject through its historical development, and to show how quantum mechanics is necessary for an understanding of the properties of electrons in solids. It does not treat the dynamics of the crystal lattice, but proceeds to examine the consequences of collective behaviour in the phenomena of magnetism and superconductivity. Throughout the mathematics is straightforward and uses standard notation. This text is suitable for a second or third year undergraduate course in physics, and would also be suitable for an introductory solid state course in materials science or materials chem

This book proposes that Philip Melanchthon was responsible for transforming traditional university natural philosophy into a specifically Lutheran one. Motivated by desire to check civil disobedience and promote a Lutheran orthodoxy, he created a natural philosophy based on Aristotle, Galen and Plato, incorporating contemporary findings of Copernicus and Vesalius. The fields of astrology, anatomy, botany and mathematics all constituted a natural philosophy in which Melanchthon wished to demonstrate God's Providential design in the physical world. Rather than dichotomizing or synthesizing the two distinct areas of 'science' and 'religion', Kusukawa advocates the need to look at 'Natural philosophy' as a discipline quite different from either 'modern science' or 'religion': a contextual assessment of the implication of the Lutheran Reformation on university education, particularly on natural philosophy.

Many of the topics in inviscid fluid dynamics are not only vitally important mechanisms in everyday life but they are also readily observable without any need for instrumentation. It is therefore stimulating when the mathematics that emerges when these phenomena are modelled is novel and suggestive of alternative methodologies. This book provides senior undergraduates who are already familiar with inviscid fluid dynamics with some of the basic facts about the modelling and analysis of viscous flows. It clearly presents the salient physical ideas and the mathematical ramifications with exercises designed to be an integral part of the text. By showing the basic theoretical framework which has developed as a result of the study of viscous flows, the book should be ideal reading for students of applied mathematics who should then be able to delve further into the subject and be well placed to exploit mathematical ideas throughout the whole of applied science.

Ergodic theory is a field that is stimulating on its own, and also in its interactions with other branches of mathematics and science. In recent years, the interchanges with harmonic analysis have been especially noticeable and productive. This book contains survey papers describing the relationship of ergodic theory with convergence, rigidity theory and the theory of joinings. These papers present the background of each area of interaction, the most outstanding results and promising lines of research. They should form perfect starting points for anyone beginning research in one of these areas. Thirteen related research papers describe the work; several treat questions arising from the Furstenberg multiple recurrence theory, while the remainder deal with convergence and a variety of other topics in dynamics.

Many of the topics in inviscid fluid dynamics are not only vitally important mechanisms in everyday life but they are also readily observable without any need for instrumentation. It is therefore stimulating when the mathematics that emerges when these phenomena are modelled is novel and suggestive of alternative methodologies. This book provides senior undergraduates who are already familiar with inviscid fluid dynamics with some of the basic facts about the modelling and analysis of viscous flows. It clearly presents the salient physical ideas and the mathematical ramifications with exercises designed to be an integral part of the text. By showing the basic theoretical framework which has developed as a result of the study of viscous flows, the book should be ideal reading for students of applied mathematics who should then be able to delve further into the subject and be well placed to exploit mathematical ideas throughout the whole of applied science.

Sir Arthur Eddington, the celebrated astrophysicist, made great strides towards his own 'theory of everything' in his last two books published in 1936 and 1946. Unlike his earlier lucid and authoritative works, these are strangely tentative and obscure - as if he were nervous of the significant advances that he might be making. This 1995 volume examines both how Eddington came to write these uncharacteristic books - in the context of the physics and history of the day - and what value they have to modern physics. The result is an illuminating description of the development of theoretical physics, in the first half of the twentieth century, from a unique point of view: how it affected Eddington's thought. This will provide fascinating reading for scholars in the philosophy of science, theoretical physics, applied mathematics and the history of science.

This is a first course in propositional modal logic, suitable for mathematicians, computer scientists and philosophers. Emphasis is placed on semantic aspects, in the form of labelled transition structures, rather than on proof theory. The book covers all the basic material - propositional languages, semantics and correspondence results, proof systems and completeness results - as well as some topics not usually covered in a modal logic course. It is written from a mathematical standpoint. To help the reader, the material is covered in short chapters, each concentrating on one topic. These are arranged into five parts, each with a common theme. An important feature of the book is the many exercises and an extensive set of solutions is provided.

With an approach that stresses the fundamental solid state behaviour of minerals, and with emphasis on both theory and experiment, this 1995 text surveys the physics and chemistry of earth materials. It starts with a systematic tour of crystal chemistry of both simple and complex structures (with completely new structural drawings) and discusses how structural and thermodynamic information is obtained experimentally. The quantitative concepts of chemical bonding - band theory, molecular orbit and ionic models - are reviewed. The book goes on to discuss physical properties and to relate microscopic features to macroscopic thermodynamic behaviour. The book then discusses high pressure phase transitions, amorphous materials and solid state reactions, and concludes with a look at the interface between mineral physics and materials science. Highly illustrated throughout, this book fills the gap between undergraduate texts and specialised review volumes, for students in earth sciences and ma

This collection of essays is on the relation between probabilities, especially conditional probabilities, and conditionals. It provides negative results which sharply limit the ways conditionals can be related to conditional probabilities. There are also positive ideas and results which will open up areas of research. The collection is intended to honour Ernest W. Adams, whose seminal work is largely responsible for creating this area of inquiry. As well as describing, evaluating, and applying Adams's work the contributions extend his ideas in directions he may or may not have anticipated, but that he certainly inspired. In addition to a wide range of philosophers of science, the volume should interest computer scientists and linguists.

With an approach that stresses the fundamental solid state behaviour of minerals, and with emphasis on both theory and experiment, this 1995 text surveys the physics and chemistry of earth materials. It starts with a systematic tour of crystal chemistry of both simple and complex structures (with completely new structural drawings) and discusses how structural and thermodynamic information is obtained experimentally. The quantitative concepts of chemical bonding - band theory, molecular orbit and ionic models - are reviewed. The book goes on to discuss physical properties and to relate microscopic features to macroscopic thermodynamic behaviour. The book then discusses high pressure phase transitions, amorphous materials and solid state reactions, and concludes with a look at the interface between mineral physics and materials science. Highly illustrated throughout, this book fills the gap between undergraduate texts and specialised review volumes, for students in earth sciences and ma

This book is about abduction, 'the logic of Sherlock Holmes', and about how some kinds of abductive reasoning can be programmed in a computer. The work brings together Artificial Intelligence and philosophy of science and is rich with implications for other areas such as, psychology, medical informatics, and linguistics. It also has subtle implications for evidence evaluation in areas such as accident investigation, confirmation of scientific theories, law, diagnosis, and financial auditing. The book is about certainty and the logico-computational foundations of knowledge; it is about inference in perception, reasoning strategies, and building expert systems.

Psychology is now ready for unified theories of cognition--so says Allen Newell, a leading investigator in computer science and cognitive psychology. Not everyone will agree on a single set of mechani

The concepts of a locally presentable category and an accessible category have turned out to be useful in formulating connections between universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the applications of these categories at a level accessible to graduate students. Firstly the properties of l-presentable objects, locally l-presentable categories, and l-accessible categories are discussed in detail, and the equivalence of accessible and sketchable categories is proved. The authors go on to study categories of algebras and prove that Freyd's essentially algebraic categories are precisely the locally presentable categories. In the final chapters they treat some topics in model theory and some set theoretical aspects. For researchers in category theory, algebra, computer science, and model theory, this book will be a necessary purchase.

Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theore

A textbook for sophomores and juniors in engineering, science, mathematics, and computer science, or sourcebook for practicing engineers and scientists who need to use numerical analysis to solve prob

Situation theory is the result of an interdisciplinary effort to create a full-fledged theory of information. Created by scholars and scientists from cognitive science, computer science and AI, lingui

These notes are based on a series of lectures given at the Advanced Research Institute of Discrete Applied Mathematics held at Rutgers University. Their aim is to link together algorithmic problems arising in knot theory, statistical physics and classical combinatorics. Apart from the theory of computational complexity concerned with enumeration problems, introductions are given to several of the topics treated, such as combinatorial knot theory, randomised approximation algorithms, percolation and random cluster models. To researchers in discrete mathematics, computer science and statistical physics, this book will be of great interest, but any non-expert should find it an appealing guide to a very active area of research.

Professor Colin Blakemore presents a fascinating insight to all the major topics in visual science research. Experts from around the world show how this vast subject can be unified from the viewpoint that describes the way in which visual systems efficiently encode and represent the outside world. The approach, which is both rigorous and general, was championed by H. B. Barlow in the fifties and has recently acquired a new significance in the light of exciting developments in computer science and artificial intelligence and vision. The book is essential reading for advanced undergraduates, postgraduates and researchers in the field of vision research and neuroscience.

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

A thorough review of general mathematics and its applications in radiography as well as a handy reference for basic formulas and calculations used by radiographers. This book starts with basic mathem

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.

This book is an up-to-date introduction to the quantum theory of measurement, a fast developing field of intense current interest to scientists and engineers for its potential high technology applications. It is also a subject of importance to students for its central role in the foundations of quantum mechanics. Although the main principles of the field were elaborated in the 1930s by Bohr, Schrödinger, Heisenberg, von Neumann and Mandelstam, it was not until the 1980s that technology became sufficiently advanced to allow its application in real experiments. Quantum measurement is now central to many ultra-high technology developments, such as squeezed light, single atom traps, and searches for gravitational radiation. It is also considered to have great promise for computer science and engineering, particularly for its applications in information processing and transfer. The book contains a pedagogical introduction to the relevant theory written at a level accessible to those with on

This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour. The authors' treatment of transitions to chaos, the theory of stochastic layers and webs, and the numerous applications of this theory, particularly to pattern symmetry, will make the book of importance to scientists from many disciplines.The authors have been meticulous in providing a detailed presentation of the material, enabling the reader to learn the necessary computational methods and to apply them in other problems. The inclusion of a significant amount of computer graphics is also an important aid to understanding. The final section of the book contains a fascinating collection of patterns in art and living nature. The book will be of interest to graduate students and researchers in physics and mathematics who

This textbook is designed as a first book on concurrent programming for computer science undergraduates, and provides a comprehensive introduction to the problems of concurrency. Concurrency is of vital importance in many areas of computer science, particularly in operating systems. It is also increasingly being taught in undergraduate courses. The book builds on the student's familiarity with sequential programming in a high level language, which will make it very accessible to computer science students. The book is concerned mainly with the high level aspects of concurrency, which will be equally applicable to traditional time sliced or more recent truly parallel systems.

Textbook for undergraduate or beginning graduate students in mathematics, science, or engineering presents ideas and examples about the geometry of dynamics and bifurcations of ordinary differential a

This book is an introduction, for mathematics students, to the theories of information and codes. They are usually treated separately but, as both address the problem of communication through noisy channels (albeit from different directions), the authors have been able to exploit the connection to give a reasonably self-contained treatment, relating the probabilistic and algebraic viewpoints. The style is discursive and, as befits the subject, plenty of examples and exercises are provided. Some examples and exercises are provided. Some examples of computer codes are given to provide concrete illustrations of abstract ideas.

There has recently been a rapid growth of activity in nonlinear optics. Effects such as frequency doubling, stimulated Raman scattering, phase conjugation and solitons are of great interest both for their fundamental properties and their many important applications in science and engineering. It is mainly these applications - especially in telecommunications and information processing - that have stimulated the recent surge of activity. This book is a self contained account of the most important principles of nonlinear optics. Assuming only a familiarity with basic mathematics, the fundamentals of nonlinear optics are fully developed from basic concepts. The essential quantum mechanical apparatus is introduced and explained. In later chapters the underlying ideas are illustrated by discussing particular experimental configurations and materials. This book will be an invaluable introduction to the field for beginning graduates in physics or engineering, and will provide an excellent ov

This 1991 volume contains the proceedings of the first international workshop on Logical Frameworks. The contributions are concerned with the application of logical reasoning and proof theory in computer science and its relevance to automatic theorem proving, and consequently topics such as artificial intelligence. It is the only source for much of this material and will be a necessary purchase for mathematicians and computer scientists undertaking research at the interface of logic and software engineering.

This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour. The authors' treatment of transitions to chaos, the theory of stochastic layers and webs, and the numerous applications of this theory, particularly to pattern symmetry, will make the book of importance to scientists from many disciplines.The authors have been meticulous in providing a detailed presentation of the material, enabling the reader to learn the necessary computational methods and to apply them in other problems. The inclusion of a significant amount of computer graphics is also an important aid to understanding. The final section of the book contains a fascinating collection of patterns in art and living nature. The book will be of interest to graduate students and researchers in physics and mathematics who

Written in an appealing and informal style, this text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics, operations research, computer science, econometrics and mathematical economics. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a cookbook approach, giving concrete and geometric explanations, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interest is in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided.