Mathematics of Discrete Structures for Computer Science

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.

The theory of modular forms and especially the so-called 'Ramanujan Conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory. This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these applications. In order to keep the presentation reasonably self-contained, Professor Sarnak begins by developing the necessary background material in modular forms. He then considers the solution of three problems: the Ruziewicz problem concerning finitely additive rotationally invariant measures on the sphere; the explicit construction of highly connected but sparse graphs: 'expander graphs' and 'Ramanujan graphs'; and the Linnik problem concerning the distribution of integers that represent a given large integer as a sum of three squares. These applications are carried out in detail. The book therefore should be accessible to a wide audience of graduate students and researchers in mathematics

This interpretation of the impact of slavery on African life emphasizes the importance of external demand for slaves - from Occidental and Oriental purchasers - in developing an active trade in slaves within Africa. The book summarizes a wide range of recent literature on slavery for all of tropical Africa. It analyzes the demography, economics, social structure, and ideology of slavery in Africa from the beginning of large-scale exports in the seventeenth century to the gradual elimination of slavery in the twentieth century. While the book is primarily a general survey, it presents interesting research and analysis, especially in the author's demographic model, computer simulation of the slave trade, and analysis of slave prices. The demographic, economic, and social analyses are carefully introduced, so that the book may serve not only as a general introduction to African slavery for an undergraduate audience, but as a primer on interdisciplinary application of social science method

It has long been clear that the way in which people interpret the world affects our emotional reactions. What has been less clear is exactly how such different interpretations lead to different emotions. This is the central question addressed by The Cognitive Structure of Emotions. Taking a cognitive science perspective, a systematic account is presented of the cognitive structures that underlie a wide range of different emotions. Detailed proposals about the factors that affect intensity are also offered. The authors propose three broad classes of emotions, each corresponding to a different attentional focus. One class consists of reactions to events, one of reactions to the actions of agents, and one of reactions to objects. By basing their analysis of the antecedents of emotions on an analysis of the perceived situational conditions that elicit them, the authors offer the prospect of accounting for variations in the emotions of different individuals, different cultures, and perhaps

Wiley-Interscience Series in Discrete Mathematics and Optimization AdvisoryEditors: Ronald L. Graham, Jan Karel Lenstra, and Robert E. TarjanDiscrete mathematics, the study of finite structures, is on

This is an introduction to the field of efficient parallel algorithms and to the techniques for efficient parallelisation. It is self-contained and presumes no special knowledge of parallel computers or particular mathematics. The book emphasises designing algorithms within the timeless and abstracted context of a high-level programming language rather than within highly specific computer architectures. This is an approach which concentrates on the essence of algorithmic theory, determining and taking advantage of the inherently parallel nature of certain types of problem. The authors present regularly-used techniques and a range of algorithms which includes some of the more celebrated and well-known. Efficient Parallel Algorithms is targeted at non-specialists who are considering entering the field of parallel algorithms. It will be particularly useful for courses aimed at advanced undergraduate or new postgraduate students of computer science and mathematics.

This 1989 book is about chaos, fractals and complex dynamics, and is addressed to all people who have some familiarity with computers and enjoy using them. The mathematics has been kept simple, with few formulae, yet the reader is introduced to and can learn about an area of current scientific research which was scarcely possible before the availability of computers. The introduction is achieved through the extensive use of computer graphics. The book is divided into two main parts: in the first the most interesting problems are described, with, in each case, a solution in the form of a computer program. A large number of exercises enable the reader to undertake his or her own experimental work. In the second part, example programs are given for specific machines and operating systems; details refer to MS-DOC and Turbo-Pascal, UNIX 4.2 BSD with Berkley Pascal and C. Other implementations of the graphics routines are given for Apple Macintosh, Apple IIE and IIGS and Atari ST.

This 1989 book is about chaos, fractals and complex dynamics, and is addressed to all people who have some familiarity with computers and enjoy using them. The mathematics has been kept simple, with few formulae, yet the reader is introduced to and can learn about an area of current scientific research which was scarcely possible before the availability of computers. The introduction is achieved through the extensive use of computer graphics. The book is divided into two main parts: in the first the most interesting problems are described, with, in each case, a solution in the form of a computer program. A large number of exercises enable the reader to undertake his or her own experimental work. In the second part, example programs are given for specific machines and operating systems; details refer to MS-DOC and Turbo-Pascal, UNIX 4.2 BSD with Berkley Pascal and C. Other implementations of the graphics routines are given for Apple Macintosh, Apple IIE and IIGS and Atari ST.

This text has been produced for the benefit of students in computer and infor- mation science and for experts involved in the design of microprocessors. It deals with the design of complex VLSI chips,

This book is an important introduction to the critical interpretation of the work of the major French thinker Michel Foucault. Through comprehensive and detailed analyses of such important texts as The History of Madness in the Age of Reason, The Birth of the Clinic, The Order of Things, and The Archaeology of Knowledge, Professor Gutting provides a lucid exposition of Foucault's 'archaeological' approach to the history of thought - a method for uncovering the 'unconscious' structures that set boundaries on the thinking of a given epoch. The book also casts Foucault in a new light, relating his work to two major but neglected influences: Gaston Bachelard's philosophy of science and Georges Canguilhem's history of science. This perspective yields a new and valuable understanding of science, balancing and complementing the more common view that he was primarily a social critic and theorist. An excellent guide for those first approaching Foucault's work, the book will also be a challengin

This book is an important introduction to the critical interpretation of the work of the major French thinker Michel Foucault. Through comprehensive and detailed analyses of such important texts as The History of Madness in the Age of Reason, The Birth of the Clinic, The Order of Things, and The Archaeology of Knowledge, Professor Gutting provides a lucid exposition of Foucault's 'archaeological' approach to the history of thought - a method for uncovering the 'unconscious' structures that set boundaries on the thinking of a given epoch. The book also casts Foucault in a new light, relating his work to two major but neglected influences: Gaston Bachelard's philosophy of science and Georges Canguilhem's history of science. This perspective yields a new and valuable understanding of science, balancing and complementing the more common view that he was primarily a social critic and theorist. An excellent guide for those first approaching Foucault's work, the book will also be a challengin

In this book the authors reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher order logic, and cartesian closed categories are essentially the same. In Part II, it is demonstrated that another formulation of higher order logic (intuitionistic type theories) is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludes with a set of exercises. Thus it is well-suited for graduate courses and research in mathematics and logic. Researchers in theoretical computer science, artificia

The designer of a software system, like the architect of a building, needs to be aware of the construction techniques available and to choose the ones that are the most appropriate. This book provides the implementer of software systems with a guide to 25 different techniques for the complete development processes, from system definition through design and into production. The techniques are described against a common background of the traditional development path, its activities and deliverable items. In addition the concepts of metrics and indicators are introduced as tools for both technical and managerial monitoring and control of progress and quality. The book is intended to widen the mental toolkit of system developers and their managers, and will also introduce students of computer science to the practical side of software development. With its wide-ranging treatment of the techniques available and the practical guidance it offers, it will prove an important and valuable work.

This short textbook provides a succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. It will be suitable for all mathematics undergraduates coming to the subject for the first time. The book is based on lectures given at the University of Cambridge and covers the basic concepts of logic: first order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. There are also chapters on recursive functions, the axiom of choice, ordinal and cardinal arithmetic and the incompleteness theorems. Dr Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics. Consequently the book, while making an attractive first textbook for those who plan to specialise in logic, will be particularly valuable for mathematics and computer sc

In this short book, the authors discuss three types of problems from combinatorial geometry: Borsuk's partition problem, covering convex bodies by smaller homothetic bodies, and the illumination problem. They show how closely related these problems are to each other. The presentation is elementary, with no more than high-school mathematics and an interest in geometry required to follow the arguments. Most of the discussion is restricted to two- and three-dimensional Euclidean space, though sometimes more general results and problems are given. Thus even the mathematically unsophisticated reader can grasp some of the results of a branch of twentieth-century mathematics that has applications in such disciplines as mathematical programming, operations research and theoretical computer science. At the end of the book the authors have collected together a set of unsolved and partially solved problems that a sixth-form student should be able to understand and even attempt to solve.

In this book, which was originally published in 1985, Arto Salomaa gives an introduction to certain mathematical topics central to theoretical computer science: computability and recursive functions, formal languages and automata, computational complexity and cryptography. Without sacrificing readability, the presentation is essentially self-contained, with detailed proofs of all statements provided. Professor Salomaa is well known for his books in this area. The present work provides an insight into the basics, together with explanations of some of the more important developments in the field.

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

Recursion theory – now a well-established branch of pure mathematics, having grown rapidly over the last 35 years – deals with the general (abstract) theory of those operations which we conceive as being `computable' by idealized machines. The theory grew out of, and is usually still regarded, as a branch of mathematical logic. This book is a collection of advanced research/survey papers by eminent research workers in the field, based on their lectures given at the Leeds Logic Colloquium 1979. As such it provides an up-to-date view of current ideas and developments in the field of recursion theory as a whole. The individual contributions fit together naturally so as to provide an overview of all the main areas of research in the field. It will therefore be an important and invaluable source for advanced researchers and research students in mathematics and computer science (particularly in Europe, USA and USSR).

The second volume continues the course of study started in Volume 1, but may be used independently by those already possessing an elementary knowledge of the subject. A summary of basic group theory is followed by accounts of group homomorphisms, rings, fields and integral domains. The related concepts of an invariant subgroup and an ideal in a ring are brought in and the reader introduced to vector spaces and Boolean algebra. The theorems behind the abstract work and the reasons for their importance are discussed in greater detail than is usual at this level. The book is intended both for those who, educated in traditional mathematics, wish to know something about modern algebra and also for those already familiar with the elements of the subject who wish to study further. Fresh ideas and structures are introduced gradually and in a simpler manner, with concrete examples and much more informal discussion. There are many graded exercises, including some worked examples. This book is th

This handbook is designed for experimental scientists, particularly those in the life sciences. It is for the non-specialist, and although it assumes only a little knowledge of statistics and mathematics, those with a deeper understanding will also find it useful. The book is directed at the scientist who wishes to solve his numerical and statistical problems on a programmable calculator, mini-computer or interactive terminal. The volume is also useful for the user of full-scale computer systems in that it describes how the large computer solves numerical and statistical problems. The book is divided into three parts. Part I deals with numerical techniques and Part II with statistical techniques. Part III is devoted to the method of least squares which can be regarded as both a statistical and numerical method. The handbook shows clearly how each calculation is performed. Each technique is illustrated by at least one example and there are worked examples and exercises throughout the vo

By the time students have done some programming in one or two languages and have learnt the common ways of representing information in a computer, they will want to embark upon further study of theoretical or applied topics in computer science. Most will encounter problems that require for their solution one or more of the techniques described in this book: for example problems depending upon the formation and solution of different equations; the task of making lists of possible alternatives and of answering questions about them; or the search for discrete optima. Written by the same authors as the highly successful Information Representation and Manipulation in a Computer, this book describes algorithms of mathematical methods and illustrates their application with examples. The mathematical background needed is elementary algebra and calculus. Numerous exercises are provided, with hints to their solutions.

Outline of a Theory of Practice is recognized as a major theoretical text on the foundations of anthropology and sociology. Pierre Bourdieu, a distinguished French anthropologist, develops a theory of practice which is simultaneously a critique of the methods and postures of social science and a general account of how human action should be understood. With his central concept of the habitus, the principle which negotiates between objective structures and practices, Bourdieu is able to transcend the dichotomies which have shaped theoretical thinking about the social world. The author draws on his fieldwork in Kabylia (Algeria) to illustrate his theoretical propositions. With detailed study of matrimonial strategies and the role of rite and myth, he analyses the dialectical process of the 'incorporation of structures' and the objectification of habitus, whereby social formations tend to reproduce themselves. A rigorous consistent materialist approach lays the foundations for a theory of

Once upon a time students of mathematics and students of science or engineering took the same courses in mathematical analysis beyond calculus. Now it is common to separate" advanced mathematics for s

A good grasp of the theory of structures - the theoretical basis by which the strength, stiffness and stability of a building can be understood - is fundamental to structural engineers and architects. Yet most modern structural analysis and design is carried out by computer, with the user isolated from the processes in action. Plastic Design of Frames; Volume 1. Fundamentals provides a broad introduction to the mathematics behind a range of structural processes. Some of the techniques used in this book may be familiar to the reader, and some may not, but each of the topics examined will give the structural engineer valuable insight into the basis of the subject. This companion book Plastic Design of Frames; Volume 2. Applications provides additional advanced topics and case studies. This lucid second volume provides a valuable read for structural engineers and others who wish to deepen their knowledge of the structural analysis and design of buildings.

Engaging introduction to that curious feature of mathematics which provides framework for so many structures in biology, chemistry, and the arts. Discussion ranges from theories of biological growth

For a wide variety of Web Programming, XHTML, and JavaScript courses found in Computer Science, CIS, MIS, IT, Business, Engineering, and Continuing Education departments.Internet and World Wide Web Ho

The nature of measurement is a topic of central concern in the philosophy of science and, indeed, measurement is the essential link between science and mathematics. Professor Ellis's book, originally published in 1966, is the first general exposition of the philosophical and logical principles involved in measurement since N. R. Campbell's Principles of Measurement and Calculation (1928), and P. W. Bridgman's Dimensional Analysis (1931). Professor Ellis writes from an empiricist standpoint. His object is to distinguish and define the basic concepts in measurement, for example: scale, quantity, unit. dimension, number and probability. He discusses the problem of classifying scales of measurement and the special logical problems associated with each kind of scale. A translation of mach's Critique on the Concept of Temperature, which gives his views on the nature of measurement more fully than in any of his other works, is given as an appendix.

These lecture notes are based on a graduate course given for several years at Vilnius University as part of the master program Financial and Actuarial Mathematics. They are intended to give a short in

This book analyzes the most important achievements in science and engineering practice concerning operational factors that cause damage to concrete and reinforced concrete structures. It includes meth

Here, the authors strive to change the way logic and discrete math are taught in computer science and mathematics: while many books treat logic simply as another topic of study, this one is unique in

Explores the practical and theoretical aspects of the DFT, one of the most widely used tools in science and engineering.

Developed as the text for the basic computer architecture course at MIT, Computation Structures integrates a thorough coverage of digital logic design with a comprehensive presentation of computer ar

Designed as a text for a one semester course to introduce graduate students in mathematics and statistics to the engineering concepts of the discrete Kalman filter and its implications. Annotation cop

This book is the second volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, alg

Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this bo

The design and analysis of efficient data structures has long been recognized as a key component of the Computer Science curriculum. Goodrich and Tomassia's approach to this classic topic is based on

Computer Vision: A Modern Approach, 2e, is appropriate for upper-division undergraduate- and graduate-level courses in computer vision found in departments of Computer Science, Computer Engineering an