Numbers-Ruth

This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves. There are chapters dealing with the many connections between matrices, graphs, digraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorial properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix, and Latin squares. The final chapter deals with algebraic characterizations of combinatorial properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jordan Canonical Form. The book is sufficiently self-contained for use

Probability theory is nowadays applied in a huge variety of fields including physics, engineering, biology, economics and the social sciences. This book is a modern, lively and rigorous account which has Doob's theory of martingales in discrete time as its main theme. It proves important results such as Kolmogorov's Strong Law of Large Numbers and the Three-Series Theorem by martingale techniques, and the Central Limit Theorem via the use of characteristic functions. A distinguishing feature is its determination to keep the probability flowing at a nice tempo. It achieves this by being selective rather than encyclopaedic, presenting only what is essential to understand the fundamentals; and it assumes certain key results from measure theory in the main text. These measure-theoretic results are proved in full in appendices, so that the book is completely self-contained. The book is written for students, not for researchers, and has evolved through several years of class testing. Exercis

This book, first published in 1991, is a general history of Roman painting written specifically for English-language readers. Large numbers of wall-paintings have survived from the Roman world, and particularly from Rome itself and from the cities of Pompeii, Herculaneum and Stabiae, buried in the eruption of Mount Vesuvius in AD 79. Their influence upon European artists of the Renaissance and Neo-Classical periods has been considerable. Recent research has provided a much clearer idea of the chronology of these paintings, of their sources of inspiration, and of their meaning to the various classes of patrons who commissioned them. All aspects of our knowledge are brought together in this survey. Among other topics the book discusses the so-called Four Pompeian Styles, their spread to the provinces, the broad developments in scheme, style and subject-matter which followed them, the factors which dictated the choice of particular subjects and the way in which they were represented, and

Life occurs, as far as we know, only as part of the earthly biosphere. Yet the earth's biotic resources are experiencing a spreading crisis that is leading not only to the most rapid loss of species in the last 65 million years, but also causing abrupt changes in the structure and function of natural communities. This disturbance, unfortunately, is the result of human carelessness in the name of advancing civilisation. As our technologies and societies continue to improve and grow, we remove ourselves more and more from our natural habitat; as a consequence, we destroy countless numbers of species of every style and complexity. To identify and begin rectifying this dangerous situation, a group of outstanding environmental scientists has compiled a collection of case studies that illustrate the changes being wrought on the biosphere by the human presence.

Superb introduction for readers with limited formal mathematical training. Topics include Euclidean algorithm and its consequences, congruences, powers of an integer modulo m, continued fractions, Gau

Winner of the 1989 PEN/Hemingway Foundation Award??for best first novel, this exquisite book??confronts real-life issues of alienation and violence??from which the author creates a stunning testament?

The collection consists of four parts: Part I presents three non-technical essays on economic development and economic systems. Four out of five essays in Part II deal with the theory and measurement of the so-called Index of Total Factor Productivity for several countries. The fifth essay is on the theory of index numbers. The first essay of Part III compares the American and Soviet patterns of economic development and finds that the path followed by each country might have been optimal for it at the time. The second essay develops a general theory of a producer cooperative. The third essay discusses a method for avoiding monopolistic exploitation, under either system, without price control. Part IV presents three applications of economic theory to historical problems - in particular, to serfdom and slavery. The first, on 'The Causes of Slavery or Serfdom', has become a classic. The second challenges the widely accepted view that Russian serfdom had become unprofitable for the serf-ow

In the Old Testament we read Gods word as it was spoken to his people Israel. Today, thousands of years later, we hear in these thirty-nine books his inspired and authoritative message for us.These tw

This book presents an evolutionary theory of technological change based upon recent scholarship in the history of technology and upon relevant material drawn from economic history and anthropology. It challenges the popular notion that technology advances by the efforts of a few heroic individuals who produce a series of revolutionary inventions owing little or nothing to the technological past. Therefore, the book's argument is shaped by analogies taken selectively from the theory of organic evolution, and not from the theory and practice of political revolution. Three themes appear, and reappear with variations, throughout the study. The first is diversity: an acknowledgment of the vast numbers of different kinds of made things (artifacts) that have long been available to humanity; the second is necessity: the belief that humans are driven to invent new artifacts in order to meet basic biological requirements such as food, shelter, and defense; and the third is technological evolutio

Landmark changes in the immigration law of 1965 admitted to the United States large numbers of immigrants from India and Pakistan. The religious groups formed by these new immigrants have exerted and will continue to exert significant influence upon the fabric of American religion and culture. This book is the first comprehensive study of the religious groups formed in the United States by Asian-Indian and Pakistani immigrants and of their patterns of adaptation and organization. Professor Williams provides an overview of the variety of religions practiced by these new immigrants, examining Hindu, Muslim, Christian, Sikh, Jain, Zoroastrian, and Jewish communities, and the size and character of the various groups formed. Through analysis of demographic statistics as well as information gathered in extensive interviews with religious group participants, Professor Williams examines the trajectories of adaptation charted by these groups through the involvement in a wide range of ecumenical

Landmark changes in the immigration law of 1965 admitted to the United States large numbers of immigrants from India and Pakistan. The religious groups formed by these new immigrants have exerted and will continue to exert significant influence upon the fabric of American religion and culture. This book is the first comprehensive study of the religious groups formed in the United States by Asian-Indian and Pakistani immigrants and of their patterns of adaptation and organization. Professor Williams provides an overview of the variety of religions practiced by these new immigrants, examining Hindu, Muslim, Christian, Sikh, Jain, Zoroastrian, and Jewish communities, and the size and character of the various groups formed. Through analysis of demographic statistics as well as information gathered in extensive interviews with religious group participants, Professor Williams examines the trajectories of adaptation charted by these groups through the involvement in a wide range of ecumenical

Turn the pages, see the mother animals and count the babies. You will find that the number of babies matches the numeral shown. All of the animals, familiar and exotic, are identified at the back of t

To an algebraist the theory of group characters presents one of those fascinating situations, where the structure of an abstract system is elucidated by a unique set of numbers inherent in the system. But the subject also has a practical aspect, since group characters have gained importance in several branches of science, in which considerations of symmetry play a decisive part. This is an introductory text, suitable for final-year undergraduates or postgraduate students. The only prerequisites are a standard knowledge of linear algebra and a modest acquaintance with group theory. Especial care has been taken to explain how group characters are computed. The character tables of most of the familiar accessible groups are either constructed in the text or included amongst the exercise, all of which are supplied with solutions. The chapter on permutation groups contains a detailed account of the characters of the symmetric group based on the generating function of Frobenius and on the Sch

Before Brave New World... Before 1984...There was...WEIn the One State of the great Benefactor, there are no individuals, only numbers. Life is an ongoing process of mathematical precision, a perfectly balanced equation. Primitive passions and instincts have been subdued. Even nature has been defeated, banished behind the Green Wall. But one frontier remains: outer space. Now, with the creation of the spaceship Integral, that frontier -- and whatever alien species are to be found there -- will be subjugated to the beneficent yoke of reason. One number, D-503, chief architect of the Integral, decides to record his thoughts in the final days before the launch for the benefit of less advanced societies. But a chance meeting with the beautiful 1-330 results in an unexpected discovery that threatens everything D-503 believes about himself and the One State. The discovery -- or rediscovery -- of inner space...and that disease the ancients called the soul. A page-turning SF adventure, a maste

The 1986 book deals with the continuing problem of poverty in Soviet society, a problem which the Revolution of 1917 was supposed to solve in a planned and expeditious manner. The topic is important both because it involves large numbers of people, and because it illustrates a major failing of Marxism-Leninism in practice. The book attempts to analyse Soviet poverty both from Soviet and western sources: the former are very limited, because discussion of poverty in the USSR falls under a strict censorship ban. This is one of the reasons why it has been so sadly neglected by western observers. The analysis concerns itself with most of the common problems of poverty and under-privilege in an industrialised society. Exclusion from the political process, and the particular social implications of the constitutional status of labour as both a right and a duty, are examined in an account that emphasises life-style and social problems, rather than merely the content of the wage-packet.

The 1986 book deals with the continuing problem of poverty in Soviet society, a problem which the Revolution of 1917 was supposed to solve in a planned and expeditious manner. The topic is important both because it involves large numbers of people, and because it illustrates a major failing of Marxism-Leninism in practice. The book attempts to analyse Soviet poverty both from Soviet and western sources: the former are very limited, because discussion of poverty in the USSR falls under a strict censorship ban. This is one of the reasons why it has been so sadly neglected by western observers. The analysis concerns itself with most of the common problems of poverty and under-privilege in an industrialised society. Exclusion from the political process, and the particular social implications of the constitutional status of labour as both a right and a duty, are examined in an account that emphasises life-style and social problems, rather than merely the content of the wage-packet.

This study of the 1870 and 1890 Ghost Dance movements among North American Indians offers an innovative theory about why these movements arose when they did. Emphasizing the demographic situation of American Indians prior to the movements, Professor Thornton argues that the Ghost Dances were deliberate efforts to accomplish a demographic revitalization of American Indians following their virtual collapse. By joining the movements, he contends, tribes sought to assure survival by increasing their numbers through returning the dead to life. Thornton supports this thesis empirically by closely examining the historical context of the two movements and by assessing tribal participation in them, revealing particularly how population size and decline influenced participation among and within American Indian tribes. He also considers American Indian population change after the Ghost Dance periods and shows that participation in the movements actually did lead the way to a demographic recovery

Briefly traces Fanny Fern's life, presents her novel about a young widow struggling to support her children, and gathers a selection of her newspaper articles

The word holor is a term coined by the authors to describe a mathematical entity that is made up of one or more independent quantities, and includes complex numbers, scalars, vectors, matrices, tensors, quaternions, and other hypernumbers. Holors, thus defined, have been known for centuries but each has been developed more or less independently, accompanied by separate nomenclature and theory. This book demonstrates how these complicated subjects can be made simple by using a single notation that applies to all holors, both tensor and nontensor. The authors consider all possible types of holors and develop holor algebra and holor calculus in the most general sense. Thus the reader will learn to develop a new holor that fits the application, rather than forcing an application onto a holor representation that is known but that does not perfectly describe the application. The discussion includes nontensors having no transformation and holors that transform in more complicated ways than al

In this volume, the author covers the mathematical methods appropriate to both linear-systems theory and signal processing. The text deals with a number of topics usually found in introductory linear-systems courses, such as complex numbers and Laplace transforms, and addresses additional topics such as complex variable theory and Fourier series and transforms. Although the discussion is mathematically self-contained, it assumes that the reader has a firm background in calculus and differential equations. Each chapter contains a number of worked examples plus exercises designed to allow the student to put concepts into practice. The author writes in a mathematically elegant yet relaxed and readable style, and provides interesting historical notes along the way. Undergraduate students of electrical engineering, applied mathematics, and related disciplines - and their teachers - will welcome this book.

The responses to questions such as 'What is the explanation for changes in the unemployment rate?' frequently involve the presentation of a mathematical relationship, a function that relates one set of variables to another set of variables. It should become apparent that as one's understanding of functions, relationships, and variables becomes richer and more detailed, one's ability to provide explanations for economic phenomena becomes stronger and more sophisticated. The author believes that a student's intuition should be involved in the study of mathematical techniques in economics and that this intuition develops not so much from solving problems as from visualizing them. Thus the author avoids the definition-theorem-proof style in favor of a structure that encourages the student's geometric intuition of the mathematical results. The presentation of real numbers and functions emphasizes the notion of linearity. Consequently, linear algebra and matrix analysis are integrated into t

Two celebrated symphonies by the great Czech composer, the Eighth and the immensely popular Ninth, "From the New World," in one volume.

Book jacket/back: Johnny Rio, a handsome narcissist but no longer a pretty boy, travels to Los Angeles, the site of past sexual conquest and remembered youthful radiance, in a frenzied attempt to recr

This book is devoted to recursion in programming, the technique by which the solution to a problem is expressed partly in terms of the solution to a simpler version of the same problem. Ultimately the solution to the simplest version must be given explicitly. In functional programming, recursion has received its full due since it is quite often the only repetitive construct. However, the programming language used here is Pascal and the examples have been chosen accordingly. It makes an interesting contrast with the use of recursion in functional and logic programming. The early chapters consider simple linear recursion using examples such as finding the highest common factor of a pair of numbers, and processing linked lists. Subsequent chapters move up through binary recursion, with examples which include the Towers of Hanoi problem and symbolic differentiation, to general recursion. The book contains well over 100 examples.

The chief aim of this book is the reconstruction of the processes and events that have determined the present flora and vegetation of the British Isles, first of all through the long ages when natural conditions prevailed and cycles of glaciations and recessions and slow geological processes were in charge, and afterwards through the nearer and much shorter span of time during which, from the Neolithic onwards, human interference has progressively and severely altered the scene. This is an exercise in biogeography that Darwin called 'that grand subject, that almost keystone to the laws of nature'. But instead of adopting Darwin's conjectural approach, based largely on circumstantial evidence, what this 1975 second edition achieves is a factual reconstruction of events by records of the actual presence of individual species or genera, in large numbers, at particular sites and specified times through the geological and historic record.

Bring home your child's classroom with the wonderfully imaginative 'Step Ahead' series of products. Proven educational methods reinforce what is taught in preschool through the elementary grades. In t

Computing is an exact science and the systematic study of any aspect necessarily involves the use of mathematical models. Moreover, the rate at which the subject is evolving demands a facility for developing new mathematical systems to keep pace with new computing systems and this requires an appreciation of how mathematics works. An understanding of the underlying mathematical structure facilitates the construction of suitable computer programs to perform computations. Assuming no specific knowledge of mathematics, the authors describe all the basic concepts required and progress from sets (rather than numbers) through a variety of algebraic structures that permit the precise description, specification and subsequent analysis of many problems in computing. The material included provides the essential mathematical foundations for core topics of computer science and extends into the areas of language theory, abstract machine theory and computer geometry. Computer Mathematics will be of

The Papers of the London Corresponding Society 1792–1799, first published in 1983, consists of eighteenth-century documents which trace the history of an early working-class reform society organized by a shoemaker and three of his friends. 'Annual Parliaments and Universal Suffrage' was their slogan and their goal. To achieve this reform they believed they must first educate the people to know what their rights were and how to exercise them. So popular were they that over 10,000 men paid to join the Society and over 100,000 people attended their open air meetings. Such numbers alarmed the government, especially since spies reported talk or arming and revolution, of assassinating Pitt and shooting 'royal game'. Unlike many groups which set out to demand their political or social rights, but which scattered as soon as they encountered opposition, the Corresponding Society met openly for over six years despite harassment by police magistrates, interference from press gangs, vilification i

Professor McKenzie proposes and formulates a method composed of operational procedures designed to facilitate the evaluation of economic projects and policies. This method is discussed fully, illustrated by simple examples, and compared with alternative procedures. An outline of a computer program that enables readers to undertake their own calculations is included. In order to present the approach clearly, the author provides an exposition of the fundamental ideas and the main alternative approaches to the problem. These rely on various forms of index numbers and consumer surplus. However, as is well known, such measures are not capable of correctly ordering the various alternatives under consideration, except under highly unrealist assumptions. In this book the author suggests the abandonment of this traditional approach based on the concept of 'willingness-to-pay' or the conpensating variation. Instead, the measure that Samuelson has called the 'money-metric' should become the corne

This introduction to recent work in p-adic analysis and number theory will make accessible to a relatively general audience the efforts of a number of mathematicians over the last five years. After reviewing the basics (the construction of p-adic numbers and the p-adic analog of the complex number field, power series and Newton polygons), the author develops the properties of p-adic Dirichlet L-series using p-adic measures and integration. p-adic gamma functions are introduced, and their relationship to L-series is explored. Analogies with the corresponding complex analytic case are stressed. Then a formula for Gauss sums in terms of the p-adic gamma function is proved using the cohomology of Fermat and Artin-Schreier curves. Graduate students and research workers in number theory, algebraic geometry and parts of algebra and analysis will welcome this account of current research.

This classic text has introduced generations of students to the economic theory of consumer behaviour. Written by 2015 Nobel Laureate Angus Deaton and John Muellbauer, the book begins with a self-contained presentation of the basic theory and its use in applied econometrics. These early chapters also include elementary extensions of the theory to labour supply, durable goods, the consumption function, and rationing. The rest of the book is divided into three parts. In the first of these the authors discuss restrictions on choice and aggregation problems. The next part consists of chapters on consumer index numbers; household characteristics, demand, and household welfare comparisons; and social welfare and inequality. The last part extends the coverage of consumer behaviour to include the quality of goods and household production theory, labour supply and human capital theory, the consumption function and intertemporal choice, the demand for durable goods, and choice under uncertainty.

Like the other Cambridge Bible Commentary volumes, this contains an introduction followed by the texts of the N.E.B. translation divided into sections. Each section of the text is followed by the commentary upon it. Mr Surdy discusses the the content, structure and authorship of the book, pointing to material from two distinct periods: 500–400 BC and some 500 years earlier.