Numbers-Ruth

Sieve theory has a rich and romantic history. The ancient question of whether there exist infinitely many twin primes (primes p such that p+2 is also prime), and Goldbach's conjecture that every even number can be written as the sum of two prime numbers, have been two of the problems that have inspired the development of the theory. This book provides a motivated introduction to sieve theory. Rather than focus on technical details which can obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. The text can be used for a senior level undergraduate course or an introductory graduate course in analytic number theory, and non-experts can gain a quick introduction to the techniques of the subject.

Dwarf galaxies offer a valuable insight into the physical processes that govern galaxy formation and evolution at high redshift. These elusive stellar systems are helping astronomers to find answers to some of the most burning questions in extragalactic astronomy. Present-day dwarf galaxies, the easily studied survivors of the primordial galaxy population, are important targets for research in the quest to provide local benchmarks for cosmological studies, in particular theories of structure formation. The proceedings of IAUC198 offer an exciting multidisciplinary collection of research results. The interpretation of the faint blue galaxy excess; the mismatch of the observed dwarf galaxy numbers with popular cosmological model predictions; and the puzzling diversity of star-formation histories among Local Group dwarf elliptical galaxies, are amongst the topical questions covered. Dwarf galaxy specialists and cosmologists map out strategies and outline a framework for progress on import

Give students the skill-building practice they need in reading, writing, math, and more with these engaging , full-color workbooks. Easy-to-follow directions and fun exercises motivate students to wo

Sieve theory has a rich and romantic history. The ancient question of whether there exist infinitely many twin primes (primes p such that p+2 is also prime), and Goldbach's conjecture that every even number can be written as the sum of two prime numbers, have been two of the problems that have inspired the development of the theory. This book provides a motivated introduction to sieve theory. Rather than focus on technical details which can obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. The text can be used for a senior level undergraduate course or an introductory graduate course in analytic number theory, and non-experts can gain a quick introduction to the techniques of the subject.

This work documents the history of techniques that statisticians have used to manipulate economic, meteorological, biological and physical data taken from observations recorded over time. The manipulation tools include per cent change, index numbers, moving averages and 'first differences', i.e., subtracting one observation from the previous value. Professor Klein argues that nineteenth-century business journals, such as The Economist, were as important to the development of time series analysis as Latin treatises on probability theory. While examining the roots of mathematical statistics in commercial practice, she traces changes in analytical forms from table to graph to equation. Klein cautions that we risk measurement without history in unduly mechanistic blending of stationary probability theory with the practical dynamics of commercial traders. This history is accessible to students with a basic knowledge of statistics as well as financial analysts, statisticians and historians o

The history of the entry into the Promised Land followed by that of the period of the judges and early monarchy may not appear to readers today as a source for expounding the Christian faith. But the

This was the first in-depth examination of relations between the Church of England and other faiths in the Prison Service Chaplaincy. It shows how the struggle for equal opportunities in a multi-faith society is politicising relations between the Church, the state and religious minorities. Drawing on a wealth of data, it considers the increasingly controversial role of Anglican chaplains in facilitating the religious and pastoral care of prisoners from non-Christian backgrounds, whose numbers among the prison population have been growing. Comparison with the United States underlines the closeness of the tie between the state and Christian churches in English prisons, and this book argues that it is time to reconsider the practice of keeping ethnic and religious minorities dependent on Anglican 'brokering' of their access to prison chaplaincy.

This first words and picture book will delight children up to the age of five who will love looking at it with their parents or by themselves.

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

This 1998 book was the first to describe ZEKE (Zero Kinetic Energy) spectroscopy, a high resolution spectroscopy of molecular ions, neutral short-lived intermediates, and other species. The author's approach is to use a minimum of equations with large numbers of figures to help the reader towards a basic understanding of the many unique concepts of this form of spectroscopy. Since 1984 ZEKE spectroscopy has matured into a very high resolution spectroscopy for the study of cations, anions and, indirectly through these species, of neutrals, including very short-lived intermediates in chemical reactions. It has even yielded the first direct spectroscopic data on elusive transition states of chemical reactions. This book will be of interest to anyone interested in the spectroscopy of ions or neutrals, particularly short-lived neutrals, and to reaction kineticists interested in the study of reactions involving such highly state-selected species.

This 2002 book examines the interaction between ocean waves and oscillating systems. With a focus on linear analysis of low-amplitude waves, the text is designed to convey a thorough understanding of wave interactions. Topics covered include the background mathematics of oscillations, gravity waves on water, the dynamics of wave-body interactions, and the absorption of wave energy by oscillating bodies. Linear algebra, complex numbers, differential equations, and Fourier transformation are utilized as bases for the analysis, and each chapter ends with problems. While the book's focus is on linear theory, the practical application of energy storage and transport is interwoven throughout. This book will be appropriate for those with backgrounds in elementary fluid dynamics or hydrodynamics and mathematical analysis. Graduate students and researchers will find it an excellent source of wave energy theory and application.

This textbook is intended to serve as a one-semester introductory course in number theory and in this second edition it has been revised throughout and many new exercises have been added. Historical perspective is included and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.

This textbook is intended to serve as a one-semester introductory course in number theory and in this second edition it has been revised throughout and many new exercises have been added. Historical perspective is included and emphasis is given to some of the subject's applied aspects; in particular the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler, and to fully illustrate the properties of numbers and concepts developed in the text, a wealth of exercises have been included. It is assumed that the reader will have 'pencil in hand' and ready access to a calculator or computer. For students new to number theory, whatever their background, this is a stimulating and entertaining introduction to the subject.

Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources.

Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources.

The world Methodist community now numbers over 75 million people in more than 130 countries. The story of Methodism is fascinating and multi-faceted because there are so many distinct traditions within it, some stemming directly from Britain and some arising in the United States. In this book, the authors address the issue of what holds all Methodists together and examine the strengths and diversity of an influential major form of Christian life and witness. They look at the ways in which Methodism has become established throughout the world, examining historical and theological developments, and patterns of worship and spirituality, in their various cultural contexts. The book reflects both the lasting contributions of John and Charles Wesley, and the on-going contribution of Methodism to the ecumenical movement and inter-religious relations. It offers both analysis and abundant resources for further study.

The world Methodist community now numbers over 75 million people in more than 130 countries. The story of Methodism is fascinating and multi-faceted because there are so many distinct traditions within it, some stemming directly from Britain and some arising in the United States. In this book, the authors address the issue of what holds all Methodists together and examine the strengths and diversity of an influential major form of Christian life and witness. They look at the ways in which Methodism has become established throughout the world, examining historical and theological developments, and patterns of worship and spirituality, in their various cultural contexts. The book reflects both the lasting contributions of John and Charles Wesley, and the on-going contribution of Methodism to the ecumenical movement and inter-religious relations. It offers both analysis and abundant resources for further study.

This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-conta

The Rights of Others examines the boundaries of political community by focusing on political membership - the principles and practices for incorporating aliens and strangers, immigrants and newcomers, refugees and asylum seekers into existing polities. Boundaries define some as members, others as aliens. But when state sovereignty is becoming frayed, and national citizenship is unravelling, definitions of political membership become much less clear. Indeed few issues in world politics today are more important, or more troubling. In her Seeley Lectures, the distinguished political theorist Seyla Benhabib makes a powerful plea, echoing Immanuel Kant, for moral universalism and cosmopolitan federalism. She advocates not open but porous boundaries, recognising both the admittance rights of refugees and asylum seekers, but also the regulatory rights of democracies. The Rights of Others is a major intervention in contemporary political theory, of interest to large numbers of students and spe

The Rights of Others examines the boundaries of political community by focusing on political membership - the principles and practices for incorporating aliens and strangers, immigrants and newcomers, refugees and asylum seekers into existing polities. Boundaries define some as members, others as aliens. But when state sovereignty is becoming frayed, and national citizenship is unravelling, definitions of political membership become much less clear. Indeed few issues in world politics today are more important, or more troubling. In her Seeley Lectures, the distinguished political theorist Seyla Benhabib makes a powerful plea, echoing Immanuel Kant, for moral universalism and cosmopolitan federalism. She advocates not open but porous boundaries, recognising both the admittance rights of refugees and asylum seekers, but also the regulatory rights of democracies. The Rights of Others is a major intervention in contemporary political theory, of interest to large numbers of students and spe

The last twenty-five years have seen dramatic rises in the prison populations of most industrialised nations. Unable to keep up with increased numbers of convicted offenders, governments and criminal justice systems have been seeking new ways to control and punish offenders. One sanction adopted in Canada and some parts of Europe and the US is community custody which attempts to recreate the punitive nature of prison but without incarceration. This book analyses the effectiveness of this approach and explores its implications for offenders and society as a whole. It demonstrates that if properly conceived and administered, community custody can reduce the number of prison admissions and at the same time promote multiple goals of sentencing. So that offenders given community custody orders are punished yet also given the opportunity to change their lives in ways that would be impossible if they were in prison.

The last twenty-five years have seen dramatic rises in the prison populations of most industrialised nations. Unable to keep up with increased numbers of convicted offenders, governments and criminal justice systems have been seeking new ways to control and punish offenders. One sanction adopted in Canada and some parts of Europe and the US is community custody which attempts to recreate the punitive nature of prison but without incarceration. This book analyses the effectiveness of this approach and explores its implications for offenders and society as a whole. It demonstrates that if properly conceived and administered, community custody can reduce the number of prison admissions and at the same time promote multiple goals of sentencing. So that offenders given community custody orders are punished yet also given the opportunity to change their lives in ways that would be impossible if they were in prison.

It is known that large asteroids and comets can collide with the Earth with severe consequences. Although the chances of a collision in a person's lifetime are small, collisions are a random process and could occur at any time. This book, which was first published in 2004, collects the latest thoughts and ideas of scientists concerned with mitigating the threat of hazardous asteroids and comets. It reviews knowledge of the population of potential colliders, including their numbers, locations, orbits, and how warning times might be improved. The structural properties and composition of their interiors and surfaces are reviewed, and their orbital response to the application of pulses of energy is discussed. Difficulties of operating in space near, or on the surface of, very low mass objects are examined. The book concludes with a discussion of the problems faced in communicating the nature of the impact hazard to the public.

Kids can learn to count with the help of this title filled with bugs that will introduce children to the natural world of strange and beautiful bugs. By the author of Icky Bug Colors. Original.

This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics.

This book was originally published in 2004. Black holes are among the most mysterious objects in the Universe. Weighing up to several billion Suns, massive black holes have long been suspected to be the central powerhouses of energetic phenomena such as quasars. Advances in astronomy have not only provided spectacular proof of this long-standing paradigm, but have revealed the unexpected result that far from being rare, exotic beasts, they inhabit the center of virtually all large galaxies. Candidate black holes have been identified in increasingly large numbers of galaxies, both inactive and active, to the point where statistical studies are possible. Fresh work has highlighted the close connection between the formation, growth, and evolution of supermassive black holes and their host galaxies. This volume contains the invited lectures from an international symposium that was held to explore this exciting theme, and is a valuable review for professional astronomers and graduate studen

Horses played a vital role in the economy of pre-industrial England. They acted as draught animals, pulled ploughs, waggons and coaches, worked machines, and transported goods around the country. As saddle animals they enabled their riders to carry out a wide variety of tasks, and at all levels of society they were regarded as status symbols in a unique relationship with man shared by no other animal. During the Tudor and Stuart period, horses were needed in ever-growing numbers, and for a greater variety of tasks. As demand grew, improvements became necessary in the means of supply and distribution. The agents of change, the specialist dealers, were often condemned as rogues and cheats, whose actions raised prices and caused shortages. Dr Edwards argues that, far from being generally unscrupulous, the dealers were no better or worse than those amongst whom they lived and worked.

General editor Lloyd J. Ogilvie brings together a team of skilled and exceptional communicators to blend sound scholarship with life-related illustrations.The design for the Preacher's Commentary give

General editor Lloyd J. Ogilvie brings together a team of skilled and exceptional communicators to blend sound scholarship with life-related illustrations.The design for the Preacher's Commentary give

When seen hunting over a meadow, barn owls have an ethereal grace and beauty that can be matched by no other bird. The barn owl has an almost global distribution and has lived in close proximity to humans since settlement and farming created the forest clearings needed for hunting and places in which to nest. However, in many countries, barn owl numbers are falling rapidly. This book explores the relationships between barn owls and their prey worldwide, and demonstrates how an understanding of such relationships can help in the conservation of the species. In this comprehensive account, Iain Taylor describes the biology and ecology of this species, including the factors affecting breeding success, and causes of mortality affecting the final recruitment of new birds into the population. He concludes by suggesting ways in which we can manage and conserve this beautiful bird for the future.

This book illustrates a set of tools - story grammars, relational data models, and network models - that can be profitably used for the collection, organization, and analysis of narrative data in socio-historical research. A story grammar, or Subject-Action-Object and their modifiers, is the linguistic tool the author uses to structure narrative for the purpose of collecting event data. Relational database models make such complex data collection schemes practically feasible in a computer environment. Finally, network models are a statistical tool best suited to analyze this type of data. Driven by the metaphors of the journal (from … to) and the alchemy (words into numbers), the book leads the reader throughout a number of paths, from substantive to methodological issues, across time and disciplines: sociology, linguistics, literary criticism, history, statistics, computer science, philosophy, cognitive psychology, political science.

This textbook is an introduction to algebra via examples. The book moves from properties of integers, through other examples, to the beginnings of group theory. Applications to public key codes and to error correcting codes are emphasised. These applications, together with sections on logic and finite state machines, make the text suitable for students of computer science as well as mathematics students. Attention is paid to historical development of the mathematical ideas. This second edition contains new material on mathematical reasoning skills and a new chapter on polynomials has been added. The book was developed from first-level courses taught in the UK and USA. These courses proved successful in developing not only a theoretical understanding but also algorithmic skills. This book can be used at a wide range of levels: it is suitable for first- or second-level university students, and could be used as enrichment material for upper-level school students.

In this fascinating study, architect and Egyptologist Corinna Rossi analyses the relationship between mathematics and architecture in ancient Egypt by exploring the use of numbers and geometrical figures in ancient architectural projects and buildings. While previous architectural studies have searched for abstract 'universal rules' to explain the history of Egyptian architecture, Rossi attempts to reconcile the different approaches of archaeologists, architects and historians of mathematics into a single coherent picture. Using a study of a specific group of monuments, the pyramids, and placing them in the context of their cultural and historical background, Rossi argues that theory and practice of construction must be considered as a continuum, not as two separated fields, in order to allow the original planning process of a building to re-emerge. Highly illustrated with plans, diagrams and figures, this book is essential reading for all scholars of Ancient Egypt and the architecture

How many people do you need in a room before there’ll be a birthday in common? Why is 70 weird, and what can we do about it? How can 56 people eat 1 pizza? In 100 bite-size chapters of no more than th