Introduction to Python Programming And Data Structure By Liang

Axiomatic categorical domain theory is crucial for understanding the meaning of programs and reasoning about them. This book is the first systematic account of the subject and studies mathematical structures suitable for modelling functional programming languages in an axiomatic (i.e. abstract) setting. In particular, the author develops theories of partiality and recursive types and applies them to the study of the metalanguage FPC; for example, enriched categorical models of the FPC are defined. Furthermore, FPC is considered as a programming language with a call-by-value operational semantics and a denotational semantics defined on top of a categorical model. To conclude, for an axiomatisation of absolute non-trivial domain-theoretic models of FPC, operational and denotational semantics are related by means of computational soundness and adequacy results. To make the book reasonably self-contained, the author includes an introduction to enriched category theory.

Spray forming combines the metallurgical processes of metal casting and powder metallurgy to fabricate metal products with enhanced properties. This book provides an introduction to the various modelling and simulation techniques employed in spray forming, and shows how they are applied in process analysis and development. The author begins by deriving and describing the main models. He then presents their application in the simulation of the key features of spray forming. Wherever possible he discusses theoretical results with reference to experimental data. Building on the features of metal spray forming, he also derives common characteristic modelling features that may be useful in the simulation of related spray processes. The book is aimed at researchers and engineers working in process technology, chemical engineering and materials science.

The paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.

This is a self-contained account of how some modern ideas in differential geometry can be used to tackle and extend classical results in integral geometry. The authors investigate the influence of total curvature on the metric structure of complete, non-compact Riemannian 2-manifolds, though their work, much of which has never appeared in book form before, can be extended to more general spaces. Many classical results are introduced and then extended by the authors. The compactification of complete open surfaces is discussed, as are Busemann functions for rays. Open problems are provided in each chapter, and the text is richly illustrated with figures designed to help the reader understand the subject matter and get intuitive ideas about the subject. The treatment is self-contained, assuming only a basic knowledge of manifold theory, so is suitable for graduate students and non-specialists who seek an introduction to this modern area of differential geometry.

Cross-country comparisons of sectoral balance sheets offer crucial indications of differences in overall financial structure, which in turn underlie contrasts in financing and economic behaviour. In this context, this book aims to confront theory and extant empirical work with aggregate financial data across the G-7, covering the period from 1970 to 2000. Viewed in the light of the main theoretical and empirical results in the economic literature, it explores the contrasting patterns and development of financial structures in the UK, the US, Germany, Japan, Canada, France and Italy. It uses as raw material sectoral balance sheet data published by national statistical authorities across the corporate, household, general government, foreign, financial, banking and institutional-investor sectors.

Demography has developed into a remarkably coherent field and now stands as a firmly established discipline with strong ties to policy-making agencies. However, in recent years there has been increasing recognition within demography of the limits of existing theories and methods, particularly its absence of a strong critical tradition and its isolation from recent theoretical developments in other social sciences. In this study, Nancy Riley and James McCarthy use the lens of postmodernism to structure a critical analysis of the field of demography. Paying particular attention to the fundamental epistemologies and methodologies that currently underlie the field, they explore how postmodern perspectives might serve to energize the field and how demography could be enhanced by the introduction of insights from other social sciences. Drawing on examples of new kinds of research in demography and related fields, this is an important new book that seeks to reinvigorate the field of demograph

Demography has developed into a remarkably coherent field and now stands as a firmly established discipline with strong ties to policy-making agencies. However, in recent years there has been increasing recognition within demography of the limits of existing theories and methods, particularly its absence of a strong critical tradition and its isolation from recent theoretical developments in other social sciences. In this study, Nancy Riley and James McCarthy use the lens of postmodernism to structure a critical analysis of the field of demography. Paying particular attention to the fundamental epistemologies and methodologies that currently underlie the field, they explore how postmodern perspectives might serve to energize the field and how demography could be enhanced by the introduction of insights from other social sciences. Drawing on examples of new kinds of research in demography and related fields, this is an important new book that seeks to reinvigorate the field of demograph

Despite his enduring popularity, Martial has recently suffered from serious critical neglect. The present work is the first edition of selections from Martial to be published for decades, and includes a fully representative selection of the oeuvre of the poet, who has often been criticised, unfairly, the authors argue, for obscenity and flattery of the Emperor Domitian. The epigrams included in the selection are organised under various heads, e.g. Martial and poetry, sexual mores, satirical pieces. A very full introduction deals with such topics as the prejudices and predilections of his audience which conditioned Martial's choice of subject matter, Martial's language, the structure and style of the epigrams, the epigrammatic tradition and Martial's creative engagement with it. The detailed commentary is suitable for use with undergraduates and is distinguished by its focus on social history as well as literary interpretation.

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.

The book is an introduction to the branch of fluid mechanics concerned with the production of sound by hydrodynamic flows. It is designed for a one semester introductory course at advanced undergraduate or graduate level. Great care is taken to explain underlying fluid mechanical and acoustic concepts, and to describe as fully as possible the steps in a complicated derivation. The discussion deals specifically with low Mach number flows, which enables the sound produced by 'vortex-surface' interactions to be analysed using the 'compact Green's function'. This provides a routine procedure for estimating the sound, and an easy identification of those parts of a structure that are likely to be important sources of sound. Each chapter ends with a set of problems, many of which can form the basis of an extended student project. The final chapter contains worked examples that have been investigated by students at Boston University.

The book is an introduction to the branch of fluid mechanics concerned with the production of sound by hydrodynamic flows. It is designed for a one semester introductory course at advanced undergraduate or graduate level. Great care is taken to explain underlying fluid mechanical and acoustic concepts, and to describe as fully as possible the steps in a complicated derivation. The discussion deals specifically with low Mach number flows, which enables the sound produced by 'vortex-surface' interactions to be analysed using the 'compact Green's function'. This provides a routine procedure for estimating the sound, and an easy identification of those parts of a structure that are likely to be important sources of sound. Each chapter ends with a set of problems, many of which can form the basis of an extended student project. The final chapter contains worked examples that have been investigated by students at Boston University.

In a rural community in Southern Ethiopia, there are two types of rituals performed by the same people. Historical evidence suggests that one has shown remarkable stability over the years, while the other has undergone massive transformations. External factors are the same, so how is this to be explained? In this 2002 book, Dena Freeman focuses on ethnographical and historical data from the Gamo Highlands of Southern Ethiopia to tackle the question of cultural change and transformation. She uses a comparative perspective and contrasts the continuity in sacrificial rituals with the rapid divergence and differentiation in initiations. Freeman argues that although external change drives internal cultural transformation, the way in which it does is greatly influenced by the structural organization of the cultural systems themselves. This insight leads to a rethinking of the analytic tension between structure and agency that is at the heart of contemporary anthropological theory.

This is a collection of essays by Simon Kuznets, winner of the 1971 Nobel Memorial Prize in Economic Sciences, published posthumously. It represents the primary concerns of his research at a late phase of his career, as well as themes from his earlier work. The first four chapters deal with 'modern economic growth'. Chapters five to seven introduce the main theme of the remainder of the volume: interrelations between demographic change and income inequality. Chapters eight to ten draw on a wider set of data to make comparisons of income inequality among societies at widely different levels of development. Chapter eleven returns to data for the United States to develop more fully the importance of differing childbearing patterns for income inequality. In the introduction Professor Richard Easterlin discusses the relationship of the essays to the balance of Kuznets's writings. In the afterword Professor Robert Fogel discusses the methodologies favoured by Kuznets.

This authoritative introduction to African American English (AAE) is the first textbook to look at the grammar as a whole. Clearly organised, it describes patterns in the sentence structure, sound system, word formation and word use in AAE. The book uses linguistic description and data from conversation to explain that AAE is not a compilation of random deviations from mainstream English but that it is a rule-governed system. The textbook examines topics such as education, speech events in the secular and religious world, and the use of language in literature and the media to create black images. This much-needed book includes exercises to accompany each chapter and will be essential reading for students in linguistics, education, anthropology, African American studies and literature.

An introduction to the wolf, including some of the different types, pack structure, reproduction, hunting, and dangers faced by wolves in the wild.

By the middle of the 20th century, abstraction was the accepted language of art as practiced by painters and articulated by critics, who began to investigate its historical and theoretical dimensions. Abstract Art in the Late Twentieth Century includes seminal essays on abstract painting by eleven of its most incisive critics and written over four decades, between 1960 and 2000. Tracing the post-Greenbergian development of such critical issues as hard-edge painting, deductive and serial structure, monochrome abstraction, the psychological analogy, regionalism, and the 'death of painting' in post-modernism, they examine works by Ad Reinhardt, Frank Stella, Brice Marden, Sherrie Levine, and Gerhard Richter, among others. The introduction and commentary by Frances Colpitt situates the essays historically and examines their philosophical sources and influences, from formalism and phenomenology, to structuralism and poststructuralism. What emerges is a coherent and optimistic picture of abs

This 2002 introduction to the use of radar for remote sensing of natural surfaces provides the reader with a thorough grounding in practical applications, focusing particularly on terrestrial studies that may be extended to other planets. An historical overview of the subject is followed by an introduction to the nomenclature and methodology pertaining to radar data collection, image interpretation and surface roughness analysis. The author then presents a summary (illustrated with black and white examples from the natural environment) of theoretical explanations for the backscatter properties of continuous rough surfaces, collections of discrete objects, and layered terrain. Case studies of radar surveys of the Moon, Mercury, Venus and Mars complete the book. The level is appropriate for students and professionals across a broad range of scientific disciplines including Earth and planetary sciences, electrical engineering, and remote sensing. Particular emphasis is given to practical

This edition of the economic history classic One Kind of Freedom reprints the entire text of the first edition together with an introduction by the authors and an extensive bibliography of works in Southern history published since the appearance of the first edition. The book examines the economic institutions that replaced slavery and the conditions under which ex-slaves were allowed to enter the economic life of the United States following the Civil War. The authors contend that although the kind of freedom permitted to black Americans allowed substantial increases in their economic welfare, it effectively curtailed further black advancement and retarded Southern economic development. Quantitative data are used to describe the historical setting but also shape the authors' economic analysis and test the appropriateness of their interpretations. Ransom and Sutch's revised findings enrich the picture of the era and offer directions for future research.

This edition of the economic history classic One Kind of Freedom reprints the entire text of the first edition together with an introduction by the authors and an extensive bibliography of works in Southern history published since the appearance of the first edition. The book examines the economic institutions that replaced slavery and the conditions under which ex-slaves were allowed to enter the economic life of the United States following the Civil War. The authors contend that although the kind of freedom permitted to black Americans allowed substantial increases in their economic welfare, it effectively curtailed further black advancement and retarded Southern economic development. Quantitative data are used to describe the historical setting but also shape the authors' economic analysis and test the appropriateness of their interpretations. Ransom and Sutch's revised findings enrich the picture of the era and offer directions for future research.

Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.

Independent Component Analysis (ICA) has recently become an important tool for modelling and understanding empirical datasets. It is a method of separating out independent sources from linearly mixed data, and belongs to the class of general linear models. ICA provides a better decomposition than other well-known models such as principal component analysis. This self-contained book contains a structured series of edited papers by leading researchers in the field, including an extensive introduction to ICA. The major theoretical bases are reviewed from a modern perspective, current developments are surveyed and many case studies of applications are described in detail. The latter include biomedical examples, signal and image denoising and mobile communications. ICA is discussed in the framework of general linear models, but also in comparison with other paradigms such as neural network and graphical modelling methods. The book is ideal for researchers and graduate students in the field.

This book provides an accessible and up-to-date introduction to how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. Beginning with a summary of key ideas from perturbative quantum field theory and an introduction to the Hopf algebra structure of renormalization, early chapters discuss the rationality of ladder diagrams and simple link diagrams. The necessary basics of knot theory are then presented and the number-theoretic relationship between the topology of Feynman diagrams and knot theory is explored. Later chapters discuss four-term relations motivated by the discovery of Vassiliev invariants in knot theory and draw a link to algebraic structures recently observed in noncommutative geometry. Detailed references are included. Dealing with material at perhaps the most productive interface between mathematics and physics, the book will be of interest to theoretical and particle physicists, and mathematicians.

This book, first published in 2000, provides students with an overview of the main theories of the state found in International Relations. Many International Relation scholars are proclaiming the state to be 'dead', while others lament the lack of an adequate theory of the state in International Relations. John Hobson seeks to resolve this confusion by introducing readers to state theory, arguing that existing theories of the state are limited, and proposing a framework based around the 'agent-structure' debate. The book surveys realist, liberal, Marxist, constructivist and neo-Weberian approaches to the state, and places each perspective's view of the state in relation to its theory of International Relations as a whole. It offers readers a unique introduction to state theory in International Relations, and will be of interest to students and scholars of sociology and politics, as well as International Relations.

Computer vision aims to detect and reconstruct features of surfaces from the images produced by cameras, in some way mimicking the way in which humans reconstruct features of the world around them by using their eyes. In this book the authors describe research in computer vision aimed at recovering the 3D shape of surfaces from image sequences of their 'outlines'. They provide all the necessary background in differential geometry (assuming knowledge of elementary algebra and calculus) and in the analysis of visual motion, emphasising intuitive visual understanding of the geometric techniques with computer-generated illustrations. They also give a thorough introduction to the mathematical techniques and the details of the implementations and apply the methods to data from real images using the most current techniques.

This 1999 edition of The Neural Crest contains comprehensive information about the neural crest, a structure unique to the vertebrate embryo, which has only a transient existence in early embryonic life. The ontogeny of the neural crest embodies the most important issues in developmental biology, as the neural crest is considered to have played a crucial role in evolution of the vertebrate phylum. Data that analyse neural crest ontogeny in murine and zebrafish embryos have been included in this revision. This revised edition also takes advantage of recent advances in our understanding of markers of neural crest cell subpopulations, and a full chapter is now devoted to cell lineage analysis. The major research breakthrough since the first edition has been the introduction of molecular biology to neural crest research, enabling an elucidation of many molecular mechanisms of neural crest development. This book is essential reading for students and researchers in developmental biology, ce

Infrared astronomy has been revolutionised in the last few years by the advent of large, sensitive, infrared arrays, and the success of several infrared satellites. This handbook provides a clear, concise and accessible reference on all aspects of infrared astronomy. Throughout, the emphasis is on fundamental concepts, practical considerations and useful data. Starting with a review of the basic infrared emission mechanisms, we are shown how the earth's atmosphere affects and limits observations from ground-based telescopes. The important systematics of photometric accuracy are treated in detail. Spectroscopy - both stellar and otherwise - is explained, and illustrated with useful examples. An important chapter is devoted to dust, which plays such a central role. Finally, the technical background to infrared instrumentation is covered. This volume provides both an essential introduction for graduate students making infrared observations or reducing infrared data for the first time, and

Infrared astronomy has been revolutionised in the last few years by the advent of large, sensitive, infrared arrays, and the success of several infrared satellites. This handbook provides a clear, concise and accessible reference on all aspects of infrared astronomy. Throughout, the emphasis is on fundamental concepts, practical considerations and useful data. Starting with a review of the basic infrared emission mechanisms, we are shown how the earth's atmosphere affects and limits observations from ground-based telescopes. The important systematics of photometric accuracy are treated in detail. Spectroscopy - both stellar and otherwise - is explained, and illustrated with useful examples. An important chapter is devoted to dust, which plays such a central role. Finally, the technical background to infrared instrumentation is covered. This volume provides both an essential introduction for graduate students making infrared observations or reducing infrared data for the first time, and

Heyman (engineering, U. of Cambridge) offers a non-mathematical introduction to the theory of structures, by which engineers and scientists can calculate the forces within a structure and, if it is a

The pi-calculus differs from other models of communicating behaviour mainly in its treatment of mobility. The movement of a piece of data inside a computer program is treated exactly the same as the transfer of a message - or indeed an entire computer program - across the internet. One can also describe networks which reconfigure themselves. The calculus is very simple but powerful; its most prominent ingredient is the notion of a name. Its theory has two important ingredients: the concept of behavioural (or observational) equivalence, and the use of a new theory of types to classify patterns of interactive behaviour. The internet, and its communication protocols, fall within the scope of the theory just as much as computer programs, data structures, algorithms and programming languages. This book is the first textbook on the subject; it has been long-awaited by professionals and will be welcomed by them, and their students.

The pi-calculus differs from other models of communicating behaviour mainly in its treatment of mobility. The movement of a piece of data inside a computer program is treated exactly the same as the transfer of a message - or indeed an entire computer program - across the internet. One can also describe networks which reconfigure themselves. The calculus is very simple but powerful; its most prominent ingredient is the notion of a name. Its theory has two important ingredients: the concept of behavioural (or observational) equivalence, and the use of a new theory of types to classify patterns of interactive behaviour. The internet, and its communication protocols, fall within the scope of the theory just as much as computer programs, data structures, algorithms and programming languages. This book is the first textbook on the subject; it has been long-awaited by professionals and will be welcomed by them, and their students.

Engineers face numerous uncertainties in the design and development of products and processes. To deal with the uncertainties inherent in measured information, they make use of a variety of statistical techniques. This 1999 book presents single-variable statistical distributions that are useful in engineering design and analysis. It lists significant properties of these distributions and describes methods for estimating parameters and their standard errors, constructing confidence intervals, testing hypotheses, and plotting data. Figures are used extensively to clarify concepts. Methods are illustrated by numerous fully worked examples in the form of Mathcad documents that readers can use as templates for their own data, eliminating the need for programming. Intended as both a text and reference, the book assumes an elementary knowledge of calculus and probability. Graduate and advanced undergraduate students, as well as practising engineers and scientists, will be able to use this bo

This book, drawn from the Global Trade Analysis Project (GTAP), aims to help readers conduct quantitative analysis of international trade issues in an economy-wide framework. In addition to providing a succinct introduction to the GTAP modelling framework and data base, this book contains seven of the most refined GTAP applications undertaken to date, covering topics ranging from trade policy to the global implications of environmental policies, factor accumulation and technological change. The authors of the applications are representative of the broader group of GTAP users. Some are academics, while others are professional economists in national and international agencies. All of their studies can be independently replicated by the reader through accessing software and files via the Internet. Readers can also explore the sensitivity of results to varying assumptions and use the applications to launch independent research projects.

This textbook provides advanced undergraduate and graduate students with a complete introduction to modern cosmology. It successfully bridges the gap between undergraduate and advanced graduate texts by discussing topics of current research, starting from first principles. Throughout this authoritative volume, emphasis is given to the simplest, most intuitive explanation for key equations used by researchers. The first third of the book carefully develops the necessary background in general relativity and quantum fields. The rest of the book then provides self-contained accounts of all the key topics in contemporary cosmology, including inflation, topological defects, gravitational lensing, galaxy formation, large-scale structure and the distance scale. To aid understanding, the book is well illustrated with helpful figures and includes outline solutions to nearly 100 problems. All necessary astronomical jargon is clearly explained, ensuring the book is self-contained for any student w

This introduction to the field of many-body atomic physics is suitable for researchers and graduate students. Drawing from three major subject areas, atomic structure, atomic photoionization, and electron-atom collisions, this book begins with an introduction to many-body diagrams, and continues with several chapters devoted to each subject area written by leading theorists in that field. Topics in atomic structure include the relativistic theory for highly charged atomic ions and calculations of parity nonconservation. Topics in atomic photoionization include single and double photoionization processes, and photoelectron angular distributions. Topics in electron-atom collisions include the theory of electron impact ionization, perturbation series methods, target dependence of the triply differential cross section, Thomas processes, R-matrix theory, close coupling, and distorted-wave theory. This coherent and carefully edited volume has been prepared by leading atomic physicists as a t

The representation theory of reductive algebraic groups and related finite reductive groups is a subject of great topical interest and has many applications. The articles in this volume provide introductions to various aspects of the subject, including algebraic groups and Lie algebras, reflection groups, abelian and derived categories, the Deligne-Lusztig representation theory of finite reductive groups, Harish-Chandra theory and its generalisations, quantum groups, subgroup structure of algebraic groups, intersection cohomology, and Lusztig's conjectured character formula for irreducible representations in prime characteristic. The articles are carefully designed to reinforce one another, and are written by a team of distinguished authors: M. Broué, R. W. Carter, S. Donkin, M. Geck, J. C. Jantzen, B. Keller, M. W. Liebeck, G. Malle, J. C. Rickard and R. Rouquier. This volume as a whole should provide a very accessible introduction to an important, though technical, subject.

This 1998 book is both an introduction to, and a survey of, some topics of singularity theory; in particular the studying of singularities by means of differential forms. Here some ideas and notions that arose in global algebraic geometry, namely mixed Hodge structures and the theory of period maps, are developed in the local situation to study the case of isolated singularities of holomorphic functions. The author introduces the Gauss–Manin connection on the vanishing cohomology of a singularity, that is on the cohomology fibration associated to the Milnor fibration, and draws on the work of Brieskorn and Steenbrink to calculate this connection, and the limit mixed Hodge structure. This will be an excellent resource for all researchers whose interests lie in singularity theory, and algebraic or differential geometry.

At first glance, studying behavior is easy, but as every budding ethologist quickly realises, there are a host of complex practical, methodological and analytical problems to solve before designing and conducting the study. How do you choose which species or which behavior to study? What equipment will you need to observe and record behavior successfully? How do you record data in the dark, in the wet, or without missing part of the action? How do you analyse and interpret the data to yield meaningful information? This new expanded edition of the Handbook of Ethological Methods provides a complete step-by-step introduction to ethological methods from topic choice and behavioral description to data collection and statistical analysis. This book will be a must for beginning students and experienced researchers studying animal behavior in the field or laboratory.

The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for the specification and analysis of these structures. Of particular importance is their capacity to transform recursive definitions of tree-like structures into functional or differential equations, and vice versa. The goal of this book is to present the basic elements of the theory and to give a unified account of its developments and applications. It offers a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis and differential equations. This book will be a valuable reference to graduate students and researchers in combinatorics, analysis, and theoretical computer science.

Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. In this way, all the key ideas are covered without getting involved in the complications of more advanced systems, but concentrating rather on the principles that make the theory work in practice. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm which lies at the heart of every such system. Also featured are two other interesting algorithms that have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making the book at a level which can be used as an introduction to type theory for comp

This controversial book examines one of the most fundamental questions of modern cosmology: how much matter is there in the Universe? This issue affects theories of the origin and evolution of the Universe as well as its geometrical structure and ultimate fate. The authors discuss all the relevant cosmological and astrophysical evidence and come to the conclusion that the balance of arguments presently lies with a density of around twenty per cent of the critical density required for the Universe to ultimately recollapse. Because the arguments presented constitute a 'state-of-the-art' analysis of the observational and theoretical arguments surrounding the existence of dark matter, primordial nucleosynthesis, large-scale structure formation and the cosmic microwave background radiation, this study provides the reader with an indispensable introduction to the most exciting recent developments in modern cosmology. Written by two eminent cosmologists, this topical and provocative book will