Introduction to MATLAB

This book provides a self-contained and systematic introduction to classical electron theory and its quantization, non-relativistic quantum electrodynamics. The first half of the book covers the classical theory. It discusses the well-defined Abraham model of extended charges in interaction with the electromagnetic field, and gives a study of the effective dynamics of charges under the condition that, on the scale given by the size of the charge distribution, they are far apart and the applied potentials vary slowly. The second half covers the quantum theory, leading to a coherent presentation of non-relativistic quantum electrodynamics. Topics discussed include non-perturbative properties of the basic Hamiltonian, the structure of resonances, the relaxation to the ground state through emission of photons, the non-perturbative derivation of the g-factor of the electron and the stability of matter.

This is a collection of lecture notes from the Summer School 'Cycles Algébriques; Aspects Transcendents, Grenoble 2001'. The topics range from introductory lectures on algebraic cycles to more advanced material. The advanced lectures are grouped under three headings: Lawson (co)homology, motives and motivic cohomology and Hodge theoretic invariants of cycles. Among the topics treated are: cycle spaces, Chow topology, morphic cohomology, Grothendieck motives, Chow-Künneth decompositions of the diagonal, motivic cohomology via higher Chow groups, the Hodge conjecture for certain fourfolds, an effective version of Nori's connectivity theorem, Beilinson's Hodge and Tate conjecture for open complete intersections. As the lectures were intended for non-specialists many examples have been included to illustrate the theory. As such this book will be ideal for graduate students or researchers seeking a modern introduction to the state-of-the-art theory in this subject.

This graduate-level text gives a self-contained exposition of fundamental topics in equilibrium and nonequilibrium statistical thermodynamics. The text follows a balanced approach between the macroscopic (thermodynamic) and microscopic (statistical) points of view. The first half of the book deals with equilibrium thermodynamics and statistical mechanics. In addition to standard subjects, the reader will find a detailed account of broken symmetries, critical phenomena and the renormalization group, as well as an introduction to numerical methods. The second half of the book is devoted to nonequilibrium phenomena, first following a macroscopic approach, with hydrodynamics as an important example. Kinetic theory receives a thorough treatment through analysis of the Boltzmann-Lorentz model and the Boltzmann equation. The book concludes with general nonequilibrium methods such as linear response, projection method and the Langevin and Fokker-Planck equations, including numerical simulation

In this elegantly written book, Lee Wandel discusses the relationship between the reform of poor relief and the Protestant Reformation in early sixteenth-century Zurich. In the introduction she traces the various ways that poverty had been evaluated, and its social and religious connotations, up to the sixteenth century. The first chapter provides a portrait of sixteenth-century Zurich. The next three chapters explore the discussion of the poor in various media of the town. The second chapter examines the sermons and pamphlets of Huldrych Zwingli, who was preaching that the poor were the true images of God. The third chapter addresses printed images depicting Christ calling beggars and other poor folk to Him, which appeared on title pages of Zwingli's pamphlets. The fourth chapter turns to the language of legislation, and in particular the poor ordinances of 1520 and 1525.

This book presents an introduction to, and modern account of, magnetohydrodynamic (MHD) turbulence, an active field both in general turbulence theory and in various areas of astrophysics. The book starts by introducing the MHD equations, certain useful approximations and the transition to turbulence. The second part of the book covers incompressible MHD turbulence, the macroscopic aspects connected with the different self-organization processes, the phenomenology of the turbulence spectra, two-point closure theory, and intermittency. The third considers two-dimensional turbulence and compressible (in particular, supersonic) turbulence. Because of the similarities in the theoretical approach, these chapters start with a brief account of the corresponding methods developed in hydrodynamic turbulence. The final part of the book is devoted to astrophysical applications: turbulence in the solar wind, in accretion disks, and in the interstellar medium. This book is suitable for graduate stud

The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the leve

The revised edition of Robert Stern's book brings India's story up to date. Since its original publication in 1993, much has altered and yet central to the author's argument remains his belief in the remarkable continuity and vitality of India's social systems and its resilience in the face of change. This is a colourful, readable and comprehensive introduction to modern India. In a journey through its family households and villages, the author explains its long-lived and little understood caste and class systems, its venerable faiths and extraordinary ethnic diversity, its history as 'the jewel in the crown' of British imperialism and its post-Independence career as a major agricultural and industrial nation. While paradoxes abound in an India which is constantly transforming, Stern demonstrates how and why it remains the largest and most enduring democracy in the developing world.

The Physics of Plasmas provides a comprehensive introduction to the subject, illustrating the basic theory with examples drawn from fusion, space and astrophysical plasmas. A particular strength of the book is its discussion of the various models used to describe plasma physics and the relationships between them. These include particle orbit theory, fluid equations, ideal and resistive magnetohydrodynamics, wave equations and kinetic theory. The reader will gain a firm grounding in the fundamentals, and develop this into an understanding of some of the more specialised topics. Throughout the text, there is an emphasis on the physical interpretation of plasma phenomena. Exercises are provided throughout. Advanced undergraduate and graduate students of physics, applied mathematics, astronomy and engineering will find a clear but rigorous explanation of the fundamental properties of plasmas with minimal mathematical formality. This book will also appeal to research physicists, nuclear and

The sounds of language can be divided into consonants, vowels, and tones - the use of pitch to convey word meaning. Seventy percent of the world's languages use pitch in this way. Assuming little or no prior knowledge of the topic, this textbook provides a clearly organized introduction to tone and tonal phonology. Comprehensive in scope, it examines the main types of tonal systems found in Africa, the Americas, and Asia, using examples from the widest possible range of tone languages. It provides students with a basic grasp of the simple phonetics of tone, and covers key topics such as the distinctive feature systems suitable for tonal contrasts, allophonic and morphophonological tonal alterations, and how to analyze them within Optimality Theory. The book also examines the perception and acquisition of tone, as well as the interface between tonal phonology and the morphosyntax.

The author presents an accessible and self-contained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. The reader is then presented with a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A self-contained presentation of 'exotic' functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a 'Coulomb moving frame' is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces.

This volume contains selected papers by leading researchers from the international conference entitled Tits Buildings and the Model Theory of Groups, held in Würzburg in 2000. The first part of the book provides a general introduction to many aspects of buildings and their geometries, based on short lecture courses given at the conference. The rest of the book comprises survey and research articles on model theoretic results and techniques, showing the vitality and richness of these branches of mathematics. Among the most fruitful techniques, amalgamation constructions à la Hrushovski are explained and classified as they continue to play an important role both in model theory and geometry. The articles succeed in demonstrating the close connection between geometry, group theory and model theory. The book will be invaluable to graduate students as well as experienced researchers working in these areas of mathematics.

The projective, Möbius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces. This book summarizes all known major results and open problems related to these classical point-line geometries and their close (nonclassical) relatives. Topics covered include: classical geometries; methods for constructing nonclassical geometries; classifications and characterizations of geometries. This work is related to many other fields including interpolation theory, convexity, the theory of pseudoline arrangements, topology, the theory of Lie groups, and many more. The authors detail these connections, some of which are well-known, but many much less so. Acting both as a reference for experts and as an accessible introduction for graduate students, this book will interest anyone wishing to know more about point-line geometries and the way they interact.

Industrial mathematics is growing enormously in popularity around the world. This book deals with real industrial problems from real industries. Presented as a series of case studies by some of the world's most active and successful industrial mathematicians, this volume shows clearly how the process of mathematical collaboration with industry can not only work successfully for the industrial partner, but also lead to interesting and important mathematics. The book begins with a brief introduction, where the equations that most of the studies are based upon are summarised. Thirteen different problems are then considered, ranging from cooking of cereal to the analysis of epidemic waves in animal populations. Throughout the work the emphasis is on telling industry what they really want to know. This book is suitable for all final year undergraduates, master's students, and Ph.D. students who are working on practical mathematical modeling.

The introduction of numerical methods, particularly finite element (FE) analysis, represents a significant advance in metal forming operations. Numerical methods are used increasingly to optimize product design and deal with problems in metal forging, rolling, and extrusion processes. Metal Forming Analysis, first published in 2001, describes the most important numerical techniques for simulating metal forming operations. The first part of the book describes principles and procedures and includes numerous examples and worked problems. The remaining chapters focus on applications of numerical analysis to specific forming operations. Most of these results are drawn from the authors' research in the areas of metal testing, sheet metal forming, forging, extrusion, and similar operations. Sufficient information is presented so that readers can understand the nonlinear finite element method as applied to forming problems without a prior background in structural finite element analysis. Gradu

This is a collection of surveys and research papers on topics of interest in combinatorics, given at a conference in Mátraháza, Hungary. Originally published in journal form, it is here reissued as a book due to its special interest. It is dedicated to Paul Erdös, who attended the conference and who is represented by two articles in the collection, including one, unfinished, which he was writing on the eve of his sudden death. Erdös was one of the greatest mathematicians of his century and often the subject of anecdotes about his somewhat unusual lifestyle. A preface, written by friends and colleagues, gives a flavour of his life, including many such stories, and also describes the broad outline and importance of his work in combinatorics and other related fields. Here is a succinct introduction to important ideas in combinatorics for researchers and graduate students.

Shakespeare has an astonishingly rich and varied performance tradition in Japan, stretching from the Westernizing and modernizing ferment of the nineteenth-century Meiji era to the postmodern performance culture. How has the tradition evolved? Where is it going? How is it to be accounted for in theatrical and cultural terms? What does it mean to perform Shakespeare in Japan? Such questions are raised in this 2001 book's introduction and pursued in fourteen essays on key aspects, moments and personalities in the performance tradition. These are followed by provocative interviews with four leading directors (Deguchi Norio, Ninagawa Yukio, Suzuki Tadashi and Noda Hideki) and with one leading performer (Hira Mikijiro). Unlike the very few existing books on Japanese Shakespeare, this book concentrates on modern and postmodern theatre, from c.1970, and contains contributions from both Japanese and Western scholars and theatre practitioners.

Optimal Reliability Design, first published in 2000, provides a detailed introduction to systems reliability and reliability optimization. Techniques for maximizing system reliability are described, focusing on component reliability enhancement and redundancy arrangement. The authors present several case studies and show how optimization techniques are applied in practice. They also pay particular attention to finding methods that give the optimal trade-off between reliability and cost. The book begins with a review of key background material, and a discussion of a range of optimization models. The authors go on to cover optimization tools, such as heuristics, discrete optimization, nonlinear programming, mixed integer programming, optimal arrangement, and metaheuristic algorithms. They also describe the computational implementation of these tools. Many numerical examples are included, and the book contains over 180 homework exercises. It is suitable as a textbook for graduate-level co

This book, first published in 2000, was the first since Jorge Huerta's earlier study Chicano Theater: Themes and Forms to explore the diversity and energy of Chicano theatre. Huerta takes as his starting point 1979, the year Luis Valdez's play, Zoot Suit, was produced on Broadway. Huerta looks at plays by and about Chicana and Chicanos, as they explore, through performance, the community and its identity caught between the United States and Mexico. Through informative biographies of each playwright and analyses of their plays, Huerta offers an accessible introduction to this important aspect of American theatre and culture. Overall, Huerta establishes a pattern of theatrical activity that is closely linked with both Western European traditions of realism and an indigenous philosophy seen in contemporary Chicano culture. The book contains photographs from key productions and will be invaluable to students, scholars and general theatregoers.

This book, first published in 2000, was the first since Jorge Huerta's earlier study Chicano Theater: Themes and Forms to explore the diversity and energy of Chicano theatre. Huerta takes as his starting point 1979, the year Luis Valdez's play, Zoot Suit, was produced on Broadway. Huerta looks at plays by and about Chicana and Chicanos, as they explore, through performance, the community and its identity caught between the United States and Mexico. Through informative biographies of each playwright and analyses of their plays, Huerta offers an accessible introduction to this important aspect of American theatre and culture. Overall, Huerta establishes a pattern of theatrical activity that is closely linked with both Western European traditions of realism and an indigenous philosophy seen in contemporary Chicano culture. The book contains photographs from key productions and will be invaluable to students, scholars and general theatregoers.

How did our minds evolve? Can evolutionary considerations illuminate the question of the basic architecture of the human mind? These are two of the main questions addressed in Evolution and the Human Mind by a distinguished interdisciplinary team of philosophers, psychologists, anthropologists and archaeologists. The essays focus especially on issues to do with modularity of mind, the evolution and significance of natural language, and the evolution of our capacity for meta-cognition (thought about thought), together with its implications for consciousness. The editors have provided an introduction that lays out the background to the questions which the essays address, and a consolidated bibliography that will be a valuable reference resource for all those interested in this area. The volume will be of great interest to all researchers and students interested in the evolution and nature of the mind.

How did our minds evolve? Can evolutionary considerations illuminate the question of the basic architecture of the human mind? These are two of the main questions addressed in Evolution and the Human Mind by a distinguished interdisciplinary team of philosophers, psychologists, anthropologists and archaeologists. The essays focus especially on issues to do with modularity of mind, the evolution and significance of natural language, and the evolution of our capacity for meta-cognition (thought about thought), together with its implications for consciousness. The editors have provided an introduction that lays out the background to the questions which the essays address, and a consolidated bibliography that will be a valuable reference resource for all those interested in this area. The volume will be of great interest to all researchers and students interested in the evolution and nature of the mind.

This is a graduate text on turbulent flows, an important topic in fluid dynamics. It is up-to-date, comprehensive, designed for teaching, and is based on a course taught by the author at Cornell University for a number of years. The book consists of two parts followed by a number of appendices. Part I provides a general introduction to turbulent flows, how they behave, how they can be described quantitatively, and the fundamental physical processes involved. Part II is concerned with different approaches for modelling or simulating turbulent flows. The necessary mathematical techniques are presented in the appendices. This book is primarily intended as a graduate level text in turbulent flows for engineering students, but it may also be valuable to students in applied mathematics, physics, oceanography and atmospheric sciences, as well as researchers and practising engineers.

This book, first published in 2000, deals with the micromechanical characterization of polymer materials. Particular attention is given to microhardness as a technique capable of detecting a variety of morphological and textural changes in polymers. A comprehensive introduction to the microhardness of polymers is provided, including descriptions of the various testing methods in materials science and engineering. The book also includes the micromechanical study of glassy polymers and discusses the relevant aspects of microhardness of semicrystalline polymers. The volume also presents selected application examples of the microhardness technique for the characterization of polymeric materials, including the influence of polymer processing, the use in weathering tests, the characterization of modified polymer surfaces, and others. This book will be of use to graduate-level materials science students, as well as research workers in materials science, mechanical engineering and physics dep

This text provides a comprehensive introduction to the physical principles and design of particle detectors, covering all major detector types in use today. The book begins with a reprise of the size and energy scales involved in different physical processes. It then considers non-destructive methods, including the photoelectric effect, photomultipliers, scintillators, Cerenkov and transition radiation, scattering and ionisation and the use of magnetic fields in drift and wire chambers. A complete chapter is devoted to silicon detectors. In the final part of the book, the author discusses destructive measurement techniques including Thompson and Compton scattering, Bremsstrahlung and calorimetry. Throughout the book, emphasis is placed on explaining the physical principles on which detection is based, and showing, by considering appropriate examples, how those principles are best utilised in real detectors. This approach also reveals the limitations that are intrinsic to different devi

Functional programming is a style of programming that emphasizes the use of functions (in contrast to object-oriented programming, which emphasizes the use of objects). It has become popular in recent years because of its simplicity, conciseness, and clarity. This book teaches functional programming as a way of thinking and problem solving, using Haskell, the most popular purely functional language. Rather than using the conventional (boring) mathematical examples commonly found in other programming language textbooks, the author uses examples drawn from multimedia applications, including graphics, animation, and computer music, thus rewarding the reader with working programs for inherently more interesting applications. Aimed at both beginning and advanced programmers, this tutorial begins with a gentle introduction to functional programming and moves rapidly on to more advanced topics. Details about progamming in Haskell are presented in boxes throughout the text so they can be easil

Functional programming is a style of programming that emphasizes the use of functions (in contrast to object-oriented programming, which emphasizes the use of objects). It has become popular in recent years because of its simplicity, conciseness, and clarity. This book teaches functional programming as a way of thinking and problem solving, using Haskell, the most popular purely functional language. Rather than using the conventional (boring) mathematical examples commonly found in other programming language textbooks, the author uses examples drawn from multimedia applications, including graphics, animation, and computer music, thus rewarding the reader with working programs for inherently more interesting applications. Aimed at both beginning and advanced programmers, this tutorial begins with a gentle introduction to functional programming and moves rapidly on to more advanced topics. Details about progamming in Haskell are presented in boxes throughout the text so they can be easil

This is an exceptionally accessible, accurate, and non-technical introduction to quantum mechanics. After briefly summarizing the differences between classical and quantum behaviour, this engaging account considers the Stern-Gerlach experiment and its implications, treats the concepts of probability, and then discusses the Einstein-Podolsky-Rosen paradox and Bell's theorem. Quantal interference and the concept of amplitudes are introduced and the link revealed between probabilities and the interference of amplitudes. Quantal amplitude is employed to describe interference effects. Final chapters explore exciting new developments in quantum computation and cryptography, discover the unexpected behaviour of a quantal bouncing-ball, and tackle the challenge of describing a particle with no position. Thought-provoking problems and suggestions for further reading are included. Suitable for use as a course text, The Strange World of Quantum Mechanics enables students to develop a genuine unde

This is an exceptionally accessible, accurate, and non-technical introduction to quantum mechanics. After briefly summarizing the differences between classical and quantum behaviour, this engaging account considers the Stern-Gerlach experiment and its implications, treats the concepts of probability, and then discusses the Einstein-Podolsky-Rosen paradox and Bell's theorem. Quantal interference and the concept of amplitudes are introduced and the link revealed between probabilities and the interference of amplitudes. Quantal amplitude is employed to describe interference effects. Final chapters explore exciting new developments in quantum computation and cryptography, discover the unexpected behaviour of a quantal bouncing-ball, and tackle the challenge of describing a particle with no position. Thought-provoking problems and suggestions for further reading are included. Suitable for use as a course text, The Strange World of Quantum Mechanics enables students to develop a genuine unde

Researchers in a growing number of fields - public policy, law, business, medicine, psychology, engineering, and others - are working to understand and improve human judgment and decision making. This book, which presupposes no formal training, brings together a selection of key articles in the area, with careful organization, introduction and commentaries. Issues involving medical diagnosis, weather forecasting, labor negotiations, risk, public policy, business strategy, eyewitnesses, jury decisions issues, and more are treated in this largely expanded volume, indicating the variety of problems - and scope in judgment and decision making. This is a revision of Arkes and Hammond's 1986 collection of papers on judgment and decision making. Updated and extended, the focus of this volume is interdisciplinary and applied. The papers selected are scientific in nature, but chosen specifically to appeal to the scholar, student and layperson alike.

Researchers in a growing number of fields - public policy, law, business, medicine, psychology, engineering, and others - are working to understand and improve human judgment and decision making. This book, which presupposes no formal training, brings together a selection of key articles in the area, with careful organization, introduction and commentaries. Issues involving medical diagnosis, weather forecasting, labor negotiations, risk, public policy, business strategy, eyewitnesses, jury decisions issues, and more are treated in this largely expanded volume, indicating the variety of problems - and scope in judgment and decision making. This is a revision of Arkes and Hammond's 1986 collection of papers on judgment and decision making. Updated and extended, the focus of this volume is interdisciplinary and applied. The papers selected are scientific in nature, but chosen specifically to appeal to the scholar, student and layperson alike.

This reader provides a unique mix of American and European contributions to the study of particular markets, often combined with a critical evaluation of antitrust regulations, decisions or judgments. Part I explains market structure as a function of sunk costs and market size. Part II illustrates the central role of pricing schemes (including parallel pricing, delivered pricing and competition clauses) in sustaining equilibrium outcomes in oligopolistic markets. Parts III and IV give a game-theoretic foundation to competition policy and merger control. Louis Phlips offers a comprehensive introduction to the text in which he very carefully explains the reasoning behind his choice of papers, and provides a superb synthesis of the material. Particular highlights include the discussion and evaluation of antitrust regulations, which involve a systematic comparative analysis of European and American regulations, decisions and judgments in this area.

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 book examines a selection of philosophical issues in the context of specific episodes in the development of physical theories. Advances in science are presented against the historical and philosophical backgrounds in which they occurred. A major aim is to impress upon the reader the essential role that philosophical considerations have played in the actual practice of science. The book begins with some necessary introduction to the history of ancient and early modern science, with major emphasis being given to the two great watersheds of twentieth-century physics: relativity and, especially, quantum mechanics. At times the term 'construction' may seem more appropriate than 'discovery' for the way theories have developed and, especially in the later chapters, the question of the influence of historical, philosophical and even social factors on the very form and content of scientific theories is discussed.

This is a major student edition of the text described as 'the first modern classic of English history'. Bacon's penetration into human motives, his life-long experience of politics and government, and his remarkable literary skills, render this History of the Reign of King Henry VII a major work of English literature and an important document in the history of political thought. The introduction places Bacon's History in the context of Renaissance historiography, revealing its debt to Tacitus, and shows Bacon's originality in re-ordering traditional material to make a coherent psychological analysis of the King's actions. In addition to the usual series features and supporting contextual material (including relevant Essays by Bacon), generous editorial footnotes explain the historical and political issues of the reign of Henry VII, and a substantial glossary clarifies Bacon's rich but sometimes unfamiliar vocabulary.

A self-contained introduction to magnetohydrodynamics (MHD), with emphasis on nonlinear processes. Chapters 2 to 4 outline the conventional aspects of MHD theory, magnetostatic equilibrium and linear stability theory, which form a natural basis for the topics in the subsequent chapters. The main part, chapters 5 to 7, presents nonlinear theory, starting with the evolutions and saturations of individual ideas and resistive instabilities, continuing with a detailed analysis of magnetic reconnection, and concluding with the most complex nonlinear behaviour, that of MHD turbulence. The last chapters describe three important applications of the theory: disruptive processes in tokamaks, MHD effects in reversed-field pinches, and solar flares. In the presentation the focus is more on physical mechanisms than on special formalisms. The book is essential reading for researchers and graduate students interested in MHD processes both in laboratory and in astrophysical plasmas.

This book deals with flows over propellers operating behind ships, and the hydrodynamic forces and moments which the propeller generates on the shaft and on the ship hull. The first part of the book is devoted to fundamentals of the flow about hydrofoil sections and wings, propellers in uniform flow and pragmatic design guides for analysis and performance. The second part covers the development of unsteady section and blade forces arising from operation in non-uniform hull wakes. The problem of a non-cavitating, wide-bladed propeller in a wake is treated by a new and completely developed theory. A final chapter discusses the optimisation of efficiency of compound propulsors. The authors have taken great care to clearly describe physical concepts and mathematical steps. An appendix provides a concise introduction to (or reprise of) the mathematical techniques used.

Prior to publication of this 1996 book, much had been written on Plato as a critic of literature, but no commentaries had appeared in English on the Ion, or the opening books of the Republic in which Plato launches his famous attack on poetry, since the early years of this century. This volume brings together these texts and the relevant section of Republic 10. It aims to provide the reader with a commentary which takes account of modern scholarship on the subject, and which explores the ambivalence of Plato's pronouncements on poetry through an analysis of his own skill as a writer. A general introduction sets Plato's views in the wider context of attitudes to poetry in Greek society before his time, and indicates the main ways in which his writings on poetry have influenced the history of aesthetic thought in European culture.

Ovid's Heroides, a collection of twenty-one epistles in elegiac verse, consists of two groups, the first comprising fourteen poems addressed by heroines of mythology to their absent lovers or husbands. In this edition, Professor Knox offers a commentary on seven of these epistles, addressing problems of language and style, and focusing on the relationship of the Heroides to the classic works of Greek and Roman literature on which Ovid bases his representation of these women. In addition, he has included a commentary on the Epistula Sapphus, a separate poem of doubtful authorship which was composed in the manner of Ovid and is believed by many to be by him. The Introduction provides an account of the genre, a survey of language, style and metre, and an outline of the problems concerning the authenticity of parts of the collection.

In this distinctive 1996 book the authors combine an introduction to welfare economics, a discussion of project appraisal principles in developing countries and a survey of the cost-benefit problems raised by externalities, risk and the environment. There are references throughout to contemporary research work in developing economics, and a number of important development policy issues, such as trade reform, commodity price stabilization and the rate of exploitation of natural resources, are considered within a unified cost-benefit framework. A particular feature is the use at an elementary level of general equilibrium models which extend the analysis beyond the limits of the well known partial measures of producer and consumer surplus. The book is primarily intended for courses in development economics, but will also be of interest to students of public policy, both in teaching and administration.

This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and