Classical Recursion Theory

Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thou

Abstract economic theory may be timeless and potentially universal in its application, but macroeconomics has to be seen in its historical context. The nature of the policy regime, the behaviour of the economy and the beliefs of professional economists all interact, and influence each other. This short historical account of monetary regimes since 1900 shows how the role of policy has changed, and how this has related to experience of inflation and the real economy, as well as to changes in political philosophies. The narrative concentrates on developments in America, Europe and Japan from the era of the classical gold standard, via the era of policy intervention and reduced faith in the market to the present 'neo-liberal' regimes. The 'grand narrative' of the century is a journey 'to Utopia and back'. It is argued that no school of macroeconomics is right for all time; different theoretical models may be appropriate, for different periods and regimes.

This timely and synoptic text contains the essentials of queueing networks, from the classical product-form theory to the more recent developments such as diffusion and fluid limits, stochastic compa

Since its introduction in 1828, using Green's functions has become a fundamental mathematical technique for solving boundary value problems. Most treatments, however, focus on its theory and classical

Probabilistic risk analysis aims to quantify the risk caused by high technology installations. Increasingly, such analyses are being applied to a wider class of systems in which problems such as lack of data, complexity of the systems, uncertainty about consequences, make a classical statistical analysis difficult or impossible. The authors discuss the fundamental notion of uncertainty, its relationship with probability, and the limits to the quantification of uncertainty. Drawing on extensive experience in the theory and applications of risk analysis, the authors focus on the conceptual and mathematical foundations underlying the quantification, interpretation and management of risk. They cover standard topics as well as important new subjects such as the use of expert judgement and uncertainty propagation. The relationship of risk analysis with decision making is highlighted in chapters on influence diagrams and decision theory. Finally, the difficulties of choosing metrics to quanti

The predominant view of moral virtue can be traced back to Aristotle. He believed that moral virtue must involve intellectual excellence. To have moral virtue one must have practical wisdom - the ability to deliberate well and to see what is morally relevant in a given context. Julia Driver challenges this classical theory of virtue, arguing that it fails to take into account virtues which do seem to involve ignorance or epistemic defect. Some 'virtues of ignorance' are counterexamples to accounts of virtue which hold that moral virtue must involve practical wisdom. Modesty, for example, is generally considered to be a virtue even though the modest person may be making an inaccurate assessment of his or her accomplishments. Driver argues that we should abandon the highly intellectualist view of virtue and instead adopt a consequentialist perspective which holds that virtue is simply a character trait which systematically produces good consequences.

In Virginia Woolf and the Visible World, Emily Dalgarno examines Woolf's engagement with notions of the subject and codes of the visible. Dalgarno examines how Woolf's writing engages with visible and non-visible realms of experience, and draws on ideas from the diverse fields of psychoanalytic theory, classical Greek tragedy, astronomy, photography and photojournalism. The solar eclipse of 1927 marks a dividing line in Woolf's career, after which she portrayed the visible world in terms of light, and shifted her interest from painting to photography. Dalgarno offers textual analyses of Woolf's individual works, including To the Lighthouse, The Waves and Three Guineas, arguing for the importance of her ongoing interest in Greek translation. In later chapters, she explores the theory of the subject that emerges from Woolf's representation of the visible in her autobiography.

Four concise, brilliant lectures on mathematical methods in quantum mechanics from Nobel Prize-winning quantum pioneer build on idea of visualizing quantum theory through the use of classical mechani

This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations, they turn their attention, in the two final chapters, to the non-periodic setting, concentrating on problems

Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.

This book is suitable for students and statisticians with a knowledge of graduate-level statistical theory. At least some background in classical likelihood theory is recommended, but the opening cha

Spectral sequences are among the most elegant, most powerful, and most complicated methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first third of the book treats the algebraic foundations for this sort of homological algebra, starting from informal calculations, to give the novice a familiarity with the range of applications possible. The heart of the book is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.

This book presents the definitive exposition of 'prospect theory', a compelling alternative to the classical utility theory of choice. Building on the 1982 volume, Judgement Under Uncertainty, this book brings together seminal papers on prospect theory from economists, decision theorists, and psychologists, including the work of the late Amos Tversky, whose contributions are collected here for the first time. While remaining within a rational choice framework, prospect theory delivers more accurate, empirically verified predictions in key test cases, as well as helping to explain many complex, real-world puzzles. In this volume, it is brought to bear on phenomena as diverse as the principles of legal compensation, the equity premium puzzle in financial markets, and the number of hours that New York cab drivers choose to drive on rainy days. Theoretically elegant and empirically robust, this volume shows how prospect theory has matured into a new science of decision making.

Spectral sequences are among the most elegant, most powerful, and most complicated methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first third of the book treats the algebraic foundations for this sort of homological algebra, starting from informal calculations, to give the novice a familiarity with the range of applications possible. The heart of the book is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.

This book provides a comprehensive and self-contained exposition of the algebro-geometric theory of singularities of plane curves, covering both its classical and its modern aspects. The book gives a unified treatment, with complete proofs, presenting modern results which have only ever appeared in research papers. It updates and correctly proves a number of important classical results for which there was formerly no suitable reference, and includes new, previously unpublished results as well as applications to algebra and algebraic geometry. This book will be useful as a reference text for researchers in the field. It is also suitable as a textbook for postgraduate courses on singularities, or as a supplementary text for courses on algebraic geometry (algebraic curves) or commutative algebra (valuations, complete ideals).

This volume introduces some of the basic philosophical and conceptual questions underlying the formulation of quantum mechanics, one of the most baffling and far-reaching aspects of modern physics. The book consists of articles by leading thinkers in this field, who have been inspired by the profound work of the late John Bell. Some of the deepest issues concerning the nature of physical reality are debated, including the theory of physical measurements, how to test quantum mechanics, and how classical and quantum physics are related. This book will be of interest to students with a background in quantum physics, who wish to explore in more detail its philosophical aspects, practising scientists who are not content with blindly applying the rules of quantum mechanics, and anyone interested in gaining a deeper understanding of the philosophy of physics.

Most books on the theory and analysis of beams and plates deal with the classical (Euler-Bernoulli/Kirchoff) theories but few include shear deformation theories in detail. The classical beam/plate the

This revised and updated second edition of a highly successful book is the only text at this level to embrace a universal approach to three major developments in classical physics; namely nonlinear waves, solitons and chaos. The authors now include new material on biology and laser theory, and go on to discuss important recent developments such as soliton metamorphosis. A comprehensive treatment of basic plasma and fluid configurations and instabilities is followed by a study of the relevant nonlinear structures. Each chapter concludes with a set of problems. This text will be particularly valuable for students taking courses in nonlinear aspects of physics. In general, it will be of value to final year undergraduates and beginning graduate students studying fluid dynamics, plasma physics and applied mathematics.

Most natural and industrial flows are turbulent. The atmosphere and oceans, automobile and aircraft engines, all provide examples of this ubiquitous phenomenon. In recent years, turbulence has become a very lively area of scientific research and application, attracting many newcomers who need a basic introduction to the subject. An Introduction to Turbulent Flow, first published in 2000, offers a solid grounding in the subject of turbulence, developing both physical insight and the mathematical framework needed to express the theory. It begins with a review of the physical nature of turbulence, statistical tools, and space and time scales of turbulence. Basic theory is presented next, illustrated by examples of simple turbulent flows and developed through classical models of jets, wakes, and boundary layers. A deeper understanding of turbulence dynamics is provided by spectral analysis and its applications. The final chapter introduces the numerical simulation of turbulent flows. This

Fundamentals of Ethics for Scientists and Engineers represents a new approach to introductory ethics that is both practical and accessible. Classical virtue theory is employed to provide a time-tested

This collection offers a critical assessment of the published works of Piero Sraffa, one of the leading economists of the twentieth century, and their legacy for the economics profession. The topics covered explore Sraffa's interpretation of the classical economists; his theory of value and distribution; his critique of partial and general neoclassical equilibrium theory; his focus on the problem of capital; and his critique of Hayek's monetary overinvestment theory of the business cycle. Specific issues investigated include intertemporal general equilibrium theory and the capital problem; the probability of reswitching; Ricardo, Malthus, and the corn model; and the meaning and implication of the capital controversy. Among the contributors are many of the world's leading students of Sraffian economics, including Nobel Laureate Paul Samuelson, Christian Bidard, Edwin Burmeister, John Eatwell, Pierangelo Garegnani, Samuel Hollander, Heinz Kurz, Lynn Mainwaring, Neri Salvadori, Bertram Sc

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.

This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a mod

In this first book-length treatment of integration theory for many years, Ben Rosamond provides an accessible and stimulating critical introduction to the full range of classical and contemporary per

Presents a classical approach to the general topics of the geometry of curves, including the theory of curves in n -dimensional Euclidean space. Yu (Ukranian Academy of Sciences) investigates proble

The Companion to Major Social Theorists offers a broad-ranging survey of classical and contemporary social theory. In original essays especially commissioned for this volume, leading experts and pract

Quantum field theory forms the present theoretical framework for our understanding of the fundamental interactions of particle physics. This up-dated and expanded text examines gauge theories and their symmetries with an emphasis on their physical and technical aspects. Beginning with a new chapter giving a systematic introduction to classical field theories and a short discussion of their canonical quantization and the discrete symmetries C, P and T, the book provides a brief exposition of perturbation theory, the renormalization programme, and the use of the renormalization group equation. It then explores topics of current research interest including chiral symmetry and its breaking, anomalies, and low energy effective lagrangians and some basics of supersymmetry. A chapter on basics of the electroweak theory is now included. Professor Pokorski, a distinguished theoretical physicist, has presented here a self-contained text for graduate courses in physics; the only prerequisite is s

Covers major vector variational methods developed to solve nonlinear elasticity problems. Discusses the classical existence theory, makes a brief incursion into problems where nonexistence is fundamen

Most texts on electromagnetic theory follow the classical approach of steady state solutions of Maxwell's equations. In Interstellar Propagation of Electromagnetic Signals, the authors, H. Harmuth

Low-speed aerodynamics is important in the design and operation of aircraft flying at low Mach number, and ground and marine vehicles. This 2001 book offers a modern treatment of the subject, both the theory of inviscid, incompressible, and irrotational aerodynamics and the computational techniques now available to solve complex problems. A unique feature of the text is that the computational approach (from a single vortex element to a three-dimensional panel formulation) is interwoven throughout. Thus, the reader can learn about classical methods of the past, while also learning how to use numerical methods to solve real-world aerodynamic problems. This second edition has a new chapter on the laminar boundary layer (emphasis on the viscous-inviscid coupling), the latest versions of computational techniques, and additional coverage of interaction problems. It includes a systematic treatment of two-dimensional panel methods and a detailed presentation of computational techniques for thr

This book, first published in 2000, is a comprehensive introduction to holomorphic dynamics, that is the dynamics induced by the iteration of various analytic maps in complex number spaces. This has been the focus of much attention in recent years, with, for example, the discovery of the Mandelbrot set, and work on chaotic behaviour of quadratic maps. The treatment is mathematically unified, emphasizing the substantial role played by classical complex analysis in understanding holomorphic dynamics as well as giving an up-to-date coverage of the modern theory. The authors cover entire functions, Kleinian groups and polynomial automorphisms of several complex variables such as complex Henon maps, as well as the case of rational functions. The book will be welcomed by graduate students and professionals in pure mathematics and science who seek a reasonably self-contained introduction to this exciting area.

The theory of schemes is the foundation for algebraic geometry proposed and elaborated by Alexander Grothendieck and his co-workers. It has allowed major progress in classical areas of algebraic geo

Since the time of Lagrange and Euler, it has been well known that an understanding of algebraic curves can illuminate the picture of rigid bodies provided by classical mechanics. A modern view of the role played by algebraic geometry has been established iby many mathematicians. This book presents some of these techniques, which fall within the orbit of finite dimensional integrable systems. The main body of the text presents a rich assortment of methods and ideas from algebraic geometry prompted by classical mechanics, whilst in appendices the general, abstract theory is described. The methods are given a topological application to the study of Liouville tori and their bifurcations. The book is based on courses for graduate students given by the author at Strasbourg University but the wealth of original ideas will make it also appeal to researchers.

This text describes novel treatments of quantum problems using enhanced quantization procedures. When treated conventionally, certain systems yield trivial and unacceptable results. This book describes enhanced procedures, generally involving extended correspondence rules for the association of a classical and a quantum theory, which, when applied to such systems, yield nontrivial and acceptable results. The text begins with a review of classical mechanics, Hilbert space, quantum mechanics, and scalar quantum field theory. Next, analytical skills are further developed, a special class of models is studied, and a discussion of continuous and discontinuous perturbations is presented. Later chapters cover two further classes of models both of which entail discontinuous perturbations. The final chapter offers a brief summary, concluding with a conjecture regarding interacting covariant scalar quantum field theories. Symmetry is repeatedly used as a tool to help develop solutions for simple

This book features summaries and excerpts of major works in political theory, including authors as diverse in their political thinking as Karl Marx and Alexander Hamilton, as well as classical writers

This 1999 book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theorems and with the Hausdorff dimension of the associated null sets. After setting out the necessary background material, the authors give a full discussion of Hausdorff dimension and its uses in Diophantine approximation. A wide range of techniques from the number theory arsenal are used to obtain the upper and lower bounds required, and this is an indication of the difficulty of some of the questions considered. The authors go on to consider briefly the p-adic case, and they conclude with a chapter on some applications of metric Diophantine approximation. All researchers with an interest in Diophantine approximation will welcome this book.

The theme of this book is the study of the distribution of integer powers modulo a prime number. It provides numerous new, sometimes quite unexpected, links between number theory and computer science as well as to other areas of mathematics. Possible applications include (but are not limited to) complexity theory, random number generation, cryptography, and coding theory. The main method discussed is based on bounds of exponential sums. Accordingly, the book contains many estimates of such sums, including new estimates of classical Gaussian sums. It also contains many open questions and proposals for further research.

This book helps explain one of the most intriguing and politically salient puzzles in comparative political economy: why some countries have much higher unemployment rates than others. Contrary to new classical economics the focus is on explaining distribution and equilibrium unemployment, and contrary to neo-corporatist theory the role of monetary policy and rational expectation is integral to the analysis. The book makes two central arguments. The first is that monetary policies affect equilibrium employment whenever wages are set above the firm level. The second argument focuses on the distributive effects of different institutions, and models institutional design as a strategic game between partisan governments and cross-class alliances of unions and employers.

This book helps explain one of the most intriguing and politically salient puzzles in comparative political economy: why some countries have much higher unemployment rates than others. Contrary to new classical economics the focus is on explaining distribution and equilibrium unemployment, and contrary to neo-corporatist theory the role of monetary policy and rational expectation is integral to the analysis. The book makes two central arguments. The first is that monetary policies affect equilibrium employment whenever wages are set above the firm level. The second argument focuses on the distributive effects of different institutions, and models institutional design as a strategic game between partisan governments and cross-class alliances of unions and employers.

This book contains a collection of Michael D. Bordo's essays, written singly and with colleagues, on the classical gold standard and related regimes based directly or indirectly on gold convertibility. The gold standard (and its variants) was the basis for both international and domestic monetary arrangements from the third quarter of the nineteenth century until 1971 when President Nixon closed the US gold window, effectively ending the Bretton Woods International Monetary System. Although the gold standard and its variants are now history, it still has great appeal for policymakers and scholars. Several desirable features of the gold standard have resources for the ongoing issue of international monetary reform. They include its record as a stable nominal anchor; its automaticity; and its role as a credible commitment mechanism. The essays in this collection are organized around several themes: gold and the international monetary system; the commodity theory of money; the gold standa