Classical Recursion Theory

The Rhetorical Tradition — the first comprehensive anthology of primary texts covering the history of rhetoric — examines rhetorical theory from classical antiquity through the modern period. Extensiv

This is a book about Aristotle's philosophy of language, interpreted in a framework that provides a comprehensive interpretation of Aristotle's metaphysics, philosophy of mind, epistemology and science. The aim of the book is to explicate the description of meaning contained in De Interpretatione and to show the relevance of that theory of meaning to much of the rest of Aristotle's philosophy. In the process Deborah Modrak reveals how that theory of meaning has been much maligned. This is a major reassessment of an underestimated aspect of Aristotle that will be of particular interest to classical philosophers, classicists and historians of psychology and cognitive science.

This study examines children's films from various critical perspectives, including those provided by classical and current film theory.

This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to sel

From Homer to Hollywood, the western storytelling tradition has canonised a distinctive set of narrative values characterised by tight economy and closure. This book traces the formation of that classical paradigm in the development of ancient storytelling from Homer to Heliodorus. To tell this story, the book sets out to rehabilitate the idea of 'plot', notoriously disconnected from any recognised system of terminology in literary theory. The first part of the book draws on developments in narratology and cognitive science to propose a way of formally describing the way stories are structured and understood. This model is then used to write a history of the emergence of the classical plot type in the four ancient genres that shaped it - Homeric epic, fifth-century tragedy, New Comedy, and the Greek novel - with insights into the fundamental narrative poetics of each.

This textbook is intended for undergraduate and graduate students taking an intermediate or advanced course in electromagnetism. It presents electromagnetism as a classical theory, based, like mechani

The articles in Naked Truths demonstrate the application of feminist theory to a diverse repertory of classical art: they offer topical and controversial readings on the material culture of the ancien

Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be

A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engin

Europe's most authoritative culinary reference comes to the New World A sound and comprehensive knowledge of cooking theory and technique is as essential to a great cook as a full complement of w

This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, off

The theory of distributions is an extension of classical analysis which has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without presupposing a knowledge, or using more than a bare minimum, of this. This book, first published in 1999, adopts this course and is based on graduate lectures given over a number of years. The prerequisites are few, but a reasonable degree of mathematical maturity is expected of the reader, as the treatment is rigorous throughout. From the outset the theory is developed in several variables, unlike most elementary texts; it is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces.

The theory of distributions is an extension of classical analysis which has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without presupposing a knowledge, or using more than a bare minimum, of this. This book, first published in 1999, adopts this course and is based on graduate lectures given over a number of years. The prerequisites are few, but a reasonable degree of mathematical maturity is expected of the reader, as the treatment is rigorous throughout. From the outset the theory is developed in several variables, unlike most elementary texts; it is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces.

Boundary-layer separation from a rigid body surface is one of the fundamental problems of classical and modern fluid dynamics. The major successes achieved since the late 1960s in the development of the theory of separated flows at high Reynolds numbers are in many ways associated with the use of asymptotic methods. The most fruitful of these has proved to be the method of matched asymptotic expansions, which has been widely used in mechanics and mathematical physics. There have been many papers devoted to different problems in the asymptotic theory of separated flows and we can confidently speak of the appearance of a very productive direction in the development of theoretical hydrodynamics. This book will present this theory in a systematic account. The book will serve as a useful introduction to the theory, and will draw attention to the possibilities that application of the asymptotic approach provides.

Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the bas

The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.

Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. Thi

In this innovative introduction, Robert Layton reviews the ideas that have inspired anthropologists in their studies of societies around the world. An Introduction to Theory in Anthropology provides a clear and concise analysis of the theories, and traces the way in which they have been translated into anthropological debates. The opening chapter sets out the classical theoretical issues formulated by Hobbes, Rousseau, Marx and Durkheim. Successive chapters discuss Functionalism, Structuralism, Interactionist theories, and Marxist anthropology, while the final chapters address the competing paradigms of Socioecology and Postmodernism. Using detailed case studies, Professor Layton illustrates the way in which various theoretical perspectives have shaped competing, or complementary, accounts of specific human societies.

This volume presents an authoritative, up-to-date review of analytic number theory. It contains outstanding contributions from leading international figures in this field. Core topics discussed include the theory of zeta functions, spectral theory of automorphic forms, classical problems in additive number theory such as the Goldbach conjecture, and Diophantine approximations and equations. This will be a valuable book for graduates and researchers working in number theory.

This 1997 book covers the period which saw the establishment in France of a centralized official theatre - not only the Comédie-Française (the first 'national' theatre), but an Italian theatre and a state opera; the often subversive independent theatres are also discussed. Nearly 1,000 documents deal with censorship and other aspects of external control, company management, the acting profession, dramatic theory and criticism, theatre architecture, settings and costumes, audience composition and behaviour. Over 120 pictorial documents - architectural drawings, technical engravings, frontispieces, portraits, etc. - provide a visual dimension where relevant. A full linking narrative and a copious bibliography help to make this an important reference work and a valuable research tool.

The articles in Naked Truths demonstrate the application of feminist theory to a diverse repertory of classical art: they offer topical and controversial readings on the material culture of the ancien

This compelling book contains a comprehensive analytical treatment of the theory of production in a long-period framework. Although the authors take a 'Classical' approach to their subject, the scope of investigation and methods employed should interest all economic theorists. Professors Kurz and Salvadori explore economic systems that are characterised by a particular kind of primary input in the production process, such as different kinds of labour and natural resources. These systems and the corresponding prices can be understood to reflect characteristic features of a capitalist market economy in an ideal way: they express the pure logic of the relationship between value and distribution in an economic system. Specific chapters deal with prices and income distribution, economic growth, joint production, fixed capital, scarce natural resources (both renewable and exhaustible), and heterogeneous labour. The historical origins of the concepts used are also discussed in considerable de

In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, st

This high-level, analytical treatment introduces the theory required for interpretation of an increasingly sophisticated range of molecular scattering experiments. Topics include classical scattering

This book is about the conceptual foundations of an intermediate way between liberalism and socialism: a synthesis of classical (Ricardian) and Keynesian political economy. Classical theory deals with proportions between individuals or collectives and society in tackling problems of distribution and value. Keynesian theory is concerned with the scale of economic activity as explained by effective demand. The economy considered is primarily a monetary production economy, not a market or a planned economy. The author sets up a system linking political economy with other social sciences, i.e. sociology, law and politics in the traditional sense, thus establishing the unity of the social sciences. To complete the picture, issues of method associated with the theory of knowledge in the social sciences and the problem of linking theory with historical reality are also covered.

Number theory is concerned with the properties of the natural numbers: 1, 2, 3 … During the seventeenth and eighteenth centuries, number theory became established through the work of Fermat, Euler and Gauss. With the hand calculators and computers of today the results of extensive numerical work are instantly available and the road leading to their discoveries may be traversed with comparative care. Now in its second edition, this book consists of a sequence of exercises that will lead readers from quite simple number work to the point where they can prove algebraically the classical results of elementary number theory for themselves. A modern secondary school course in mathematics is sufficient background for the whole book which is designed to be used as an undergraduate course in number theory to be pursued by independent study without supporting lectures.

The topics treated fall into three main groups, all of which deal with classical problems which originated in the work of Kolmogorov. The first section looks at probability limit theorems, the second

The classical bases in additive number theory are the polygonal numbers, the squares, cubes, and higher powers, and the primes. This book contains many of the great theorems in this subject: Cauchy's

This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.

Fluid mechanics is one of the greatest accomplishments of classical physics. The Navier-Stokes equations, first derived in the eighteenth century, serve as an accurate mathematical model with which to

This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory fo

This compelling book contains a comprehensive analytical treatment of the theory of production in a long-period framework. Although the authors take a 'Classical' approach to their subject, the scope of investigation and methods employed should interest all economic theorists. Professors Kurz and Salvadori explore economic systems that are characterised by a particular kind of primary input in the production process, such as different kinds of labour and natural resources. These systems and the corresponding prices can be understood to reflect characteristic features of a capitalist market economy in an ideal way: they express the pure logic of the relationship between value and distribution in an economic system. Specific chapters deal with prices and income distribution, economic growth, joint production, fixed capital, scarce natural resources (both renewable and exhaustible), and heterogeneous labour. The historical origins of the concepts used are also discussed in considerable de

This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, off

This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further t

Bridging the gap between political theory, comparative history and government, and constitutional prudence, Rahe challenges prevailing interpretations of ancient Greek republicanism, early modern poli

Gaskinetic Theory is an introductory text on the molecular theory of gases and on modern transport theory. It is suitable for upper division undergraduates in physics and first year graduate students in aerospace engineering, upper atmospheric science and space research. The first part introduces basic concepts, including the distribution function, classical theory of specific heats, binary collisions, mean free path, and reaction rates. Transport theory is used to express coefficients such as viscosity and heat conductivity in terms of molecular properties. The second part of the book covers advanced transport theory. Generalised transport equations are derived from the Boltzmann equation. The Chapman–Enskog and the Grad methods are discussed to obtain higher order transport equations for low density gases. The aerodynamics of solid bodies is explored and the book concludes with the kinetic description of shock waves.

Steven J. Brams' Theory of Moves, though based on the classical theory of games, proposes changes in its rules to render it a truly dynamic theory. By postulating that players think ahead not just to the immediate consequences of making moves, but also to the consequences of countermoves to these moves, counter-countermoves, and so on, it extends the strategic analysis of conflicts into the more distant future. It elucidates the role that different kinds of power - moving, order and threat - may have on conflict outcomes, and it also shows how misinformation affects player choices. Applied to a series of cases drawn from politics, economics, sociology, fiction and the Bible, the theory provides not only a parsimonious explanation of their outcomes, but also shows why they unfolded as they did. This book, which assumes no prior knowledge of game theory or special mathematical background, will be of interest to scholars and students throughout the social sciences.

This is a systematic presentation of quantum field theory from first principles, emphasizing both theoretical concepts and experimental applications. Starting from introductory quantum and classical mechanics, this book develops the quantum field theories that make up the 'Standard Model' of elementary processes. It derives the basic techniques and theorems that underly theory and experiment, including those that are the subject of theoretical development. Special attention is also given to the derivations of cross sections relevant to current high-energy experiments and to perturbative quantum chromodynamics, with examples drawn from electron-positron annihilation, deeply inelastic scattering and hadron-hadron scattering. The first half of the book introduces the basic ideas of field theory. The discussion of mathematical issues is everywhere pedagogical and self contained. Topics include the role of internal symmetry and relativistic invariance, the path integral, gauge theories and

Aimed at a diverse scientific audience, including physicists,astronomers, chemists, geologists, and economists, this book explainsthe theory underlying the classical statistical methods. Its level isb

This book originates from graduate courses given in Cambridge and London. It provides a brisk, thorough treatment of the foundations of algebraic number theory, and builds on that to introduce more advanced ideas. Throughout, the authors emphasise the systematic development of techniques for the explicit calculation of the basic invariants, such as rings of integers, class groups, and units. Moreover they combine, at each stage of development, theory with explicit computations and applications, and provide motivation in terms of classical number-theoretic problems. A number of special topics are included that can be treated at this level but can usually only be found in research monographs or original papers, for instance: module theory of Dedekind domains; tame and wild ramifications; Gauss series and Gauss periods; binary quadratic forms; and Brauer relations. This is the only textbook at this level which combines clean, modern algebraic techniques together with a substantial arithme