Classical Recursion Theory

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

This collection of essays is concerned with philosophy, politics and society. The first group examines what philosophers such as Hegel, Wittgenstein and Chomsky have said or implied about the nature of society in general. A second group examines the cognitive predicament, questions concerning the nature of the possibility of knowledge, as handled by a thinker such as Descartes, or the Pragmatist tradition. The third group handles the political predicament and deals specifically with problems such as nationalism, the nature of the liberalisation process, the future of the welfare and consumer state and the option facing underdeveloped societies. The essays deal not only with classical theories concerning these problems but also with various recent discussions. The volume will interest many individual philosophers and social theorists and those with a more general interest in our culture and political discussions.

This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves. There are chapters dealing with the many connections between matrices, graphs, digraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorial properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix, and Latin squares. The final chapter deals with algebraic characterizations of combinatorial properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jordan Canonical Form. The book is sufficiently self-contained for use

This book deals with the twistor treatment of certain linear and non-linear partial differential equations. The description in terms of twistors involves algebraic and differential geometry, algebraic topology and results in a new perspective on the properties of space and time. The authors firstly develop the mathematical background, then go on to discuss Yang-Mills fields and gravitational fields in classical language, and in the final part a number of field-theoretic problems are solved. Issued here for the first time in paperback, this self-contained volume should be of use to graduate mathematicians and physicists and research workers in theoretical physics, relativity, and cosmology.

By using familiar concepts from classical measurement methods and basic statistics, this book introduces the basics of item response theory (IRT) and explains the application of IRT methods to problem

Block theory is a part of the theory of modular representation of finite groups and deals with the algebraic structure of blocks. In this volume Burkhard Külshammer starts with the classical structure theory of finite dimensional algebras, and leads up to Puigs main result on the structure of the so called nilpotent blocks, which he discusses in the final chapter. All the proofs in the text are given clearly and in full detail, and suggestions for further reading are also included. For researchers and graduate students interested in group theory or representation theory, this book will form an excellent self contained introduction to the theory of blocks.

An advanced monograph on a central topic in the theory of differential equations, Heat Kernels and Spectral Theory investigates the theory of second-order elliptic operators. While the study of the heat equation is a classical subject, this book analyses the improvements in our quantitative understanding of heat kernels. The author considers variable coefficient operators on regions in Euclidean space and Laplace-Beltrami operators on complete Riemannian manifolds. He also includes results pertaining to the heat kernels of Schrödinger operators; such results will be of particular interest to mathematical physicists, and relevant too to those concerned with properties of Brownian motion and other diffusion processes.

For engineers working on guidance, navigation and control problems, and those in industrial process control. Includes a review of system modeling and classical linear control in the transform domain,

A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas. Readers are assumed to have some background in algebraic geometry, including sheaf cohomology, and for them this work will provide an illustration of the power of modern abstract techniques appli

With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.

This book represents a major new statement on the issue of property rights. It argues for the justification of some rights of private property while showing why unequal distributions of private property are indefensible. Three features of the book are especially salient: it offers a challenging new pluralist theory of justification; the argument integrates perceptive analyses of the great classical theorists Aristotle, Locke, Hegel and Marx with a discussion of contemporary philosophers such as Nozick and Rawls; and the author moves with assurance among philosophy, law and economics to present a very broad, interdisciplinary study.

The ancient Greeks invented democracy. They also invented political theory. This book seeks to show that these were not unrelated achievements. The development of political theory accompanied the growth of democracy at Athens in the fifth century BC. By analysing the writings of Protagoras the sophist, Thucydides the historian, and Democritus the cosmologist in the context of political developments and speculation about the universe, Dr Farrar reveals the existence of a distinctive approach to the characterisation of democratic order, and in doing so demonstrates the virtues of Thucydides' historical conception of politics. Thucydides' history is shown to be an argument for the political force of historical judgement.

This advanced undergraduate-level text provides a formulation of the quantum theory in terms of qualitative and imaginative concepts outside classical theory. A broad range of specific applications fo

Professor Roemer's goal in this book is to give a rigorous view of classical Marxian economic theory by presenting specific analytic models. The theory is not extended to deal with new problems, but it is deepened: Marxian theory is given micro-foundations and upon those foundations the author begins to rebuild a tightly constructed Marxian economics. The book begins, after a methodological introduction, with an examination of the Marxian notion of equilibrium and the theory of exploitation, and goes on to deal with the theory of the falling rate of profit. The next section explores one of the points made in the first section of the book, that the Marxian theory of exploitation can be constructed completely independently of the labor theory of value as a theory of exchange. Technical study of this problem allows comment on various issues, such as the relative importance of 'marginal utilities' and 'class struggle' in determining relative prices. The final part examines models of variou

This book is a comprehensive guide to extreme value theory in engineering. Written for the end user with intermediate and advanced statistical knowledge, it covers classical methods as well as recent

This is part two of a two-volume set."Democracy is, in part, a debate about what democracy is. With The Theory of Democracy Revisted, Sartori offers an overview of classical and contemporary issues. A

In recent years serious attempts have been made to systematize and develop the moral and political themes of great philosophers of the past. Kant, Locke, Marx, and the classical utilitarians all have

This book addresses one of the major theoretical issues that underlies, implicitly or explicitly, some recurrent controversies in macroeconomics - namely, whether a competitive monetary economy has built-in mechanisms that are strong enough to remove excess demands and supplies on all markets, through an automatic adjustment of the price system. Jean-Michel Grandmont sheds light on this complex subject by using the analytical techniques of general equilibrium theory alongside the methods of monetary analysis. The book warns against the indiscriminate use of the rational expectations hypothesis when approaching this topic, and conversely stresses the common-sense observation that short-run learning processes are among the most important characteristics of economic agents. Grandmont argues that such processes are deserving of careful theoretical study, and the result is a clear and rigorous analysis of all the issues involved.

This 1985 textbook presents the theory of thermodynamics in a highly interesting way. The presentation of the theory of heat is logical, compact and uncluttered, with an emphasis on the underlying physical model. Unlike other texts published at this time, in this approach the student adopts at the outset the master equation which describes the rate of scattering from one quantum state into another. This makes the link between thermodynamics and kinetics more obvious. Temperature and entropy are initially introduced as statistical concepts. Unlike most other treatments, this book has early sections on the Boltzmann distribution and classical thermodynamics, which may be used as a basis for first-year courses. The book also contains extensive graded exercises.

This is a textbook on graph theory, especially suitable for computer scientists but also suitable for mathematicians with an interest in computational complexity. Although it introduces most of the classical concepts of pure and applied graph theory (spanning trees, connectivity, genus, colourability, flows in networks, matchings and traversals) and covers many of the major classical theorems, the emphasis is on algorithms and thier complexity: which graph problems have known efficient solutions and which are intractable. For the intractable problems a number of efficient approximation algorithms are included with known performance bounds. Informal use is made of a PASCAL-like programming language to describe the algorithms. A number of exercises and outlines of solutions are included to extend and motivate the material of the text.

In past decades, democratic theory has been on the defensive, largely as a result of the disappointments of democratic practice. The essays in this volume reflect critically on the theory in the light of those failures and with the corresponding assumption of an indissoluble connection between theory and practice. If theory maintains a monastic impeccability, untouched by the world, it will be sterile and fit merely for arid disputes. Nor can practice stand alone: it varies and changes and is subject to different interpretations. Success will come to it partly through the impact of empirical and prescriptive analysis. The volume is organised in sections, dealing in turn with the changing meanings and evaluations of democracy with classical theories with the revisions and critiques of these theories deriving from existing circumstances and with attempts to extend and to consolidate more adequate and secure theories of democracy. Among the thinkers considered are Mill, de Tocqueville, Ma

Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematic

What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr Cutland begins with a mathematical characterisation of computable functions using a simple idealised computer (a register machine); after some comparison with other characterisations, he develops the mathematical theory, including a full discussion of non-computability and undecidability, and the theory of recursive and recursively enumerable sets. The later chapters provide an introduction to more advanced topics such as Gödel's incompleteness theorem, degrees of uns

This excellent, semi-technical account includes a review of classical physics (origin of space and time measurements, Ptolemaic and Copernican astronomy, laws of motion, inertia, and more) and covera

Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has occupied a prominent place in the development of algebraic topology. This monograph provides an account of the subject which bridges the gap between the fundamental concepts of topology and the more complex treatment to be found in original papers. The first six chapters describe the essential ideas of homotopy theory: homotopy groups, the classical theorems, the exact homotopy sequence, fibre-spaces, the Hopf invariant, and the Freudenthal suspension. The final chapters discuss J. H. C. Whitehead's cell-complexes and their application to homotopy groups of complexes.

This book is devoted to the systematic presentation of the Theory of Inventive Problem Solving (TRIZ) and is the most comprehensive book in the classical TRIZ and beyond. It details methods for formulating non-standard problems and various ways to solve them, etc. The book is illustrated by many examples, problems, and graphical material (approximately 300 examples and problems, and approximately 400 illustrations). It describes more than 300 concepts. Materials for independent work is provided at the end of each chapter. Some reference solutions are included. The book is intended for students of engineering disciplines who would like to have in-depth understanding of. It can also be useful for engineers and inventors, scientists, university professors, and those who solve creative problems. Professor and TRIZ Master Vladimir Petrov, is one of the most authoritative students and best friends of the Father of TRIZ, Genrich S. Altshuller. Since 1972, TRIZ Master Vladimir Petrov often con

This book argues that neither theories of secularisation nor theories of lived religion offer satisfactory accounts of religion and social change. Drawing from Deleuze and Gauttari’s idea of the assemblage, Paul-Francois Tremlett outlines an alternative.Informed by classical and contemporary theories of religion as well as empirical case studies and ethnography conducted in Manila and London, this book re-frames religion as spatially organised flows. Foregrounding the agency of hon-human actors, it offers a compelling and original account of religion and social change.

This book evaluates the potential of the pragmatist notion of habit possesses to influence current debates at the crossroads between philosophy, cognitive sciences, neurosciences, and social theory. It deals with the different aspects of the pragmatic turn involved in 4E cognitive science and traces back the roots of such a pragmatic turn to both classical and contemporary pragmatism. Written by renowned philosophers, cognitive scientists, neuroscientists, and social theorists, this volume fills the need for an interdisciplinary account of the role of 'habit'. Researchers interested in the philosophy of mind, cognitive science, neuroscience, psychology, social theory, and social ontology will need this book to fully understand the pragmatist turn in current research on mind, action and society.

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory that is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this second volume, the authors show how factorization algebras arise from interacting field theories, both classical and quantum, and how they encode essential information such as operator product expansions, Noether currents, and anomalies. Along with a systematic reworking of the Batalin–Vilkovisky formalism via derived geometry and factorization algebras, this book offers concrete examples from physics, ranging from angular momentum and Virasoro symmetries to a five-dimensional gauge theory.

The Standard Model of particle physics is an amazingly successful theory describing the fundamental particles and forces of nature. This text, written for a two-semester graduate course on the Standard Model, develops a practical understanding of the theoretical concepts it's built upon, to prepare students to enter research. The author takes a historical approach to demonstrate to students the process of discovery which is often overlooked in other textbooks, presenting quantum field theory and symmetries as the necessary tools for describing and understanding the Standard Model. He develops these tools using a basic understanding of quantum mechanics and classical field theory, such as Maxwell's electrodynamics, before discussing the important role that Noether's theorem and conserved charges play in the theory. Worked examples feature throughout the text, while homework exercises are included for the first five parts, with solutions available online for instructors. Inspired by the

The embrace of reception theory has been one of the hallmarks of classical studies over the last 30 years. This volume builds on the critical insights thereby gained to consider reception within Greek antiquity itself. Reception, like 'intertextuality', places the emphasis on the creative agency of the later 'receiver' rather than the unilateral influence of the 'transmitter'. It additionally shines the spotlight on transitions into new cultural contexts, on materiality, on intermediality and on the body. Essays range chronologically from the archaic to the Byzantine periods and address literature (prose and verse; Greek, Roman and Greco-Jewish), philosophy, papyri, inscriptions and dance. Whereas the conventional image of ancient Greek classicism is one of quiet reverence, this book, by contrast, demonstrates how rumbustious, heterogeneous and combative it could be.

This book evaluates the potential of the pragmatist notion of habit possesses to influence current debates at the crossroads between philosophy, cognitive sciences, neurosciences, and social theory. It deals with the different aspects of the pragmatic turn involved in 4E cognitive science and traces back the roots of such a pragmatic turn to both classical and contemporary pragmatism. Written by renowned philosophers, cognitive scientists, neuroscientists, and social theorists, this volume fills the need for an interdisciplinary account of the role of 'habit'. Researchers interested in the philosophy of mind, cognitive science, neuroscience, psychology, social theory, and social ontology will need this book to fully understand the pragmatist turn in current research on mind, action and society.

The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations and harmonic analysis on solvable Lie groups. Covering a range of topics from stratification methods for linear solvable actions in a finite-dimensional vector space, to complete proofs of essential elements of Mackey theory and a unified development of the main features of the orbit method for solvable Lie groups, the authors provide both well-known and new examples, with a focus on those relevant to contemporary applications. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers.

What are the features of a good scientific theory? Samuel Schindler's book revisits this classical question in the philosophy of science and develops new answers to it. Theoretical virtues matter not only for choosing theories 'to work with', but also for what we are justified in believing: only if the theories we possess are good ones (qua virtues) can we be confident that our theories' claims about nature are actually correct. Recent debates have focussed rather narrowly on a theory's capacity to predict new phenomena successfully, but Schindler argues that the justification for this focus is thin. He discusses several other theory properties such as testability, accuracy, and consistency, and highlights the importance of simplicity and coherence. Using detailed historical case studies and careful philosophical analysis, Schindler challenges the received view of theoretical virtues and advances arguments for the view that science uncovers reality through theory.

Classical social choice theory relies heavily on the assumption that all individuals have fixed preference orderings. This highly original book presents a new theory of social preferences that explicitly accounts for important social phenomena such as coordination, compromise, negotiation and altruism. Drawing on cybernetics and network theory, it extends classical social choice theory by constructing a framework that allows for dynamic preferences that are modulated by the situation-dependent social influence that they exert on each other. In this way the book shows how members of a social network may modulate their preferences to account for social context. This important expansion of social choice theory will be of interest to readers in a wide variety of disciplines, including economists and political scientists concerned with choice theory as well as computer scientists and engineers working on network theory.

Roman Law in the State of Nature offers a new interpretation of the foundations of Hugo Grotius' natural law theory. Surveying the significance of texts from classical antiquity, Benjamin Straumann argues that certain classical texts, namely Roman law and a specifically Ciceronian brand of Stoicism, were particularly influential for Grotius in the construction of his theory of natural law. The book asserts that Grotius, a humanist steeped in Roman law, had many reasons to employ Roman tradition and explains how Cicero's ethics and Roman law - secular and offering a doctrine of the freedom of the high seas - were ideally suited to provide the rules for Grotius' state of nature. This fascinating new study offers historians, classicists and political theorists a fresh account of the historical background of the development of natural rights, natural law and of international legal norms as they emerged in seventeenth-century early modern Europe.