Classical Recursion Theory

From classical foundations to advanced modern theory, this self-contained and comprehensive guide to probability weaves together mathematical proofs, historical context and richly detailed illustrative applications. A theorem discovery approach is used throughout, setting each proof within its historical setting and is accompanied by a consistent emphasis on elementary methods of proof. Each topic is presented in a modular framework, combining fundamental concepts with worked examples, problems and digressions which, although mathematically rigorous, require no specialised or advanced mathematical background. Augmenting this core material are over 80 richly embellished practical applications of probability theory, drawn from a broad spectrum of areas both classical and modern, each tailor-made to illustrate the magnificent scope of the formal results. Providing a solid grounding in practical probability, without sacrificing mathematical rigour or historical richness, this insightful bo

Game theory explains how to make good choices when different decision makers have conflicting interests. The classical approach assumes that decision makers are committed to making the best choices for themselves regardless of the effect on others, but such an approach is less appropriate when cooperation, compromise and negotiation are important. This book describes conditional games, a form of game theory that accommodates multiple stakeholder decision-making scenarios where cooperation and negotiation are significant issues and where notions of concordant group behavior are important. Using classical binary preference relations as a point of departure, the book extends the concept of a preference ordering that permits stakeholders to modulate their preferences as functions of the preferences of others. As these conditional preferences propagate through a group of decision makers, they create social bonds that lead to notions of group concordance. This book is intended for all studen

Determining orbits for natural and artificial celestial bodies is an essential step in the exploration and understanding of the Solar System. However, recent progress in the quality and quantity of data from astronomical observations and spacecraft tracking has generated orbit determination problems which cannot be handled by classical algorithms. This book presents new algorithms capable of handling the millions of bodies which could be observed by next generation surveys, and which can fully exploit tracking data with state-of-the-art levels of accuracy. After a general mathematical background and summary of classical algorithms, the new algorithms are introduced using the latest mathematical tools and results, to which the authors have personally contributed. Case studies based on actual astronomical surveys and space missions are provided, with applications of these new methods. Intended for graduate students and researchers in applied mathematics, physics, astronomy and aerospace

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.

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.

Ergodic theory grew out of an important problem of statistical mechanics which was resolved by Birkhoff and von Neumann in the 1930s. Since that time the subject has made its way to the centre of pure mathematics, drawing on the techniques of many other areas and, in turn, influencing those areas. The author has provided in this slim volume a speedy introduction to a considerable number of topics and examples. He includes sections on the classical ergodic theorems, topological dynamics, uniform distribution, Martingales, information theory and entropy. There is a chapter on mixing and one on special examples. The book concludes with an appendix on the spectral multiplicity theory of unitary operators.

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.

Modern experimental developments in condensed matter and ultracold atom physics present formidable challenges to theorists. This book provides a pedagogical introduction to quantum field theory in many-particle physics, emphasizing the applicability of the formalism to concrete problems. This second edition contains two new chapters developing path integral approaches to classical and quantum nonequilibrium phenomena. Other chapters cover a range of topics, from the introduction of many-body techniques and functional integration, to renormalization group methods, the theory of response functions, and topology. Conceptual aspects and formal methodology are emphasized, but the discussion focuses on practical experimental applications drawn largely from condensed matter physics and neighboring fields. Extended and challenging problems with fully worked solutions provide a bridge between formal manipulations and research-oriented thinking. Aimed at elevating graduate students to a level wh

Noncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988–92, which developed his own approach to the subject. The basic definitions, examples and exercises provided here allow non-specialists and students with a background in elementary functional analysis, commutative algebra and differential geometry to get to grips with the subject. Quillen's development of cyclic theory emphasizes analogies between commutative and noncommutative theories, in which he reinterpreted classical results of Hamiltonian mechanics, operator algebras and differential graded algebras into a new formalism. In this book, cyclic theory is developed from motivating examples and background towards general results. Themes covered are relevant to current research, including homomorphisms modulo powers of ideals, traces on

Noncommutative geometry combines themes from algebra, analysis and geometry and has significant applications to physics. This book focuses on cyclic theory, and is based upon the lecture courses by Daniel G. Quillen at the University of Oxford from 1988–92, which developed his own approach to the subject. The basic definitions, examples and exercises provided here allow non-specialists and students with a background in elementary functional analysis, commutative algebra and differential geometry to get to grips with the subject. Quillen's development of cyclic theory emphasizes analogies between commutative and noncommutative theories, in which he reinterpreted classical results of Hamiltonian mechanics, operator algebras and differential graded algebras into a new formalism. In this book, cyclic theory is developed from motivating examples and background towards general results. Themes covered are relevant to current research, including homomorphisms modulo powers of ideals, traces on

Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.

The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.

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

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

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

Integrating original texts with explanations, interpretations, and theory, Introduction to Mythology: Contemporary Approaches to Classical and World Myths, Fourth Edition, introduces students to a wid

Liu, Li, and Huang present in an elementary way recent significant developments in the qualitative theory of planar dynamical systems, addressing problems that were posed more than 110 years ago. Amon

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

In this book, Caroline van Eck examines how rhetoric and the arts interacted in early modern Europe. She argues that rhetoric, though originally developed for persuasive speech, has always used the visual as an important means of persuasion, and hence offers a number of strategies and concepts for visual persuasion as well. The book is divided into three major sections - theory, invention, and design. Van Eck analyzes how rhetoric informed artistic practice, theory, and perception in early modern Europe. This is the first full-length study to look at the issue of visual persuasion in both architecture and the visual arts, and to investigate what roles rhetoric played in visual persuasion, both from the perspective of artists and that of viewers.

In this book, Caroline van Eck examines how rhetoric and the arts interacted in early modern Europe. She argues that rhetoric, though originally developed for persuasive speech, has always used the visual as an important means of persuasion, and hence offers a number of strategies and concepts for visual persuasion as well. The book is divided into three major sections - theory, invention, and design. Van Eck analyzes how rhetoric informed artistic practice, theory, and perception in early modern Europe. This is the first full-length study to look at the issue of visual persuasion in both architecture and the visual arts, and to investigate what roles rhetoric played in visual persuasion, both from the perspective of artists and that of viewers.

Information theory lies at the heart of modern technology, underpinning all communications, networking, and data storage systems. This book sets out, for the first time, a complete overview of both classical and quantum information theory. Throughout, the reader is introduced to key results without becoming lost in mathematical details. Opening chapters present the basic concepts and various applications of Shannon's entropy, moving on to the core features of quantum information and quantum computing. Topics such as coding, compression, error-correction, cryptography and channel capacity are covered from classical and quantum viewpoints. Employing an informal yet scientifically accurate approach, Desurvire provides the reader with the knowledge to understand quantum gates and circuits. Highly illustrated, with numerous practical examples and end-of-chapter exercises, this text is ideal for graduate students and researchers in electrical engineering and computer science, and practitione

In this book, Rachel Kousser draws on contemporary reception theory to present an approach to Hellenistic and Roman ideal sculpture. She analyzes the Romans' preference for retrospective, classicizing statuary based on Greek models as opposed to the innovative creations prized by modern scholars. Using a case study of a particular sculptural type, a forceful yet erotic image of Venus, Kousser argues that the Romans self-consciously employed such sculptures to represent their ties to the past in a rapidly evolving world. Kousser presents Hellenistic and Roman ideal sculpture as an example of a highly effective artistic tradition that was, by modern standards, extraordinarily conservative. At the same time, the Romans' flexible and opportunistic use of past forms also had important implications for the future: it constituted the origins of classicism in Western art.

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.

Infinitary logic, the logic of languages with infinitely long conjunctions, plays an important role in model theory, recursion theory and descriptive set theory. This book is the first modern introduction to the subject in forty years, and will bring students and researchers in all areas of mathematical logic up to the threshold of modern research. The classical topics of back-and-forth systems, model existence techniques, indiscernibles and end extensions are covered before more modern topics are surveyed. Zilber's categoricity theorem for quasiminimal excellent classes is proved and an application is given to covers of multiplicative groups. Infinitary methods are also used to study uncountable models of counterexamples to Vaught's conjecture, and effective aspects of infinitary model theory are reviewed, including an introduction to Montalbán's recent work on spectra of Vaught counterexamples. Self-contained introductions to effective descriptive set theory and hyperarithmetic theor

Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.

The Companion provides an accessible critical survey of Western visual art theory from sources in Classical, Medieval and Renaissance thought through to contemporary writings.

This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories. It focuses on the meaning of probability, discussing some definitions and surveying their scope of applicability. The behavioral definition of subjective probability serves as a way to present the classical theories, culminating in Savage's theorem. The limitations of this result as a definition of probability lead to two directions - first, similar behavioral definitions of more general theories, such as non-additive probabilities and multiple priors, and second, cognitive derivations based on case-based techniques.

This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories. It focuses on the meaning of probability, discussing some definitions and surveying their scope of applicability. The behavioral definition of subjective probability serves as a way to present the classical theories, culminating in Savage's theorem. The limitations of this result as a definition of probability lead to two directions - first, similar behavioral definitions of more general theories, such as non-additive probabilities and multiple priors, and second, cognitive derivations based on case-based techniques.

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

Classical statistical techniques fail to cope well with deviations from a standard distribution. Robust statistical methods take into account these deviations while estimating the parameters of parame

"This class-tested text provides a comprehensive overview of the classical and current theories of moral development and applications of these theories in various counseling and educational settings"-

"This class-tested text provides a comprehensive overview of the classical and current theories of moral development and applications of these theories in various counseling and educational settings"-

Social Theory, Health and Healthcare provides a systematic guide to both classical and contemporary social theories, identifying the relevance and research implications of each theory. Students are sh

Wexler (sociology of education, Hebrew University of Education, Jerusalem) shows how classical sociology sets the frame for theory and research in education. He concentrates on Durkheimian, Marxist, a

Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of con

Many of the great works of world literature are composed in metrical verse, that is, in lines which are measured and patterned. Meter in Poetry: A New Theory is the first book to present a single simple account of all known types of metrical verse, which is illustrated with detailed analyses of poems in many languages, including English, Spanish, Italian, French, classical Greek and Latin, Sanskrit, classical Arabic, Chinese, Vietnamese, and Latvian. This outstanding contribution to the study of meter is aimed both at students and scholars of literature and languages, as well as anyone interested in knowing how metrical verse is made.

Many of the great works of world literature are composed in metrical verse, that is, in lines which are measured and patterned. Meter in Poetry: A New Theory is the first book to present a single simple account of all known types of metrical verse, which is illustrated with detailed analyses of poems in many languages, including English, Spanish, Italian, French, classical Greek and Latin, Sanskrit, classical Arabic, Chinese, Vietnamese, and Latvian. This outstanding contribution to the study of meter is aimed both at students and scholars of literature and languages, as well as anyone interested in knowing how metrical verse is made.

Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbo

This book provides the fundamental knowledge of the classical matching theory problems. It builds up the bridge between the matching theory and the 5G wireless communication resource allocation proble

This book examines a variety of psychological disorders from the perspective of the psychology of learning. Grounded in the study of classical and instrumental conditioning, learning theory provides a