Classical Recursion Theory

Collisional transport theory is of central importance to modern plasma physics. This book provides a self-contained treatment of the subject, starting from elementary concepts and developing the theory through to the research frontier. Basic tools of kinetic plasma theory, such as the drift kinetic equation and the Coulomb collision operator, are derived, and are then used to calculate classical and neoclassical transport occurring in high-temperature plasmas. Important phenomena such as neo-classical diffusion, bootstrap current, and plasma rotation are carefully explained. Students, theoreticians and experimentalists in both fusion and space plasma physics will benefit from this book, which emerged from a graduate student level course taught at MIT.

A Return to Aesthetics confronts postmodernism's rejection of aesthetics by showing that this critique rests on central concepts of classical aesthetic theory, namely autonomous form, disinterest, and

Loesberg confronts postmodernism's rejection of aesthetics by showing that its critique rests on three central concepts of classical aesthetic theory: autonomous form, disinterest, and symbolic discou

Although general equilibrium theory originated in the late nineteenth century, the modern elaboration and development of the theory began in the 1930s and 1940s. This book focuses on the version of t

Discrete mathematics is fundamental to computer science, and this text covers its ideas and mathematical language. Features counting and listing, functions, decision trees and recursion, and basic con

This a comprehensive modern account of the theory of Lie groupoids and Lie algebroids, and their importance in differential geometry, in particular their relations with Poisson geometry and general connection theory. It covers much work done since the mid 1980s including the first treatment in book form of Poisson groupoids, Lie bialgebroids and double vector bundles, as well as a revised account of the relations between locally trivial Lie groupoids, Atiyah sequences, and connections in principal bundles. As such, this book will be of great interest to all those concerned with the use of Poisson geometry as a semi-classical limit of quantum geometry, as well as to all those working in or wishing to learn the modern theory of Lie groupoids and Lie algebroids.

The topic of 'circle packing' was born of the computer age but takes its inspiration and themes from core areas of classical mathematics. A circle packing is a configuration of circles having a specified pattern of tangencies, as introduced by William Thurston in 1985. This book, first published in 2005, lays out their study, from first definitions to latest theory, computations, and applications. The topic can be enjoyed for the visual appeal of the packing images - over 200 in the book - and the elegance of circle geometry, for the clean line of theory, for the deep connections to classical topics, or for the emerging applications. Circle packing has an experimental and visual character which is unique in pure mathematics, and the book exploits that to carry the reader from the very beginnings to links with complex analysis and Riemann surfaces. There are intriguing, often very accessible, open problems throughout the book and seven Appendices on subtopics of independent interest. Th

This book provides a comprehensive, systematic treatise on development economics, combining classical political economy, modern institutional theory, and current development issues. It addresses one

This book proposes a fresh and original interpretation of Keats' use of classical mythology in his verse. Dr Aske argues that classical antiquity appears to Keats as a supreme fiction, authoritative yet disconcerting, and his poems represent hard endeavours to come to terms with the influence of that fiction. The major poems (most notably Endymion, Hyperion, the Ode on a Grecian Urn and Lamia) form a stage, as it were, upon which is played out a psychic drama between the modern poet and his classical muse. The study is especially bold in its assimilation of historical scholarship and literary theory to a close reading of the texts. Individual poems are discussed in the context of late Enlightenment and Romantic attitudes towards antiquity and in the light of recent critical theory, in particular the theory of literary history and influence formulated by Harold Bloom and Geoffrey Hartman. Keats emerges as a significant example of the way in which a poet tries to establish a distinct ide

Hurst (College of Wooster) explains to undergraduate students how classical social theories articulated a hundred years old can be applied to contemporary society. He discusses Karl Marx, Emile Durkhe

This 2005 book is a critical examination of Michel Foucault's relation to ancient Greek thought, in particular his famous analysis of Greek history of sexuality. Wolfgang Detel offers an understanding of Foucault's theories of power and knowledge based on modern analytical theories of science and concepts of power. He offers a complex reading of the texts which Foucault discusses, covering topics such as Aristotle's ethics and theory of sex, Hippocratic dietetics, the earliest treatises on economics, and Plato's theory of love. The result is a philosophically rich and probing critique of Foucault's later writings, and a persuasive account of the relation between ethics, power and knowledge in classical antiquity. His book will have a wide appeal to readers interested in Foucault and in Greek thought and culture.

This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: the elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) spaces. While these topics can be traced back to Banach himself, our primary interest is in the postwar renaissance of Banach space theory brought about by James, Lindenstrauss, Mazur, Namioka, Pelczynski, and others. Their elegant and insightful results are useful in many contemporary research endeavors and deserve greater publicity. By way of prerequisites, the reader will need an elementary understanding of functional analysis and at least a passing familiarity with abstract measure theory. An introductory course in topology would also be helpful; however, the text includes a brief appendix on the topology needed for the course.

This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: the elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) spaces. While these topics can be traced back to Banach himself, our primary interest is in the postwar renaissance of Banach space theory brought about by James, Lindenstrauss, Mazur, Namioka, Pelczynski, and others. Their elegant and insightful results are useful in many contemporary research endeavors and deserve greater publicity. By way of prerequisites, the reader will need an elementary understanding of functional analysis and at least a passing familiarity with abstract measure theory. An introductory course in topology would also be helpful; however, the text includes a brief appendix on the topology needed for the course.

Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. The author organizes the theory around natural questions about algebraic numbers, and exercises with hints and proof sketches encourage students' participation in the development. For readers with Maple or Mathematica, the text introduces tools for hands-on experimentation with finite extensions of the rational numbers, enabling a familiarity never before available to students of the subject. Exploratory Galois Theory includes classical applications, from ruler-and-compass constructions to solvability by radicals, and also outlines the generalization from subfields of the complex numbers to arbitrary fields. The text is appropriate for traditional lecture courses, for sem

Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. The author organizes the theory around natural questions about algebraic numbers, and exercises with hints and proof sketches encourage students' participation in the development. For readers with Maple or Mathematica, the text introduces tools for hands-on experimentation with finite extensions of the rational numbers, enabling a familiarity never before available to students of the subject. Exploratory Galois Theory includes classical applications, from ruler-and-compass constructions to solvability by radicals, and also outlines the generalization from subfields of the complex numbers to arbitrary fields. The text is appropriate for traditional lecture courses, for sem

In this provocative book, Paul Glimcher argues that economic theory may provide analternative to the classical Cartesian model of the brain and behavior. Glimcher argues thatCartesian dualism operates

Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This 2004 book develops an approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutationticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with phenomenological proposals for stochasti

Dr Burkill gives a straightforward introduction to Lebesgue's theory of integration. His approach is the classical one, making use of the concept of measure, and deriving the principal results required for applications of the theory.

The book provides an introduction to the theory of cluster sets, a branch of topological analysis which has made great strides in recent years. The cluster set of a function at a particular point is the set of limit values of the function at that point which may be either a boundary point or (in the case of a non-analytic function) an interior point of the function's domain. In topological analysis, its main application is to problems arising in the theory of functions of a complex variable, with particular reference to boundary behaviour such as the theory of prime ends under conformal mapping. An important and novel feature of the book is the discussion of more general applications to non-analytic functions, including arbitrary functions. The authors assume a general familiarity with classical function theory but include the more specialised material required for the development of the theory of cluster sets, so making the treatment accessible to graduate students.

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.

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 2004 textbook provides a pedagogical introduction to the formalism, foundations and applications of quantum mechanics. Part I covers the basic material which is necessary to understand the transition from classical to wave mechanics. Topics include classical dynamics, with emphasis on canonical transformations and the Hamilton-Jacobi equation, the Cauchy problem for the wave equation, Helmholtz equation and eikonal approximation, introduction to spin, perturbation theory and scattering theory. The Weyl quantization is presented in Part II, along with the postulates of quantum mechanics. Part III is devoted to topics such as statistical mechanics and black-body radiation, Lagrangian and phase-space formulations of quantum mechanics, and the Dirac equation. This book is intended for use as a textbook for beginning graduate and advanced undergraduate courses. It is self-contained and includes problems to aid the reader's understanding.

A practical guide for today's wireless engineerHigh Frequency Techniques: An Introduction to RF and Microwave Engineering is a clearly written classical circuit and field theory text illustrated with

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.

This textbook offers a systematic, self-contained account of the main contributions of modern game theory and its applications to economics. Starting with a detailed description of how to model strategic situations, the discussion proceeds by studying basic solution concepts, their main refinements, games played under incomplete information, and repeated games. For each of these theoretical developments, there is a companion set of applications that cover the most representative instances of game-theoretic analysis in economics, e.g. oligopolistic competition, public goods, coordination failures, bargaining, insurance markets, implementation theory, signaling and auctions. The theory and applications covered in the first part of the book fall under the so-called 'classical' approach to game theory, which is founded on the paradigm of players' unlimited rationality. The second part shifts towards topics that no longer abide by that paradigm. This leads to the study of topics such as the

This textbook offers a systematic, self-contained account of the main contributions of modern game theory and its applications to economics. Starting with a detailed description of how to model strategic situations, the discussion proceeds by studying basic solution concepts, their main refinements, games played under incomplete information, and repeated games. For each of these theoretical developments, there is a companion set of applications that cover the most representative instances of game-theoretic analysis in economics, e.g. oligopolistic competition, public goods, coordination failures, bargaining, insurance markets, implementation theory, signaling and auctions. The theory and applications covered in the first part of the book fall under the so-called 'classical' approach to game theory, which is founded on the paradigm of players' unlimited rationality. The second part shifts towards topics that no longer abide by that paradigm. This leads to the study of topics such as the

This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for re

aiming at a more conceptual understanding of classical and qu- tum ?eld theory from a novel mathematical point of view.

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.

This sound introduction to classical and modern control theory concentrates on fundamental concepts. Employing the minimum of mathematical elaboration, it investigates the many applications of control

Human conflict - from family feuds, to labor strikes, to national warfare - is an ever-present and universal social problem and the methods to manage it, a challenge for everyone, from average citizens to policymakers and social theorists. Using Conflict Theory will educate students about how, under what conditions, and why conflict erupts, and how it can be managed. It is a unique classroom book blending theory and practical application and the first to bridge for students the science of social theory and the art of practice. The authors extract from classical sociological theory (Marx, Dahrendorf, Weber, Durkheim, and Parsons), and interpret for the student how these theoretical perspectives have contributed to understanding social conflict (its sources, the causes of escalation and de-escalation of violence, the negotiations process). The perspectives of contemporary theorists (such as Randall Collins, James Coleman, Joseph Himes, Hubert Blalock) are also brought to bear on these q

Human conflict - from family feuds, to labor strikes, to national warfare - is an ever-present and universal social problem and the methods to manage it, a challenge for everyone, from average citizens to policymakers and social theorists. Using Conflict Theory will educate students about how, under what conditions, and why conflict erupts, and how it can be managed. It is a unique classroom book blending theory and practical application and the first to bridge for students the science of social theory and the art of practice. The authors extract from classical sociological theory (Marx, Dahrendorf, Weber, Durkheim, and Parsons), and interpret for the student how these theoretical perspectives have contributed to understanding social conflict (its sources, the causes of escalation and de-escalation of violence, the negotiations process). The perspectives of contemporary theorists (such as Randall Collins, James Coleman, Joseph Himes, Hubert Blalock) are also brought to bear on these q

This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauß-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Bäcklund-Darboux transformations. This text is appropriate for us

Gödel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and

This book describes the remarkable connections that exist between the classical differential geometry of surfaces and modern soliton theory. The authors also explore the extensive body of literature from the nineteenth and early twentieth centuries by such eminent geometers as Bianchi, Darboux, Bäcklund, and Eisenhart on transformations of privileged classes of surfaces which leave key geometric properties unchanged. Prominent amongst these are Bäcklund-Darboux transformations with their remarkable associated nonlinear superposition principles and importance in soliton theory. It is with these transformations and the links they afford between the classical differential geometry of surfaces and the nonlinear equations of soliton theory that the present text is concerned. In this geometric context, solitonic equations arise out of the Gauß-Mainardi-Codazzi equations for various types of surfaces that admit invariance under Bäcklund-Darboux transformations. This text is appropriate for us

Explains the motivation and reviewing the classical theory in a new form; Discusses conservation laws and Euler equations; For one-dimensional cases, the models presented are completely integrable

This book systematically reconstructs the origins and new advances in economic sociology. By presenting both classical and contemporary theory and research, the volume identifies and describes the con

In order to explore a patient's resistance and refusal to grieve, Stark (psychoanalysis, Harvard Medical School) draws on concepts from classical psychoanalysis, object relations theory, and self-psyc

"...effectively demonstrates the enduring importance of 'classical' social movement theory...and provides a cutting edge critical review of recent theoretical developments. This is one of the most imp

Collisional transport theory is of central importance to modern plasma physics. This book provides a self-contained treatment of the subject, starting from elementary concepts and developing the theory through to the research frontier. Basic tools of kinetic plasma theory, such as the drift kinetic equation and the Coulomb collision operator, are derived, and are then used to calculate classical and neoclassical transport occurring in high-temperature plasmas. Important phenomena such as neo-classical diffusion, bootstrap current, and plasma rotation are carefully explained. Students, theoreticians and experimentalists in both fusion and space plasma physics will benefit from this book, which emerged from a graduate student level course taught at MIT.