Classical Recursion Theory

This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text

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.

Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

Classical circuit theory is a mathematical theory of linear, passive circuits, namely, circuits composed of resistors, capacitors and inductors. Like many a thing classical, it is old and enduring, st

Based on the subjects from the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop titled 'Recent Progress in Dynamics' in September and October 2004, this volume contains surveys and research articles by leading experts in several areas of dynamical systems that have experienced substantial progress. One of the major surveys is on symplectic geometry, which is closely related to classical mechanics and an exciting addition to modern geometry. The survey on local rigidity of group actions gives a broad and up-to-date account of another flourishing subject. Other papers cover hyperbolic, parabolic, and symbolic dynamics as well as ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this book fascinating. The book also includes a fifty-page commented problem list that takes the reader beyond the areas covered by the surveys, to inspire and guide further research.

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.

Africana Critical Theory innovatively identifies and analyzes continental and diasporan African contributions to classical and contemporary critical theory through the works of W. E. B. Du Bois, C.L.R

The third international conference on classical influences took place in Cambridge in 1977 under the title 'Classical Influences in Western Education, Philosophy and Social Theory'. Dr Bolgar has here collected and edited the proceedings and produced a volume which attempts to relate the progress of classical studies to the general history of ideas from the mid-seventeenth to the mid-nineteenth century. The book should be of interest to specialists in classical studies, to students of the literature of the period, and to students of eighteenth-century French, Italian and American history.

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.

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

Elementary Number Theory, Sixth Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets. A full range of exercises, from basic to challenging, helps

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

In this revised second edition, Elements of Plasticity continues to bridge the gap between classical theory and modern computational techniques and does so by focussing on the most important elements

Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Löwenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continu

This book is a collection about cultural-historical activity theory as it has been developed and applied by Yrjö Engeström. The work of Engeström is both rooted in the legacy of Vygotsky and Leont'ev and focuses on current research concerns that are related to learning and development in work practices. His publications cross various disciplines and develop intermediate theoretical tools to deal with empirical questions. In this volume, Engeström's work is used as a springboard to reflect on the question of the use, appropriation, and further development of the classic heritage within activity theory. The book is structured as a discussion among senior scholars, including Y. Engeström himself. The work of the authors pushes on classical activity theory to address pressing issues and critical contradictions in local practices and larger social systems.

This book is a collection about cultural-historical activity theory as it has been developed and applied by Yrjö Engeström. The work of Engeström is both rooted in the legacy of Vygotsky and Leont'ev and focuses on current research concerns that are related to learning and development in work practices. His publications cross various disciplines and develop intermediate theoretical tools to deal with empirical questions. In this volume, Engeström's work is used as a springboard to reflect on the question of the use, appropriation, and further development of the classic heritage within activity theory. The book is structured as a discussion among senior scholars, including Y. Engeström himself. The work of the authors pushes on classical activity theory to address pressing issues and critical contradictions in local practices and larger social systems.

Professor Bondi discusses some of the myths that have grown up around various scientific theories and ideas, particularly special relativity and Mach's principle. His critical - and often light-hearted - approach to what are usually regarded as complicated ideas leaves the reader with the feeling that perhaps much of his subject is common sense after all. Professor Bondi's aim is to provoke thought, rather than to provide all the answers. He first discusses the limits of theory-making, the significance of depth and universality and the devising of effective tests for scientific theories. The relation of Einstein's theory to classical Newtonian mechanics is then considered, the author showing that relativity can be regarded simple as an extension of Newton's ideas on dynamics to the whole of physics. After deriving the equations of special relativity by the so-called k-calculus, he disposes rapidly of the 'clock paradox' and moves on to discuss general relativity, the significance of th

In fourth-century Greece (BCE), the debate over the nature of philosophy generated a novel claim: that the highest form of wisdom is theoria, the rational 'vision' of metaphysical truths (the 'spectator theory of knowledge'). This 2004 book offers an original analysis of the construction of 'theoretical' philosophy in fourth-century Greece. In the effort to conceptualise and legitimise theoretical philosophy, the philosophers turned to a venerable cultural practice: theoria (state pilgrimage). In this practice, an individual journeyed abroad as an official witness of sacralized spectacles. This book examines the philosophic appropriation and transformation of theoria, and analyses the competing conceptions of theoretical wisdom in fourth-century philosophy. By tracing the link between traditional and philosophic theoria, this book locates the creation of theoretical philosophy in its historical context, analysing theoria as a cultural and an intellectual practice. It develops a new, in

'Keeping time', along with artistic accentuation and intelligent phrasing, is essential to successful musical performance. Rhythm alone had rarely been the subject of specialised study until the late nineteenth century, when several books on this topic by Rudolf Westphal were published in Leipzig. Westphal's work inspired Charles Francis Abdy Williams's 1911 book which is reissued here. Williams re-examines the classical and romantic repertoire from Handel to Tchaikovsky in the light of ancient Greek musical theory, focusing particularly on the earliest writings by Artistoxenus of Tarentum (fourth century BCE). In Williams's view, the rhythmic forms used by the Greeks are universally intelligible, and appear in all ages and cultures, unlike melodies or scales, which vary hugely. He provides insights into the microstructure of works including Bach's oratorios, Beethoven's sonatas and Schubert's songs, which will continue to intrigue musicians, classicists and mathematicians today.

Jeans's primary aim with the first edition of his book, originally published in 1904, was to 'develop the theory of gases upon as exact a mathematical basis as possible'. Twenty years later and those theories were being revolutionised by Quantum Theory. In this fourth edition, Jeans does not attempt to avoid the discoveries of this topical science, but rather exposes the many difficulties that classical theory was experiencing, and how those problems disappeared with Quantum Theory. This edition therefore offers a fascinating insight into a field of physics in transition between two great models of physical science.

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

During past years many countries constructed large accelerators for investigating heavy ion collisions, and new theoretical techniques for analysing results and making predictions were developed. Semi-classical methods were studied in the early days of quantum mechanics. Their application to heavy ion collisions has led to new advances and a number of different schools have grown up, each one emphasising different aspects of the theory. The aim of this book is to present a unified treatment of various lines of development. This book will be of great interest to graduate students wishing to learn about semi-classical methods in nuclear physics and to theoretical and experimental nuclear physicists, especially those working in heavy ion physics. It will also be of interest to research workers in other areas, such as atomic physics and quantum chemistry, where similar techniques are used.

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.

Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers.

Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference begins by introducing the theory of sub-Riemannian manifolds using a variational approach in which all properties are obtained from minimum principles, a robust method that is novel in this context. The authors then present examples and applications, showing how Heisenberg manifolds (step 2 sub-Riemannian manifolds) might in the future play a role in quantum mechanics similar to the role played by the Riemannian manifolds in classical mechanics. Sub-Riemannian Geometry: General Theory and Examples is the perfect resource for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics interested in the most recent developments in sub-Riemannian geometry.

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 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.

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

The classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors pres

What are the aims of sociology? What are its objects of study? How relevant is the classical tradition to the practice of sociology today? This volume brings together internationally renowned and new

In this volume, Richard Ned Lebow introduces his own constructivist theory of political order and international relations based on theories of motives and identity formation drawn from the ancient Greeks. His theory stresses the human need for self-esteem, and shows how it influences political behavior at every level of social aggregation. Lebow develops ideal-type worlds associated with four motives: appetite, spirit, reason and fear, and demonstrates how each generates a different logic concerning cooperation, conflict and risk-taking. Expanding and documenting the utility of his theory in a series of historical case studies, ranging from classical Greece to the war in Iraq, he presents a novel explanation for the rise of the state and the causes of war, and offers a reformulation of prospect theory. This is a novel theory of politics by one of the world's leading scholars of international relations.