Classical Recursion Theory

This book contains a thorough discussion of the classical topics in information theory together with the first comprehensive treatment of network coding, a subject first emerged under information theo

This book contains a thorough discussion of the classical topics in information theory together with the first comprehensive treatment of network coding, a subject first emerged under information theo

In a systematic overview of classical and modern contributions to aesthetics, Professor Sparshott argues that all four lines of theory, and no others, are necessary to coherent thinking about art.Orig

This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy The

In a systematic overview of classical and modern contributions to aesthetics, Professor Sparshott argues that all four lines of theory, and no others, are necessary to coherent thinking about art.Orig

This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', w

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

Morse Theory: Smooth and Discrete serves as an introduction to classical smooth Morse theory and to Forman's discrete Morse theory, highlighting the parallels between the two subjects. This is the fir

This book reclaims logic as a branch of philosophy, offering a self-contained and complete introduction to the three traditional systems of classical logic (term, sentence, and predicate logic) and th

Introduction to Critical Legal Theory provides an accessible introduction to the study of law and legal theory. It covers all the seminal movements in classical, modern and postmodern legal thought, e

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

Illuminating key themes of classical sociological texts, this book shows how the ideas of Marx, Durkheim or Weber can be explored by listening to music, reading about celebrities, or watching award-wi

Illuminating key themes of classical sociological texts, this book shows how the ideas of Marx, Durkheim or Weber can be explored by listening to music, reading about celebrities, or watching award-wi

This translation of the 1987 German edition is an introduction into the classical parts of algebra with a focus on fields and Galois theory. It discusses nonstandard topics, such as the transcendence

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

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

In this monograph, the authors present their recently developed theory of electromagnetic interactions. This neoclassical approach extends the classical electromagnetic theory down to atomic scales an

This book will not only be readily welcomed in the academic study of classical optimal selection problems but will also make an impact in areas of modern finance, portfolio management and discrete Mat

Underpinning the axiomatic formulation of quantum theory presented in this undergraduate textbook is a review of early experiments, a comparison of classical and quantal terminology, a Schroedinger-equation treatment of the one-dimensional quantum box, and a survey of relevant mathematics. Among the many concepts comprehensively discussed are: operators; state vectors and wave functions; experimental observables; classical/quantal connections; and symmetry properties. The theory is applied to a wide variety of systems including the non-relativistic H-atom, external electromagnetic fields, and spin1/2. Collisions are described using wave packets. Various time-dependent and time-independent approximations are discussed; applications include electromagnetic transition rates and corrections to the H-atom energies. The final chapter deals with identical-particle symmetries and their application to the He atom, the Periodic Table and diatomic molecules. There are also brief treatments of adv

Underpinning the axiomatic formulation of quantum theory presented in this undergraduate textbook is a review of early experiments, a comparison of classical and quantal terminology, a Schroedinger-equation treatment of the one-dimensional quantum box, and a survey of relevant mathematics. Among the many concepts comprehensively discussed are: operators; state vectors and wave functions; experimental observables; classical/quantal connections; and symmetry properties. The theory is applied to a wide variety of systems including the non-relativistic H-atom, external electromagnetic fields, and spin1/2. Collisions are described using wave packets. Various time-dependent and time-independent approximations are discussed; applications include electromagnetic transition rates and corrections to the H-atom energies. The final chapter deals with identical-particle symmetries and their application to the He atom, the Periodic Table and diatomic molecules. There are also brief treatments of adv

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

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

In this careful and compelling study, Ryan K. Balot brings together political theory, classical history, and ancient philosophy in order to reinterpret courage as a specifically democratic virtue. Ran

In this careful and compelling study, Ryan K. Balot brings together political theory, classical history, and ancient philosophy in order to reinterpret courage as a specifically democratic virtue. Ran

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

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

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 book follows the interplay between allegory and physics in Europe from the inception of the laws of thermodynamics in the 1850s to the cultural acceptance of the theory of relativity in the 1920

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.

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 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.

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.

Kinetic theory provides a microscopic description of many observable, macroscopic processes and has a wide range of important applications in physics, astronomy, chemistry, and engineering. This powerful, theoretical framework allows a quantitative treatment of many non-equilibrium phenomena such as transport processes in classical and quantum fluids. This book describes in detail the Boltzmann equation theory, obtained in both traditional and modern ways. Applications and generalizations describing non-equilibrium processes in a variety of systems are also covered, including dilute and moderately dense gases, particles in random media, hard sphere crystals, condensed Bose-Einstein gases, and granular materials. Fluctuation phenomena in non-equilibrium fluids, and related non-analyticities in the hydrodynamic equations are also discussed in some detail. A thorough examination of many topics concerning time dependent phenomena in material systems, this book describes both current knowle

Written by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic Number Theory' Easter School held at Durham University in 2014. Key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research are presented in a manner accessible to young researchers, including PhD students. This book will also be useful for established mathematicians. The areas discussed include ubiquitous systems and Cantor-type sets in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, multiple recurrence and Ramsey theory, counting and equidistribution problems in homogeneous dynamics, and applications of thin groups in number theory. Both dynamical and 'classical' appr

An H(b) space is defined as a collection of analytic functions that are in the image of an operator. The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and demanding. Volume 1 of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators and Clark measures. Volume 2 focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.

Organisational theorists have become increasingly interested in the creative industries, where practices that are commonplace are of particular interest to organisations in other sectors as they look for new ways to enhance performance. Focusing on the music industry, this book sets up a unique dialogue between leading organisational theorists and music professionals. Part I explores links between organisation theory and the creative industries literature, concentrating on practices of organising and knowledge mobilisation, followed by an in-depth discussion of key theoretical concepts by subject experts. Part II provides a diverse range of 'tales from the field', including examples from classical orchestras, folk, indie and punk. The concluding chapter examines the shared dialogue to reveal what practice in the musical field can learn from organisational theory, and vice versa. This innovative book will interest graduate students and researchers in the fields of organisation studies,

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.

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.

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

This unified account of various aspects of a powerful classical method, easy to understand in its simplest forms, is illustrated by applications in several areas of number theory. As well as including diophantine approximation and transcendence, which were mainly responsible for its invention, the author places the method in a broader context by exploring its application in other areas, such as exponential sums and counting problems in both finite fields and the field of rationals. Throughout the book, the method is explained in a 'molecular' fashion, where key ideas are introduced independently. Each application is the most elementary significant example of its kind and appears with detailed references to subsequent developments, making it accessible to advanced undergraduates as well as postgraduate students in number theory or related areas. It provides over 700 exercises both guiding and challenging, while the broad array of applications should interest professionals in fields from