Classical Recursion Theory

Quantum Field Theory has become the universal language of most modern theoretical physics. This introductory textbook shows how this beautiful theory offers the correct mathematical framework to descr

Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, geometry on

This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM th

Probability theory has been extraordinarily successful at describing a variety of phenomena, from the behaviour of gases to the transmission of messages, and is, besides, a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bell-shaped curve, the law of averages, and so on, concepts that crop up in so many settings they are in some sense universal. This universality is predicted by probability theory to a remarkable degree. This book explains that theory and investigates its ramifications. Assuming a good working knowledge of basic analysis, real and complex, the author maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text.

Probability theory has been extraordinarily successful at describing a variety of phenomena, from the behaviour of gases to the transmission of messages, and is, besides, a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bell-shaped curve, the law of averages, and so on, concepts that crop up in so many settings they are in some sense universal. This universality is predicted by probability theory to a remarkable degree. This book explains that theory and investigates its ramifications. Assuming a good working knowledge of basic analysis, real and complex, the author maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text.

This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The autho

This innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spa

A comprehensive and accessible guide to classical music and music theory, including styles, form, instruments, and more than 280 composer profiles.What makes Mozart’s music so great? Why does a minor

This is the first book in a four-part series designed to give a comprehensive and coherent description of Fluid Dynamics, starting with chapters on classical theory suitable for an introductory underg

What did it mean to be reasonable in the Age of Reason? Classical probabilists from Jakob Bernouli through Pierre Simon Laplace intended their theory as an answer to this question--as "nothing mo

Professor Buchdahl presents a systematic exposition of classical thermodynamics, against a background of general physical theory and on a purely phenomenological (i.e. non-statistical) level. Although particular attention is paid to the meaning of the various concepts introduced, Professor Buchdahl is not afraid of making simplifications where these are likely to enhance the reader's understanding of the subject and the relationships between the principal and ancillary laws. The emphasis throughout is on meaning and physical significance. Specific applications of the general theory are discussed in two final chapters. This book, first published in 1966, is intended for the student who has taken a first course in analytical, though not axiomatic, development of the subject. It will supplement rather than replace, the many familiar introductory treatments of thermodynamics.

Covering essential areas of thermal physics, this book includes kinetic theory, classical thermodynamics, and quantum thermodynamics. The text begins by explaining fundamental concepts of the kinetic theory of gases, viscosity, conductivity, diffusion, and the laws of thermodynamics and their applications. It then goes on to discuss applications of thermodynamics to problems of physics and engineering. These applications are explained with the help of P-V and P-S-H diagrams where necessary and are followed by a large number of solved examples and unsolved exercises. The book includes a dedicated chapter on the applications of thermodynamics to chemical reactions. Each application is explained by taking the example of an appropriate chemical reaction, where all technical terms are explained and complete mathematical derivations are worked out in steps starting from the first principle.

A classical theorem of Jordan states that every finite transitive permutation group contains a derangement. This existence result has interesting and unexpected applications in many areas of mathematics, including graph theory, number theory and topology. Various generalisations have been studied in more recent years, with a particular focus on the existence of derangements with special properties. Written for academic researchers and postgraduate students working in related areas of algebra, this introduction to the finite classical groups features a comprehensive account of the conjugacy and geometry of elements of prime order. The development is tailored towards the study of derangements in finite primitive classical groups; the basic problem is to determine when such a group G contains a derangement of prime order r, for each prime divisor r of the degree of G. This involves a detailed analysis of the conjugacy classes and subgroup structure of the finite classical groups.

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

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

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. T

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. T

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral

The theory of relativity describes the laws of physics in a given space-time. However, a physical theory must provide observational predictions expressed in terms of measurements, which are the outcome of practical experiments and observations. Ideal for readers with a mathematical background and a basic knowledge of relativity, this book will help readers understand the physics behind the mathematical formalism of the theory of relativity. It explores the informative power of the theory of relativity, and highlights its uses in space physics, astrophysics and cosmology. Readers are given the tools to pick out from the mathematical formalism those quantities that have physical meaning and which can therefore be the result of a measurement. The book considers the complications that arise through the interpretation of a measurement, which is dependent on the observer who performs it. Specific examples of this are given to highlight the awkwardness of the problem.

This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity

"Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Interrelation of Classical and Quantum Randomness rectifies this and introduces mathemati

The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications.

In examining the ways that writing bears on cinema, Conley (romance languages, and visual and environmental studies, Harvard) takes a different direction from most film theory, which privileges the vi

Continuing its tradition of providing students with a thorough review of ancient Greek and Roman rhetorical theory and practices, A Synoptic History of Classical Rhetoric is the premier text for under

Continuing its tradition of providing students with a thorough review of ancient Greek and Roman rhetorical theory and practices, A Synoptic History of Classical Rhetoric is the premier text for under

A Synoptic History of Classical Rhetoric provides students with a thorough review of rhetorical theory and practices found in ancient Greece and Rome. This third edition integrates new research into t

Offering a unique and wide-ranging examination of the theory of knowledge, the new edition of this comprehensive collection deftly blends readings from the foremost classical sources with the work of

This volume's purpose is to provide students and scholars of classical rhetoric with a set of exemplary works in the area of Greek rhetorical theory. Many of the articles included here are not easily

The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G2, and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course.

The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G2, and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course.

This 1980 monograph develops from first principles the description of finite deformations of solids under stress and the forces acting, and also the expression of internal forces in terms of stress tensors. The important feature of the book is that elastic properties are discussed and developed consistently from classical thermodynamics. In other books, this point of view is acknowledged only by assuming the existence of an elastic energy function, thus restricting their range mainly to the problem of the spatial distribution of stresses and strains. Topics discussed as applications of the theory include thermal expansion, specific heats, stiffness and complicances, the effects of symmetry on thermodynamic properties, diffusion in a stressed solid, equilibrium in contact with a solution of the solid, phase stability, solid state phase transitions and twinning.

Oaths were ubiquitous rituals in ancient Athenian legal, commercial, civic and international spheres. Their importance is reflected by the fact that much of surviving Greek drama features a formal oath sworn before the audience. This is the first comprehensive study of that phenomenon. The book explores how the oath can mark or structure a dramatic plot, at times compelling characters like Euripides' Hippolytus to act contrary to their best interests. It demonstrates how dramatic oaths resonate with oath rituals familiar to the Athenian audiences. Aristophanes' Lysistrata and her accomplices, for example, swear an oath that blends protocols of international treaties with priestesses' vows of sexual abstinence. By employing the principles of speech act theory, this book examines how the performative power of the dramatic oath can mirror the status quo, but also disturb categories of gender, social status and civic identity in ways that redistribute and confound social authority.

Inigo Jones worked as hard on the creation of his architectural persona as he did on the design of the buildings for the early Stuart court. Through his study of continental architectural and art theory, humanist education, and courtly behavior, Jones redefined the intellectual status of architecture in England and forged a new role for the architect in public life. Since his death, he has been variously described as the first educated architect, the first classicist, the first Renaissance architect in Britain, and the savior of British building from the long winter of the Elizabethan style. This reputation has overlooked the many ways that Jones drew on English customs in order to shape classical architecture for a domestic audience. This 2006 book explores the creation of Jones as professional architect and the development of classical architecture in England through a study of his reading, writing, and architectural practice.

Inigo Jones worked as hard on the creation of his architectural persona as he did on the design of the buildings for the early Stuart court. Through his study of continental architectural and art theory, humanist education, and courtly behavior, Jones redefined the intellectual status of architecture in England and forged a new role for the architect in public life. Since his death, he has been variously described as the first educated architect, the first classicist, the first Renaissance architect in Britain, and the savior of British building from the long winter of the Elizabethan style. This reputation has overlooked the many ways that Jones drew on English customs in order to shape classical architecture for a domestic audience. This 2006 book explores the creation of Jones as professional architect and the development of classical architecture in England through a study of his reading, writing, and architectural practice.

Since 1973, Galois Theory has been educating undergraduate students on Galois groups and classical Galois theory. InGalois Theory, Fourth Edition, mathematician and popular science author Ian Stewart

Carl Schmitt’s magnum opus, written during the Weimar regime, wherein Schmitt challenges the theories and practices of Western constitutional government, claiming that classical conceptions

This textbook is intended for undergraduate and graduate students taking an intermediate or advanced course in electromagnetism. It presents electromagnetism as a classical theory, based, like mechani

This self-contained text for advanced undergraduate and graduate students is devoted to classical quasistatic problems of rate-independent plasticity theory. It discusses the finite element method for