Classical Recursion Theory

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

Algebraic geometry has benefited enormously from the powerful general machinery developed in the latter half of the twentieth century. The cost has been that much of the research of previous generations is in a language unintelligible to modern workers, in particular, the rich legacy of classical algebraic geometry, such as plane algebraic curves of low degree, special algebraic surfaces, theta functions, Cremona transformations, the theory of apolarity and the geometry of lines in projective spaces. The author's contemporary approach makes this legacy accessible to modern algebraic geometers and to others who are interested in applying classical results. The vast bibliography of over 600 references is complemented by an array of exercises that extend or exemplify results given in the book.

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.

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.

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 book provides a calculus-based perspective on classical mechanics and the theory of relativity. Unlike most conventional textbooks, the discussion on theory is pared down to a minimum in favor of

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.

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.

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.

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

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

This is a history of international monetary thought from the end of the nineteenth to the middle of the twentieth century. It provides a comprehensive survey of the literature produced on international macroeconomics for that period. It will be of interest to teachers of and graduate students in international monetary economics, monetary theory, and the history of economic thought. Professor Flanders argues that progress in the field of international monetary economics (or in the discipline as a whole) has not been linear. Instead of writing a sequential, chronological story, she has classified the literature according to groupings of ideas and classes of models. After a brief survey of the Classical doctrines, the book covers the developments of major approaches, which are labelled Neoclassical, Late Classical, and Keynesian. The models are conceptualized in two streams: stream F encompasses formal, long-run equilibrium models, all of which emerge from a common proto-model involving t

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.

This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to enginee

This 2002 book discusses the classical foundations of field theory, using the language of variational methods and covariance. It explores the limits of what can be achieved with purely classical notions, and shows how these have a deep and important connection with the second quantized field theory, which follows on from the Schwinger Action Principle. The book takes a pragmatic view of field theory, focusing on issues which are usually omitted from quantum field theory texts and cataloging results which are often hard to find in the literature. Care is taken to explain how results arise and how to interpret them physically, for graduate students starting out in the field. Many physical examples are provided, making the book an ideal supplementary text for courses on elementary field theory, group theory and dynamical systems. It will also be a valuable reference for researchers already working in these and related areas.

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

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 introductory volume illuminates current terrain in social theory by examining major classical theories (Saint-Simon, Comte, Marx, Durkheim, Dilthey, T÷nnies, Simmel and Weber), emphasizing recurr

This book illuminates several timeless principles of political philosophy that have come down to us through the ages in the writings of Plato, Aristotle, Machiavelli, Hobbes, Locke, Montesquieu, Rous

For music lovers who've always wanted to play guitar but have been put off by traditional guitar methods, these books get you playing right away without having to pick through heavy theory and music-r

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

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

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 author had initiated a revision and translation of"Classical Diophantine Equations" prior to his death.Given the rapid advances in transcendence theory anddiophantine approximation

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

Rhetoric -- the theory of oral discourse -- affected and indeed pervaded all aspects of classical thought. Bearing the stamp of its impact were the Homeric hymns, the Iliad and the Odyssey, Aeschylus'

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 excellent text covers a year’s course in advanced theoretical electromagnetism, first introducing theory, then its application. Topics include vectors D and H inside matter, conservation l

This book deals with a careful presentation of the principles on which the physical problems are based and the mathematical treatment of the problems. The fundamental solution is used as in classical potential theory to construct solutions to initial and certain boundary value problems for the linear Stokes equations.

In ancient times, scholars such as Confucius and Aristotle expounded on the virtue of the “middle way” or “intermediate,” an ideal point of moderation or balance between the extremes of human behavior. Adam Smith, widely considered the father of modern economics as we know it, also encouraged propriety in his first work, The Theory of Moral Sentiments. Since then, different schools of economics have continued to incorporate the idea of propriety into their theories, for example in such concepts as equilibrium and bounded rationality, though few economists have defined it explicitly. In light of growing uncertainty and polarization around the world, propriety economics offers alternative solutions for markets, governments, and everyday citizens.This book embarks on a thorough review of Eastern and Western philosophies of propriety over the past 2,500 years, followed by an investigation of the ideas of propriety found in five key schools of economics: classical, neoclassical, institution

Veteran home educator Susan Wise Bauer outlines the classical pattern of education called the trivium, which organizes learning around the maturing capacity of the child's mind and comprises three stages: the elementary school "grammar stage," the middle school "logic stage," and the high school "rhetoric stage." Using this theory as your model, you'll be able to instruct your child--whether full-time or as a supplement to classroom education--regardless of your own aptitude in any subjects. Thousands of parents and teachers have already used the detailed book lists and methods described in The Well-Trained Mind to create a truly superior education for the children in their care. This new revised edition contains an updated chapter on applying to colleges and links to a new set of online resources. You do have control over what and how your child learns. The Well-Trained Mind will give you the tools you'll need to teach your child with confidence and success.

British Islam and English Law presents a novel argument about the nature and place of groups in society. The encounter with Islam has led English law to tread a line between two theoretical models, liberal individualism and multiculturalism, competing for dominance over the law of organised religion. This philosophical rivalry has generated a set of seemingly intractable conflicts between individual and community, religion and state, nation and culture. This book resurrects the long-buried theory of classical pluralism to address and resolve these tensions. Applying this to five understudied institutions that give structure and form to British Islam – banks, charities, schools, elections, clans – it outlines and justifies the reforms that would optimise the relationship between law and religion. Unflinching and unorthodox, this book places law and theory in context, employs innovative methods such as nudge theory and applied history, and provides detailed answers to hard questions abou

British Islam and English Law presents a novel argument about the nature and place of groups in society. The encounter with Islam has led English law to tread a line between two theoretical models, liberal individualism and multiculturalism, competing for dominance over the law of organised religion. This philosophical rivalry has generated a set of seemingly intractable conflicts between individual and community, religion and state, nation and culture. This book resurrects the long-buried theory of classical pluralism to address and resolve these tensions. Applying this to five understudied institutions that give structure and form to British Islam – banks, charities, schools, elections, clans – it outlines and justifies the reforms that would optimise the relationship between law and religion. Unflinching and unorthodox, this book places law and theory in context, employs innovative methods such as nudge theory and applied history, and provides detailed answers to hard questions abou