Classical Recursion Theory

Boundary-layer separation from a rigid body surface is one of the fundamental problems of classical and modern fluid dynamics. The major successes achieved since the late 1960s in the development of the theory of separated flows at high Reynolds numbers are in many ways associated with the use of asymptotic methods. The most fruitful of these has proved to be the method of matched asymptotic expansions, which has been widely used in mechanics and mathematical physics. There have been many papers devoted to different problems in the asymptotic theory of separated flows and we can confidently speak of the appearance of a very productive direction in the development of theoretical hydrodynamics. This book will present this theory in a systematic account. The book will serve as a useful introduction to the theory, and will draw attention to the possibilities that application of the asymptotic approach provides.

In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, st

Boundary-layer separation from a rigid body surface is one of the fundamental problems of classical and modern fluid dynamics. The major successes achieved since the late 1960s in the development of the theory of separated flows at high Reynolds numbers are in many ways associated with the use of asymptotic methods. The most fruitful of these has proved to be the method of matched asymptotic expansions, which has been widely used in mechanics and mathematical physics. There have been many papers devoted to different problems in the asymptotic theory of separated flows and we can confidently speak of the appearance of a very productive direction in the development of theoretical hydrodynamics. This book will present this theory in a systematic account. The book will serve as a useful introduction to the theory, and will draw attention to the possibilities that application of the asymptotic approach provides.

In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, st

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.

A polarised variety is a modern generalization of the notion of a variety in classical algebraic geometry. It consists of a pair: the algebraic variety itself, together with an ample line bundle on it. Using techniques from abstract algebraic geometry that have been developed over recent decades, Professor Fujita develops classification theories of such pairs using invariants that are polarised higher-dimensional versions of the genus of algebraic curves. The heart of the book is the theory of D-genus and sectional genus developed by the author, but numerous related topics are discussed or surveyed. Proofs are given in full in the central part of the development, but background and technical results are sometimes just sketched when the details are not essential for understanding the key ideas. Readers are assumed to have some background in algebraic geometry, including sheaf cohomology, and for them this work will provide an illustration of the power of modern abstract techniques appli

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

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

This book traces the image of the pregnant male in Greek literature as it evolved over the course of the classical period. The image - as deployed in myth and in metaphor - originated as a representation of paternity and, by extension, 'authorship' of ideas, works of art, legislation, and the like. Only later, with its reception in philosophy in the early fourth century, did it also become a way to figure and negotiate the boundary between the sexes. The book considers a number of important moments in the evolution of the image: the masculinist embryological theory of Anaxagoras of Clazomenae and other fifth century pre-Socratics; literary representations of the birth of Dionysus; the origin and functions of pregnancy as a metaphor in tragedy, comedy and works of some Sophists; and finally the redeployment of some of these myths and metaphors in Aristophanes' Assemblywomen and in Plato's Symposium and Theaetetus.

This book traces the image of the pregnant male in Greek literature as it evolved over the course of the classical period. The image - as deployed in myth and in metaphor - originated as a representation of paternity and, by extension, 'authorship' of ideas, works of art, legislation, and the like. Only later, with its reception in philosophy in the early fourth century, did it also become a way to figure and negotiate the boundary between the sexes. The book considers a number of important moments in the evolution of the image: the masculinist embryological theory of Anaxagoras of Clazomenae and other fifth century pre-Socratics; literary representations of the birth of Dionysus; the origin and functions of pregnancy as a metaphor in tragedy, comedy and works of some Sophists; and finally the redeployment of some of these myths and metaphors in Aristophanes' Assemblywomen and in Plato's Symposium and Theaetetus.

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.

A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engin

Tarasti (musicology, U. of Helsinki, Finland) presents the theory or philosophy of existential semiotics that he has been developing in previous books for the past 15 years. After years under the infl

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.

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.

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

The topics treated in this book are essentially those that a graduate student of physics or electrical engineering should be familiar with in classical electromagnetism. Each topic is analyzed in deta

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

Descriptive set theory is the area of mathematics concerned with the study of the structure of definable sets in Polish spaces. Beyond being a central part of contemporary set theory, the concepts and

In this third edition of Capitalism and Classical Social Theory, John Bratton and David Denham continue to highlight the relevance of classical social theory in today’s world. Discussing the ce

Classical political theorists such as Thucydides, Kant, Rousseau, Smith, Hegel, Grotius, Mill, Locke and Clausewitz are often employed to explain and justify contemporary international politics and ar

The purpose of this book is to describe the classical problems in additive number theory, and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tool

This well-developed, accessible text details the historical development of the subject throughout. It also provides wide-ranging coverage of significant results with comparatively elementary proofs, s