Classical Recursion Theory

The most comprehensive study of ideology and utopia since Karl Mannheim's work of the 1930s, Utopia and Revolution can be understood as turning classical political theory on its head or, perhaps, insi

This volume presents a comprehensive statement in defense of the doctrine known as classical, hedonistic utilitarianism. It is presented as a viable alternative in the search for a moral theory and th

A gradual approach to learning to play the recorder, to reading music and to understanding basic music theory. As ability increases, new material is added. There are 67 familiar popular, classical and

This book is the result of a long and fruitful conversation among practitioners of two very different fields: ancient history and political theory. The topic of the conversation is classical Greek dem

This book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory. Classical results in these fields, such as the straightedge-and-c

Drawing on years of field research in Cuba, this text examines the relationship between socialism and democracy, in classical Marxist theory and in the practice of the Cuban revolution. While the auth

This comprehensive and self-contained account of the extrinsic geometry of algebraic curves applies the theory of linear series to a number of classical topics, including the geometry of the Reimann t

Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern t

This book on solid state physics has been written with an emphasis on recent developments in quantum many-body physics approaches. It starts by covering the classical theory of solids and electrons an

The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geomet

The book is devoted to the theory describing the interaction of ultra-short electromagnetic pulses (USP) with matter, including both classical and quantum cases. This theme is a hot topic in modern p

A fun, easy-to-follow introduction to classical, jazz and popular piano that exercises your brain! This is truly an All-in-One Piano Method which includes Lesson, Theory, Note Speller, Technique, Chor

This book on solid state physics has been written with an emphasis on recent developments in quantum many-body physics approaches. It starts by covering the classical theory of solids and electrons a

This volume unites, for the first time, Books IV and V of Mill's great treatise on political economy with his fragmentary Chapters on Socialism. It shows him applying his classical economic theory t

This is the first English translation of one of the classical works of Marxist economic theory. When Rudolf Hilferding’s Finance Capital was first published in 1919 it was acclaimed by reviewers as a

This is a timely study of the international relations of Islamic states, dealing both with the evolving theory of pan-Islamism from classical to post-caliphal times and the foreign-policy practice of

Noel Burch's singularly perceptive view of film and its origins will interest all who care about film theory and history. Life to Those Shadows presents a critique of "classical" approaches to film: t

The concept of rationality is the heart of modern economics. Neo-classical theory seems unable to proceed without assuming a rational agent seeking to find the optimal means to a well defined end. Yet

The volume is an enlarged edition of a classic textbook on complex analysis. It bridges the gap between the classical material of the first edition and recent advances in half-plane Loewner theory, th

L.A. Galin's book on contact problems is a remarkable work. Actually there are two books: the first, published in 1953 deals with contact problems in the classical theory of elasticity; this is the o

Book 2 includes music theory, the keys of C, G and D, exploring the neck, second position, syncopation, rhythm and lead guitar techniques, cut time, solo guitar style, and pop and classical songs lik

The volume is an enlarged edition of a classic textbook on complex analysis. It bridges the gap between the classical material of the first edition and recent advances in half-plane Loewner theory, th

The volume is an enlarged edition of a classic textbook on complex analysis. It bridges the gap between the classical material of the first edition and recent advances in half-plane Loewner theory, th

Natural Law Today gives a strong voice to classical natural law theory as the best answers to the fundamental questions of ethics and as the best framework for political and social life. It explains v

The purpose of this monograph is to provide a theory of Markov processes that are invariant under the actions of Lie groups, focusing on ways to represent such processes in the spirit of the classical

This work starts with the study of those limit theorems in probability theory for which classical methods do not work. In many cases some form of linearization can help to solve the problem, because t

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many importa

The text is aimed at final-year undergraduate students or those at the graduate level doing econometrics for the first time. It is an introductory course in the theory and practice of classical and mo

"This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of th

For more than a century, quantum mechanics has served as a very powerful theory that has expanded physics and technology far beyond their classical limits, yet it has also produced some of the mo

Are human rights part of the problem or part of the solution in the current 'clash of civilizations'? Drawing on a hitherto neglected body of work in classical social theory and combining it with idea

This is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of "the calculus of variations"

Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen–Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers inter

Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen–Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers inter

This book gives an introduction to theories of computability from a mathematically sophisticated point of view. It treats not only 'the' theory of computability (created by Alan Turing and others in the 1930s), but also a variety of other theories (of Boolean functions, automata and formal languages). These are addressed from the classical perspective of their generation by grammars and from the modern perspective as rational cones. The treatment of the classical theory of computable functions and relations takes the form of a tour through basic recursive function theory, starting with an axiomatic foundation and developing the essential methods in order to survey the most memorable results of the field. This authoritative account by one of the leading lights of the subject will prove exceptionally useful reading for graduate students, and researchers in theoretical computer science and mathematics.

This book provides a self-contained and systematic introduction to classical electron theory and its quantization, non-relativistic quantum electrodynamics. The first half of the book covers the classical theory. It discusses the well-defined Abraham model of extended charges in interaction with the electromagnetic field, and gives a study of the effective dynamics of charges under the condition that, on the scale given by the size of the charge distribution, they are far apart and the applied potentials vary slowly. The second half covers the quantum theory, leading to a coherent presentation of non-relativistic quantum electrodynamics. Topics discussed include non-perturbative properties of the basic Hamiltonian, the structure of resonances, the relaxation to the ground state through emission of photons, the non-perturbative derivation of the g-factor of the electron and the stability of matter.

This book provides a self-contained and systematic introduction to classical electron theory and its quantization, non-relativistic quantum electrodynamics. The first half of the book covers the classical theory. It discusses the well-defined Abraham model of extended charges in interaction with the electromagnetic field, and gives a study of the effective dynamics of charges under the condition that, on the scale given by the size of the charge distribution, they are far apart and the applied potentials vary slowly. The second half covers the quantum theory, leading to a coherent presentation of non-relativistic quantum electrodynamics. Topics discussed include non-perturbative properties of the basic Hamiltonian, the structure of resonances, the relaxation to the ground state through emission of photons, the non-perturbative derivation of the g-factor of the electron and the stability of matter.

Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of m

This book gives an introduction to theories of computability from a mathematically sophisticated point of view. It treats not only 'the' theory of computability (created by Alan Turing and others in the 1930s), but also a variety of other theories (of Boolean functions, automata and formal languages). These are addressed from the classical perspective of their generation by grammars and from the modern perspective as rational cones. The treatment of the classical theory of computable functions and relations takes the form of a tour through basic recursive function theory, starting with an axiomatic foundation and developing the essential methods in order to survey the most memorable results of the field. This authoritative account by one of the leading lights of the subject will prove exceptionally useful reading for graduate students, and researchers in theoretical computer science and mathematics.

The aphorism captures a huge amount of knowledge, meaning or wit in a very short statement. It has been used and studied from classical times to contemporary theory and takes on a new relevance when w