Classical Recursion Theory

This enthusiastic introduction to the fundamentals of information theory builds from classical Shannon theory through to modern applications in statistical learning. Includes over 210 student exercises, emphasising practical applications in statistics, machine learning and modern communication theory. Accompanied by online instructor solutions.

This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differenti

Extending Griffiths’ classical theory of period mappings for compact Kahler manifolds, this book develops and applies a theory of period mappings of “Hodge-de Rham type” for families of open complex m

Open Design bypasses classical theory of decision making and uses a linear programming model to capture the elements of group decision making in an attempt to develop a theory of architectural design.

This book covers both classical and modern models in deep learning. The primary focus is on the theory and algorithms of deep learning. The theory and algorithms of neural networks are particularly im

This book on quantum optics is from the point of view of an experimentalist. It approaches the theory of quantum optics with the language of optical modes of classical wave theory, with which experime

This book on quantum optics is from the point of view of an experimentalist. It approaches the theory of quantum optics with the language of optical modes of classical wave theory, with which experime

This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Ste

Dr Burkill gives a straightforward introduction to Lebesgue's theory of integration. His approach is the classical one, making use of the concept of measure, and deriving the principal results required for applications of the theory.

Quantum theory is our deepest theory of the nature of matter. It is a theory that, notoriously, produces results which challenge the laws of classical logic and suggests that the physical world is illogical. This book gives a critical review of work on the foundations of quantum mechanics at a level accessible to non-experts. Assuming his readers have some background in mathematics and physics, Peter Gibbins focuses on the questions of whether the results of quantum theory require us to abandon classical logic and whether quantum logic can resolve the paradoxes produced by quantum mechanics. He argues that quantum logic does not dispose of the problems faced by classical logic, that no reasonable interpretation of quantum mechanics in terms of 'hidden variables' can be found, and that after all these years quantum mechanics remains a mystery to us. Particles and Paradoxes provides a much-needed and valuable introduction to the philosophy of quantum mechanics and, at the same time, an e

This book is an authoritative description of the various approaches to and methods in the theory of irregularities of distribution. The subject is primarily concerned with number theory, but also borders on combinatorics and probability theory. The work is in three parts. The first is concerned with the classical problem, complemented where appropriate with more recent results. In the second part, the authors study generalizations of the classical problem, pioneered by Schmidt. Here, they include chapters on the integral equation method of Schmidt and the more recent Fourier transform technique. The final part is devoted to Roth's '1/4-theorem'.

This book is an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a window through which to view the development of some of the fundamental m

The classical music of India, its history, instruments, musicians, and theory are thoroughly discussed in this copiously illustrated reference.

The goal of this monograph is to develop Hopf theory in a new setting which features centrally a real hyperplane arrangement. The new theory is parallel to the classical theory of connected Hopf algebras, and relates to it when specialized to the braid arrangement. Joyal's theory of combinatorial species, ideas from Tits' theory of buildings, and Rota's work on incidence algebras inspire and find a common expression in this theory. The authors introduce notions of monoid, comonoid, bimonoid, and Lie monoid relative to a fixed hyperplane arrangement. They also construct universal bimonoids by using generalizations of the classical notions of shuffle and quasishuffle, and establish the Borel–Hopf, Poincaré–Birkhoff–Witt, and Cartier–Milnor–Moore theorems in this setting. This monograph opens a vast new area of research. It will be of interest to students and researchers working in the areas of hyperplane arrangements, semigroup theory, Hopf algebras, algebraic Lie theory, operads, and ca

The projective, Möbius, Laguerre, and Minkowski planes over the real numbers are just a few examples of a host of fundamental classical topological geometries on surfaces. This book summarizes all known major results and open problems related to these classical point-line geometries and their close (nonclassical) relatives. Topics covered include: classical geometries; methods for constructing nonclassical geometries; classifications and characterizations of geometries. This work is related to many other fields including interpolation theory, convexity, the theory of pseudoline arrangements, topology, the theory of Lie groups, and many more. The authors detail these connections, some of which are well-known, but many much less so. Acting both as a reference for experts and as an accessible introduction for graduate students, this book will interest anyone wishing to know more about point-line geometries and the way they interact.

aiming at a more conceptual understanding of classical and qu- tum ?eld theory from a novel mathematical point of view.

Collisional transport theory is of central importance to modern plasma physics. This book provides a self-contained treatment of the subject, starting from elementary concepts and developing the theory through to the research frontier. Basic tools of kinetic plasma theory, such as the drift kinetic equation and the Coulomb collision operator, are derived, and are then used to calculate classical and neoclassical transport occurring in high-temperature plasmas. Important phenomena such as neo-classical diffusion, bootstrap current, and plasma rotation are carefully explained. Students, theoreticians and experimentalists in both fusion and space plasma physics will benefit from this book, which emerged from a graduate student level course taught at MIT.

Collisional transport theory is of central importance to modern plasma physics. This book provides a self-contained treatment of the subject, starting from elementary concepts and developing the theory through to the research frontier. Basic tools of kinetic plasma theory, such as the drift kinetic equation and the Coulomb collision operator, are derived, and are then used to calculate classical and neoclassical transport occurring in high-temperature plasmas. Important phenomena such as neo-classical diffusion, bootstrap current, and plasma rotation are carefully explained. Students, theoreticians and experimentalists in both fusion and space plasma physics will benefit from this book, which emerged from a graduate student level course taught at MIT.

A fundamental problem of algebraic topology is the classification of homotopy types and homotopy classes of maps. In this work the author extends results of rational homotopy theory to a subring of the rationale. The methods of proof employ classical commutator calculus of nilpotent group and Lie algebra theory and rely on an extensive and systematic study of the algebraic properties of the classical homotopy operations (composition and addition of maps, smash products, Whitehead products and higher order James-Hopi invariants). The account is essentially self-contained and should be accessible to non-specialists and graduate students with some background in algebraic topology and homotopy theory.

Metric space topology, as the generalization to abstract spaces of the theory of sets of points on a line or in a plane, unifies many branches of classical analysis and is necessary introduction to functional analysis. Professor Copson's book, which is based on lectures given to third-year undergraduates at the University of St Andrews, provides a more leisurely treatment of metric spaces than is found in books on functional analysis, which are usually written at graduate student level. His presentation is aimed at the applications of the theory to classical algebra and analysis; in particular, the chapter on contraction mappings shows how it provides proof of many of the existence theorems in classical analysis.

Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probabi

This book formally introduces synthetic differential topology, a natural extension of the theory of synthetic differential geometry which captures classical concepts of differential geometry and topology by means of the rich categorical structure of a necessarily non-Boolean topos and of the systematic use of logical infinitesimal objects in it. Beginning with an introduction to those parts of topos theory and synthetic differential geometry necessary for the remainder, this clear and comprehensive text covers the general theory of synthetic differential topology and several applications of it to classical mathematics, including the calculus of variations, Mather's theorem, and Morse theory on the classification of singularities. The book represents the state of the art in synthetic differential topology and will be of interest to researchers in topos theory and to mathematicians interested in the categorical foundations of differential geometry and topology.

Structural Analysis of Polymeric Composite Materials, Second Edition introduces the mechanics of composite materials and structures and combines classical lamination theory with macromechanical failur

This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. This theory highlights several general mathematical ideas th

This book provides a comprehensive, systematic treatise on development economics, combining classical political economy, modern institutional theory, and current development issues. It addresses one

Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions and enumerative geometry. The aim

Johnson argues that nineteenth-century rhetoric was primarily synthetic, derived from the combination of classical elements and eighteenth-century belletristic and epistemological approaches to theory

This book proposes a fresh and original interpretation of Keats' use of classical mythology in his verse. Dr Aske argues that classical antiquity appears to Keats as a supreme fiction, authoritative yet disconcerting, and his poems represent hard endeavours to come to terms with the influence of that fiction. The major poems (most notably Endymion, Hyperion, the Ode on a Grecian Urn and Lamia) form a stage, as it were, upon which is played out a psychic drama between the modern poet and his classical muse. The study is especially bold in its assimilation of historical scholarship and literary theory to a close reading of the texts. Individual poems are discussed in the context of late Enlightenment and Romantic attitudes towards antiquity and in the light of recent critical theory, in particular the theory of literary history and influence formulated by Harold Bloom and Geoffrey Hartman. Keats emerges as a significant example of the way in which a poet tries to establish a distinct ide

An introduction to the theory of orbifolds from a modern perspective, combining techniques from geometry, algebraic topology and algebraic geometry. One of the main motivations, and a major source of examples, is string theory, where orbifolds play an important role. The subject is first developed following the classical description analogous to manifold theory, after which the book branches out to include the useful description of orbifolds provided by groupoids, as well as many examples in the context of algebraic geometry. Classical invariants such as de Rham cohomology and bundle theory are developed, a careful study of orbifold morphisms is provided, and the topic of orbifold K-theory is covered. The heart of this book, however, is a detailed description of the Chen-Ruan cohomology, which introduces a product for orbifolds and has had significant impact. The final chapter includes explicit computations for a number of interesting examples.

An introduction to the theory and methods of empirical asset pricing, integrating classical foundations with recent developments.This book offers a comprehensive advanced introduction to asset pricing

The complexity of the twenty-first century threat landscape contrasts markedly with the bilateral nuclear bargaining context envisioned by classical deterrence theory. Nuclear and conventional arsenal

The complexity of the twenty-first century threat landscape contrasts markedly with the bilateral nuclear bargaining context envisioned by classical deterrence theory. Nuclear and conventional arsenal

Modal logic, developed as an extension of classical propositional logic and first-order quantification theory, integrates the notions of possibility and necessity and necessary implication. Arguments

Targeted at mathematicians having at least a basic familiarity with classical bifurcation theory, this monograph provides a systematic classification and analysis of bifurcations without parameters in

Plates: Theories and Applications provides a comprehensive introduction to plate structures, covering classical theory and applications. It considers plate structures in several forms, starting from t

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, compu

Most texts on electromagnetic theory follow the classical approach of steady state solutions of Maxwell's equations. In Interstellar Propagation of Electromagnetic Signals, the authors, H. Harmuth

While the relationship between norms and the state is an omnipresent research theme in International Relations, most international theory - from classical liberalism to recent constructivism - continu

Revised and?updated, this second edition of Walter Gautschi's successful Numerical Analysis?explores?computational methods?for problems arising in the areas of classical analysis, approximation theory

Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representat