Classical Recursion Theory

Scattering theory provides a framework for understanding the scattering of waves and particles. This book presents a simple physical picture of diffractive nuclear scattering in terms of semi-classical trajectories, illustrated throughout with examples and case studies. Trajectories in a complex impact parameter plane are discussed, and it stresses the importance of the analytical properties of the phase shift function in this complex impact plane in the asymptotic limit. Several new rainbow phenomena are also discussed and illustrated. Written by Nobel Prize winner Roy J. Glauber, and Per Osland, an expert in the field of particle physics, the book illustrates the transition from quantum to classical scattering, and provides a valuable resource for researchers using scattering theory in nuclear, particle, atomic and molecular physics.

Roman Law in the State of Nature offers a new interpretation of the foundations of Hugo Grotius' natural law theory. Surveying the significance of texts from classical antiquity, Benjamin Straumann argues that certain classical texts, namely Roman law and a specifically Ciceronian brand of Stoicism, were particularly influential for Grotius in the construction of his theory of natural law. The book asserts that Grotius, a humanist steeped in Roman law, had many reasons to employ Roman tradition and explains how Cicero's ethics and Roman law - secular and offering a doctrine of the freedom of the high seas - were ideally suited to provide the rules for Grotius' state of nature. This fascinating new study offers historians, classicists and political theorists a fresh account of the historical background of the development of natural rights, natural law and of international legal norms as they emerged in seventeenth-century early modern Europe.

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

One of South Asia's most compelling artists, Jitish Kallat has built an immersive practice, ranging from ideas of time, recursion, and historical recall, to deliberations on the cosmopolis and the int

Providing an in-depth introduction to fundamental classical and non-classical logics, this textbook offers a comprehensive survey of logics for computer scientists. Logics for Computer Science&nb

This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical r

Classical electromagnetism - one of the fundamental pillars of physics - is an important topic for all types of physicists from the theoretical to the applied. The subject is widely recognized to be one of the most challenging areas of the physics curriculum, both for students to learn and for lecturers to teach. Although textbooks on electromagnetism are plentiful, hardly any are written in the question-and-answer style format adopted in this book. It contains nearly 300 worked questions and solutions in classical electromagnetism, and is based on material usually encountered during the course of a standard university physics degree.Topics covered include some of the background mathematical techniques, electrostatics, magnetostatics, elementary circuit theory, electrodynamics, electromagnetic waves and electromagnetic radiation. For the most part the book deals with the microscopic theory, although we also introduce the important subject of macroscopic electromagnetism as well. Nearly

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

Spiking neural networks (SNN) are biologically inspired computational models that represent and process information internally as trains of spikes. This monograph book presents the classical theory an

This book expands on the classical statistical multivariate analysis theory by focusing on bilinear regression models, a class of models comprising the classical growth curve model and its extensions.

This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

Building on the best-selling tradition of previous editions, Classical Mythology, Eleventh Edition, is the most comprehensive survey of classical mythology available--and the first full-color textbook

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

This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.

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.

Deterrence, Choice, and Crime explores the various dimensions of modern deterrence theory, relevant research, and practical applications. Beginning with the classical roots of deterrence theory in Ces

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

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

Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit

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

Two central problems in computer science are P vs NP and the complexity of matrix multiplication. The first is also a leading candidate for the greatest unsolved problem in mathematics. The second is of enormous practical and theoretical importance. Algebraic geometry and representation theory provide fertile ground for advancing work on these problems and others in complexity. This introduction to algebraic complexity theory for graduate students and researchers in computer science and mathematics features concrete examples that demonstrate the application of geometric techniques to real world problems. Written by a noted expert in the field, it offers numerous open questions to motivate future research. Complexity theory has rejuvenated classical geometric questions and brought different areas of mathematics together in new ways. This book will show the beautiful, interesting, and important questions that have arisen as a result.

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

The Classical Guitar Collection contains 48 classical guitar solos from classical greats such as Mozart, Grieg, Purcell, and J. S. Bach. This collection features many of Julian Bream's classic arrange

The book consists of two parts: Part 1 is a standard text of dislocation theory. Mathematics is avoided as much as possible. Part 2 describes application of dislocation theory, which includes mechanic

This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.

Inequalities in Analysis and Probability is a must for graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and

Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.

This book provides a systematic presentation of the mathematical foundation of modern physics with applications particularly within classical mechanics and the theory of relativity. Among the themes p

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

Written by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic Number Theory' Easter School held at Durham University in 2014. Key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research are presented in a manner accessible to young researchers, including PhD students. This book will also be useful for established mathematicians. The areas discussed include ubiquitous systems and Cantor-type sets in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, multiple recurrence and Ramsey theory, counting and equidistribution problems in homogeneous dynamics, and applications of thin groups in number theory. Both dynamical and 'classical' appr

This textbook is a first introduction to mathematics for music theorists, covering basic topics such as sets and functions, universal properties, numbers and recursion, graphs, groups, rings, matrices

The classical theory of Random Walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to pro

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.

Branching Brownian motion (BBM) is a classical object in probability theory with deep connections to partial differential equations. This book highlights the connection to classical extreme value theory and to the theory of mean-field spin glasses in statistical mechanics. Starting with a concise review of classical extreme value statistics and a basic introduction to mean-field spin glasses, the author then focuses on branching Brownian motion. Here, the classical results of Bramson on the asymptotics of solutions of the F-KPP equation are reviewed in detail and applied to the recent construction of the extremal process of BBM. The extension of these results to branching Brownian motion with variable speed are then explained. As a self-contained exposition that is accessible to graduate students with some background in probability theory, this book makes a good introduction for anyone interested in accessing this exciting field of mathematics.

A Unified Approach to Economic TheoryDemonstrating a balanced treatment of both classical and Keynesian economics, Macroecomomics presents macroeconomic theory in a big-picture way. Comprehensive cove

An H(b) space is defined as a collection of analytic functions that are in the image of an operator. The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and demanding. Volume 1 of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators and Clark measures. Volume 2 focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.