Classical Recursion Theory

Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure

Advanced undergraduate or beginning graduate students need a unified foundation for their study of geometry, analysis, and algebra. This book, first published in 2003, uses categorical algebra to build such a foundation, starting from intuitive descriptions of mathematically and physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings is introduced and developed as a unifying basis for advanced mathematical subjects such as algebra, geometry, analysis, and combinatorics. The formal study evolves from general axioms which express universal properties of sums, products, mapping sets, and natural number recursion. The distinctive features of Cantorian abstract sets, as contrasted with the variable and cohesive sets of geometry and analysis, are made explicit and taken as special axioms. Functor categories are introduced in order to model the variable sets used in geometry, and to illustrate the failure

Abstract regular polytopes stand at the end of more than two millennia of geometrical research, which began with regular polygons and polyhedra. They are highly symmetric combinatorial structures with distinctive geometric, algebraic or topological properties; in many ways more fascinating than traditional regular polytopes and tessellations. The rapid development of the subject in the past 20 years has resulted in a rich new theory, featuring an attractive interplay of mathematical areas, including geometry, combinatorics, group theory and topology. Abstract regular polytopes and their groups provide an appealing new approach to understanding geometric and combinatorial symmetry. This is the first comprehensive up-to-date account of the subject and its ramifications, and meets a critical need for such a text, because no book has been published in this area of classical and modern discrete geometry since Coxeter's Regular Polytopes (1948) and Regular Complex Polytopes (1974). The book

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

This sound introduction to classical and modern control theory concentrates on fundamental concepts. Employing the minimum of mathematical elaboration, it investigates the many applications of control

What is a promise? What are the consequences of the act of promising? In this bold yet subtle meditation, the author contemplates the seductive promise of speech and the seductive promise of love. Imagining an encounter between Molière’s Don Juan and J. L. Austin, between a mythical figure of the French classical theater and a twentieth-century philosopher, she explores the relation between speech and the erotic, using a literary text as the ground for a telling encounter between philosophy, linguistics, and Lacanian psychoanalytic theory. In the years since the publication of this book (which the author today calls “the boldest, the most provocative, but also the most playful” she has written), speech act theory has continued to play a central and defining role in the theories of sexuality, gender, performance studies, post-colonial studies, and cultural studies. This book remains topical as readers increasingly discover how multiply relevant the speaking body is.Moving beyond the dom

This four-volume set for middle and high school students and above covers the history, theory, technology, and uses (and misuses) of genetic knowledge, from classical to molecular to population geneti

This book brings together the essential ideas and methods behind applications of variational theory in theoretical physics and chemistry. The emphasis is on understanding physical and computational applications of variational methodology rather than on rigorous mathematical formalism. The text begins with an historical survey of familiar variational principles in classical mechanics and optimization theory, then proceeds to develop the variational principles and formalism behind current computational methodology for bound and continuum quantum states of interacting electrons in atoms, molecules, and condensed matter. It covers multiple-scattering theory, including a detailed presentation of contemporary methodology for electron-impact rotational and vibrational excitation of molecules. The book ends with an introduction to the variational theory of relativistic fields. Ideal for graduate students and researchers in any field that uses variational methodology, this book is particularly

This philosophical treatise on the foundations of semantics is a systematic effort to clarify, deepen and defend the classical doctrine that words are conventional signs of mental states, principally thoughts and ideas, and that meaning consists in their expression. This expression theory of meaning is developed by carrying out the Gricean programme, explaining what it is for words to have meaning in terms of speaker meaning, and what it is for a speaker to mean something in terms of intention. But Grice's own formulations are rejected and alternatives developed. The foundations of the expression theory are explored at length, and the author develops the theory of thought as a fundamental cognitive phenomenon distinct from belief and desire, argues for the thesis that thoughts have parts, and identifies ideas or concepts with parts of thoughts. This book will appeal to students and professionals interested in the philosophy of language.

This book studies the geometric theory of polynomials and rational functions in the plane. Any theory in the plane should make full use of the complex numbers and thus the early chapters build the foundations of complex variable theory, melding together ideas from algebra, topology and analysis. In fact, throughout the book, the author introduces a variety of ideas and constructs theories around them, incorporating much of the classical theory of polynomials as he proceeds. These ideas are used to study a number of unsolved problems, bearing in mind that such problems indicate the current limitations of our knowledge and present challenges for the future. However, theories also lead to solutions of some problems and several such solutions are given including a comprehensive account of the geometric convolution theory. This is an ideal reference for graduate students and researchers working in this area.

Striking a balance between the use of computer-aided engineering practices and classical life testing, this reference expounds on current theory and methods for designing reliability tests and analyzi

Virtue Ethics collects, for the first time, the main classical sources and the central contemporary expressions of virtue ethics approach to normative ethical theory. Edited and introduced by Stephen

Virtue Ethics collects, for the first time, the main classical sources and the central contemporary expressions of virtue ethics approach to normative ethical theory. Edited and introduced by Stephen

An introductory 2002 textbook, Process Control covers the most essential aspects of process control suitable for a two-semester course. While classical techniques are discussed, also included is a discussion of state space modeling and control, a modern control topic lacking in most introductory texts. MATLAB, a popular engineering software package, is employed as a powerful yet approachable computational tool. Text examples demonstrate how root locus, Bode plots, and time domain simulations can be integrated to tackle a control problem. Classical control and state space designs are compared. Despite the reliance on MATLAB, theory and analysis of process control are well-presented, creating a well-rounded pedagogical text. Each chapter concludes with problem sets, to which hints or solutions are provided. A web site provides excellent support in the way of MATLAB outputs of text examples and MATLAB sessions, references, and supplementary notes. Students and professionals will find it a

Contemporary architectural theory emphasizes the importance of 'tectonics', the term used to articulate the relationship between construction, structure and architectural expression. Despite the term's currency, little consideration has been given to its origins or historical significance. In this 2002 study, Werner Oechslin examines the attempts by early modern theoreticians of architecture to grapple with the relationship between appearance and essence, which is crucial to the discourse of tectonics. Referring to the writings of Joseph Lux, Karl Bötticher, and Adolf Loos, Oechslin follows this development from theories of a classical architecture without columnar orders to a Modern architecture upholding the 'truth'of its own architectural expression. Oechslin locates the culmination of this discourse in the work of Adolf Loos and in Le Corbusier's frequent references to Ancient Greece as the precedent of Modern architecture's honesty. This volume includes an anthology of primary tex

Gödel's modal ontological argument is the centerpiece of an extensive examination of intensional logic. First, classical type theory is presented semantically, tableau rules for it are introduced, and

Drawing on classical development theory and recent theoretical advances on the connection between expanding markets and technological developments, this book shows the critical role of expanding Atlantic commerce in the successful completion of England's industrialization process over the period 1650–1850. The contribution of Africans, the central focus of the book, is measured in terms of the role of diasporic Africans in large-scale commodity production in the Americas - of which expanding Atlantic commerce was a function - at a time when demographic and other socioeconomic conditions in the Atlantic basin encouraged small-scale production by independent populations, largely for subsistence. This is the first detailed study of the role of overseas trade in the Industrial Revolution. It revises inward-looking explanations that have dominated the field in recent decades, and shifts the assessment of African contribution away from the debate on profits.

Explains the motivation and reviewing the classical theory in a new form; Discusses conservation laws and Euler equations; For one-dimensional cases, the models presented are completely integrable

This book systematically reconstructs the origins and new advances in economic sociology. By presenting both classical and contemporary theory and research, the volume identifies and describes the con

Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. They have been intensely studied in the past; in particular, the solution of a number of conjectures of Kaplansky from the 1970s has led to progress on the classification of semisimple Hopf algebras and on the structure of pointed Hopf algebras. Among the topics covered are results toward the classification of finite-dimensional Hopf algebras (semisimple and non-semisimple), as well as what is known about the extension theory of Hopf algebras. Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to work in quantum groups. The book also explores the connections and applications of Hopf algebras to other fields.

The dominant moral philosophy of nineteenth-century Britain was utilitarianism, beginning with Bentham and ending with Sidgwick. Though once overshadowed by his immediate predecessors in that tradition (especially John Stuart Mill), Sidgwick is now regarded as a figure of great importance in the history of moral philosophy. Indeed his masterpiece, The Methods of Ethics (1874), has been described by John Rawls as the 'most philosophically profound' of the classical utilitarian works. In this volume a distinguished group of philosophers reassesses the full range of Sidgwick's work, not simply his ethical theory, but also his contributions as a historian of philosophy, a political theorist, and a reformer.

In order to explore a patient's resistance and refusal to grieve, Stark (psychoanalysis, Harvard Medical School) draws on concepts from classical psychoanalysis, object relations theory, and self-psyc

This graduate-level textbook on thermal physics covers classical thermodynamics, statistical mechanics and its applications. It describes theoretical methods to calculate thermodynamic properties, such as the equation of state, specific heat, Helmholtz free energy, magnetic susceptibility and phase transitions of macroscopic systems. In addition to the more standard material covered, this book also describes powerful techniques, which are not found elsewhere, to determine the correlation effects on which the thermodynamic properties are based. Particular emphasis is given to the cluster variation method and a novel formulation is developed for its expression in terms of correlation functions. Although a basic knowledge of quantum mechanics is required, the mathematical formulations are accessible and entirely self-contained. The book will therefore constitute an ideal companion text for graduate students studying courses on the theory of complex analysis, classical mechanics, classical

This graduate-level textbook on thermal physics covers classical thermodynamics, statistical mechanics and its applications. It describes theoretical methods to calculate thermodynamic properties, such as the equation of state, specific heat, Helmholtz free energy, magnetic susceptibility and phase transitions of macroscopic systems. In addition to the more standard material covered, this book also describes powerful techniques, which are not found elsewhere, to determine the correlation effects on which the thermodynamic properties are based. Particular emphasis is given to the cluster variation method and a novel formulation is developed for its expression in terms of correlation functions. Although a basic knowledge of quantum mechanics is required, the mathematical formulations are accessible and entirely self-contained. The book will therefore constitute an ideal companion text for graduate students studying courses on the theory of complex analysis, classical mechanics, classical

"...effectively demonstrates the enduring importance of 'classical' social movement theory...and provides a cutting edge critical review of recent theoretical developments. This is one of the most imp

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.

Generalising classical concepts of probability theory, the investigation of operator (semi)-stable laws as possible limit distributions of operator-normalized sums of i.i.d. random variable on finite-

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selecte

A systematic and comprehensive introduction to the study of nonlinear dynamical systems, in both discrete and continuous time, for nonmathematical students and researchers working in applied fields. An understanding of linear systems and the classical theory of stability are essential although basic reviews of the relevant material are provided. Further chapters are devoted to the stability of invariant sets, bifurcation theory, chaotic dynamics and the transition to chaos. In the final two chapters the authors approach the subject from a measure-theoretical point of view and compare results to those given for the geometrical or topological approach of the first eight chapters. Includes about one hundred exercises. A Windows-compatible software programme called DMC, provided free of charge through a website dedicated to the book, allows readers to perform numerical and graphical analysis of dynamical systems. Also available on the website are computer exercises and solutions to selecte

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.

This is a pedagogical introduction to the harmonic superspace method in extended supersymmetry. Inspired by exciting developments in superstring theory, it provides a systematic treatment of the quantum field theories with N=2 and N=3 supersymmetry in harmonic superspace. The authors present the harmonic superspace approach as a means of providing an off-shell description of the N=2 supersymmetric theories, both at the classical and quantum levels. Furthermore, they show how it offers a unique way to construct an off-shell formulation of a theory with higher supersymmetry, namely the N=3 supersymmetric Yang-Mills theory. Harmonic Superspace makes manifest many remarkable geometric properties of the N=2 theories, for example, the one-to-one correspondence between N=2 supersymmetric matter, and hyper-Kähler and quaternionic manifolds. This book will be of interest to researchers and graduate students working in the areas of supersymmetric quantum field theory, string theory and complex g

Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics.

This carefully prepared manuscript presents elimination theory in weighted projective spaces over arbitrary noetherian commutative base rings. Elimination theory is a classical topic in commutative al

This book focuses on the theory of phonon interactions in nanoscale structures with particular emphasis on modern electronic and optoelectronic devices. The continuing progress in the fabrication of semiconductor nanostructures with lower dimensional features has led to devices with enhanced functionality and even novel devices with new operating principles. The critical role of phonon effects in such semiconductor devices is well known. There is therefore a great need for a greater awareness and understanding of confined phonon effects. A key goal of this book is to describe tractable models of confined phonons and how these are applied to calculations of basic properties and phenomena of semiconductor heterostructures. The level of presentation is appropriate for undergraduate and graduate students in physics and engineering with some background in quantum mechanics and solid state physics or devices. A basic understanding of electromagnetism and classical acoustics is assumed.

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG

Statistics do not lie, nor is probability paradoxical. You just have to have the right intuition. In this lively look at both subjects, David Williams convinces mathematics students of the intrinsic interest of statistics and probability, and statistics students that the language of mathematics can bring real insight and clarity to their subject. He helps students build the intuition needed, in a presentation enriched with examples drawn from all manner of applications, e.g., genetics, filtering, the Black–Scholes option-pricing formula, quantum probability and computing, and classical and modern statistical models. Statistics chapters present both the Frequentist and Bayesian approaches, emphasising Confidence Intervals rather than Hypothesis Test, and include Gibbs-sampling techniques for the practical implementation of Bayesian methods. A central chapter gives the theory of Linear Regression and ANOVA, and explains how MCMC methods allow greater flexibility in modelling. C or WinBUG

Grimshaw's exploration of the role of vision within modern anthropology engages with current debates about ocularcentism, investigating the relationship between vision and knowledge in ethnographic enquiry. Using John Berger's notion of 'ways of seeing', the author argues that vision operates differently as a technique and theory of knowledge within the discipline. In the first part of the book she examines contrasting visions at work in the so-called classical British school, reassessing the legacy of Rivers, Malinowski and Radcliffe-Brown through the lens of early modern art and cinema. In the second part of the book, the changing relationship between vision and knowledge is explored through the anthropology of Jean Rouch, David and Judith MacDougall, and Melissa Llewelyn-Davies. Vision is foregrounded in the work of these contemporary ethnographers, focusing more general questions about technique and epistemology whether image-based media are used or not in ethnographic enquiry.

This introduction treats the classical isoperimetric inequality in Euclidean space and contrasting rough inequalities in noncompact Riemannian manifolds. In Euclidean space the emphasis is on a most general form of the inequality sufficiently precise to characterize the case of equality, and in Riemannian manifolds the emphasis is on those qualitative features of the inequality which provide insight into the coarse geometry at infinity of Riemannian manifolds. The treatment in Euclidean space features a number of proofs of the classical inequality in increasing generality, providing in the process a transition from the methods of classical differential geometry to those of modern geometric measure theory; and the treatment in Riemannian manifolds features discretization techniques, and applications to upper bounds of large time heat diffusion in Riemannian manifolds. The result is an introduction to the rich tapestry of ideas and techniques of isoperimetric inequalities.

This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also o

Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thou