Classical Recursion Theory

This graduate/research level text introduces the theory of multi-electron transitions in atomic, molecular and optical physics, emphasising the emerging topic of dynamic electron correlation. The book begins with an overview of simple binomial probabilities, classical scattering theory, quantum scattering and correlation, followed by the theory of single electron transition probabilities. Multiple electron transition probabilities are then treated in detail. Various approaches to multiple electron transitions are covered including the independent electron approximation, useful statistical methods and perturbation expansions treating correlation in both weak and strong limits. The important topic of the dynamics of electron correlation is a central theme in this book. The text contains a comprehensive summary of data for few and many-electron transitions in atoms and molecules, including transitions on different atomic centres, fast ion-atom and electron-atom interactions, and recent ob

The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, the last few years having seen the resolution of many longstanding conjectures. This volume contains important expositions and original work by some of the main contributors on topics such as topology and geometry of 3-manifolds, curve complexes, classical Ahlfors-Bers theory, computer explorations and projective structures. Researchers in these and related areas will find much of interest here.

Based on time-tested course material, this authoritative text examines the key topics, advanced mathematical concepts, and novel analytical tools needed to understand modern communication and radar systems. It covers computational linear algebra theory, VLSI systolic algorithms and designs, practical aspects of chaos theory, and applications in beamforming and array processing, and uses a variety of CDMA codes, as well as acoustic sensing and beamforming algorithms to illustrate key concepts. Classical topics such as spectral analysis are also covered, and each chapter includes a wealth of homework problems. This is an invaluable text for graduate students in electrical and computer engineering, and an essential reference for practitioners in communications and radar engineering.

Within algebraic topology, the prominent role of multiplicative cohomology theories has led to a great deal of foundational research on ring spectra and in the 1990s this gave rise to significant new approaches to constructing categories of spectra and ring-like objects in them. This book contains some important new contributions to the theory of structured ring spectra as well as survey papers describing these and relationships between them. One important aspect is the study of strict multiplicative structures on spectra and the development of obstruction theories to imposing strictly associative and commutative ring structures on spectra. A different topic is the transfer of classical algebraic methods and ideas, such as Morita theory, to the world of stable homotopy.

Scaling laws reveal the fundamental property of phenomena, namely self-similarity - repeating in time and/or space - which substantially simplifies the mathematical modelling of the phenomena themselves. This book begins from a non-traditional exposition of dimensional analysis, physical similarity theory, and general theory of scaling phenomena, using classical examples to demonstrate that the onset of scaling is not until the influence of initial and/or boundary conditions has disappeared but when the system is still far from equilibrium. Numerous examples from a diverse range of fields, including theoretical biology, fracture mechanics, atmospheric and oceanic phenomena, and flame propagation, are presented for which the ideas of scaling, intermediate asymptotics, self-similarity, and renormalisation were of decisive value in modelling.

In this book, Omar Farahat presents a new way of understanding the work of classical Islamic theologians and legal theorists who maintained that divine revelation is necessary for the knowledge of the norms and values of human actions. Through a reconstruction of classical Ashʿarī-Muʿtazilī debates on the nature and implications of divine speech, Farahat argues that the Ashʿarī attachment to revelation was not a purely traditionalist position. Rather, it was a rational philosophical commitment emerging from debates in epistemology and theology. He further argues that the particularity of this model makes its distinctive features helpful for contemporary scholars who defend a form of divine command theory. Farahat's volume thus constitutes a new reading of the issue of reason and revelation in Islam and breaks new ground in Islamic theology, law and ethics.

In this book, Omar Farahat presents a new way of understanding the work of classical Islamic theologians and legal theorists who maintained that divine revelation is necessary for the knowledge of the norms and values of human actions. Through a reconstruction of classical Ashʿarī-Muʿtazilī debates on the nature and implications of divine speech, Farahat argues that the Ashʿarī attachment to revelation was not a purely traditionalist position. Rather, it was a rational philosophical commitment emerging from debates in epistemology and theology. He further argues that the particularity of this model makes its distinctive features helpful for contemporary scholars who defend a form of divine command theory. Farahat's volume thus constitutes a new reading of the issue of reason and revelation in Islam and breaks new ground in Islamic theology, law and ethics.

Combustion Thermodynamics and Dynamics builds on a foundation of thermal science, chemistry, and applied mathematics that will be familiar to most undergraduate aerospace, mechanical, and chemical engineers to give a first-year graduate-level exposition of the thermodynamics, physical chemistry, and dynamics of advection-reaction-diffusion. Special effort is made to link notions of time-independent classical thermodynamics with time-dependent reactive fluid dynamics. In particular, concepts of classical thermochemical equilibrium and stability are discussed in the context of modern nonlinear dynamical systems theory. The first half focuses on time-dependent spatially homogeneous reaction, while the second half considers effects of spatially inhomogeneous advection and diffusion on the reaction dynamics. Attention is focused on systems with realistic detailed chemical kinetics as well as simplified kinetics. Many mathematical details are presented, and several quantitative examples are

In this book, eminent scholars of classical antiquity and ancient and medieval Judaism and Christianity explore the nature and place of forgiveness in the pre-modern Western world. They discuss whether the concept of forgiveness, as it is often understood today, was absent, or at all events more restricted in scope than has been commonly supposed, and what related ideas (such as clemency or reconciliation) may have taken the place of forgiveness. An introductory chapter reviews the conceptual territory of forgiveness and illuminates the potential breadth of the idea, enumerating the important questions a theory of the subject should explore. The following chapters examine forgiveness in the contexts of classical Greece and Rome; the Hebrew Bible, the Talmud, and Moses Maimonides; and the New Testament, the Church Fathers, and Thomas Aquinas.

This book is an introduction to the logic and analytics of group choice. To understand how political institutions work, it is important to isolate what citizens - as individuals and as members of society - actually want. This book develops a means of 'representing' the preferences of citizens so that institutions can be studied more carefully. This is the first book to integrate the classical problem of constitutions with modern spatial theory, connecting Aristotle and Montesquieu with Arrow and Buchanan.

This book is an introduction to the logic and analytics of group choice. To understand how political institutions work, it is important to isolate what citizens - as individuals and as members of society - actually want. This book develops a means of 'representing' the preferences of citizens so that institutions can be studied more carefully. This is the first book to integrate the classical problem of constitutions with modern spatial theory, connecting Aristotle and Montesquieu with Arrow and Buchanan.

This second edition was first published in 1959. The first four chapters present a compact elementary account of classical and modern conceptions of valency, suitable for the more general reader and for students preparing for university examinations. The concluding chapters are more advanced: chapter five shows how the electronic theory is applied to the heavier elements and their principal compounds; and the last chapter is devoted to current developments, and theories still in their early stages.

With the rise of naturalism in the art of the late Middle Ages and the Renaissance there developed an extensive and diverse literature about art which helped to explain, justify and shape its new aims. In this book, David Summers provides an investigation of the philosophical and psychological notions invoked in this new theory and criticism. From a thorough examination of the sources, he shows how the medieval language of mental discourse derived from an understanding of classical thought.

This classic book is a encylopaedic and comprehensive account of the classical theory of analytical dynamics. The treatment is rigorous yet readable, starting from first principles with kinematics before moving to equations of motion and specific and explicit methods for solving them, with chapters devoted to particle dyanmics, rigid bodies, vibration, and dissipative systems. Hamilton's principle is introduced and then applied to dynamical systems, including three-body systems and celestial mechanics. Very many examples and exercisies are supplied throughout.

New edition of a graduate-level textbook on that focuses on online convex optimization, a machine learning framework that views optimization as a process.In many practical applications, the environment is so complex that it is not feasible to lay out a comprehensive theoretical model and use classical algorithmic theory and/or mathematical optimization. Introduction to Online Convex Optimization presents a robust machine learning approach that contains elements of mathematical optimization, game theory, and learning theory: an optimization method that learns from experience as more aspects of the problem are observed. This view of optimization as a process has led to some spectacular successes in modeling and systems that have become part of our daily lives. Based on the “Theoretical Machine Learning” course taught by the author at Princeton University, the second edition of this widely used graduate level text features:Thoroughly updated material throughoutNew chapters on boosting, ad

Tau functions are a central tool in the modern theory of integrable systems. This volume provides a thorough introduction, starting from the basics and extending to recent research results. It covers a wide range of applications, including generating functions for solutions of integrable hierarchies, correlation functions in the spectral theory of random matrices and combinatorial generating functions for enumerative geometrical and topological invariants. A self-contained summary of more advanced topics needed to understand the material is provided, as are solutions and hints for the various exercises and problems that are included throughout the text to enrich the subject matter and engage the reader. Building on knowledge of standard topics in undergraduate mathematics and basic concepts and methods of classical and quantum mechanics, this monograph is ideal for graduate students and researchers who wish to become acquainted with the full range of applications of the theory of tau f

Sub-Riemannian geometry is the geometry of a world with nonholonomic constraints. In such a world, one can move, send and receive information only in certain admissible directions but eventually can reach every position from any other. In the last two decades sub-Riemannian geometry has emerged as an independent research domain impacting on several areas of pure and applied mathematics, with applications to many areas such as quantum control, Hamiltonian dynamics, robotics and Lie theory. This comprehensive introduction proceeds from classical topics to cutting-edge theory and applications, assuming only standard knowledge of calculus, linear algebra and differential equations. The book may serve as a basis for an introductory course in Riemannian geometry or an advanced course in sub-Riemannian geometry, covering elements of Hamiltonian dynamics, integrable systems and Lie theory. It will also be a valuable reference source for researchers in various disciplines.

Democracies are in crisis. Can republican theory contribute to reforming our political norms and institutions? The 'neo-republican turn' has seen scholars using the classical republican tradition in reconstructing and developing a vision of public life as an alternative to liberalism. This volume offers new perspectives from leading scholars on how republicanism can help transform democratic theory and respond to some of its most pressing challenges. Drawing on this recent revival of republican political thought, its chapters reflect on such issues as the republican definition of freedom as nondomination and its relation to democracy and populism, the ideal of the common good, domination in the workplace and in the family, republicanism in a globalized world, and radical republican politics. It will appeal to researchers and students in political theory, political philosophy and the history of ideas, and anyone interested in gaining greater insight into the prospects and challenges of

This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. In volume 2, four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature.

Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature.

This rigorous, self-contained book describes mathematical and, in particular, stochastic and graph theoretic methods to assess the performance of complex networks and systems. It comprises three parts: the first is a review of probability theory; Part II covers the classical theory of stochastic processes (Poisson, Markov and queueing theory), which are considered to be the basic building blocks for performance evaluation studies; Part III focuses on the rapidly expanding new field of network science. This part deals with the recently obtained insight that many very different large complex networks – such as the Internet, World Wide Web, metabolic and human brain networks, utility infrastructures, social networks – evolve and behave according to general common scaling laws. This understanding is useful when assessing the end-to-end quality of Internet services and when designing robust and secure networks. Containing problems and solved solutions, the book is ideal for graduate student

The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know th

This 2006 work began with the author's exploration of the applicability of the finite deformation theory of elasticity when various standard assumptions such as convexity of various energies or ellipticity of the field equations of equilibrium are relinquished. The finite deformation theory of elasticity turns out to be a natural vehicle for the study of phase transitions in solids where thermal effects can be neglected. This text will be of interest to those interested in the development and application of continuum-mechanical models that describe the macroscopic response of materials capable of undergoing stress- or temperature-induced transitions between two solid phases. The focus is on the evolution of phase transitions which may be either dynamic or quasi-static, controlled by a kinetic relation which in the framework of classical thermomechanics represents information that is supplementary to the usual balance principles and constitutive laws of conventional theory.

This book contains eight expository articles by well-known authors of the theory of Galois groups and fundamental groups. They focus on presenting developments, avoiding classical aspects which have already been described at length in the standard literature. The volume grew from the special semester held at the MSRI in Berkeley in 1999 and many of the results are due to work accomplished during that program. Among the subjects covered are elliptic surfaces, Grothendieck's anabelian conjecture, fundamental groups of curves and differential Galois theory in positive characteristic. Although the articles contain fresh results, the authors have striven to make them as introductory as possible, making them accessible to graduate students as well as researchers in algebraic geometry and number theory. The volume also contains a lengthy overview by Leila Schneps that sets the individual articles into the broader context of contemporary research in Galois groups.

Liberal political philosophy and natural law theory are not contradictory, but - properly understood - mutually reinforcing. Contemporary liberalism (as represented by Rawls, Guttman and Thompson, Dworkin, Raz, and Macedo) rejects natural law and seeks to diminish its historical contribution to the liberal political tradition, but it is only one, defective variant of liberalism. A careful analysis of the history of liberalism, identifying its core principles, and a similar examination of classical natural law theory (as represented by Thomas Aquinas and his intellectual descendants), show that a natural law liberalism is possible and desirable. Natural law theory embraces the key principles of liberalism, and it also provides balance in resisting some of its problematic tendencies. Natural law liberalism is the soundest basis for American public philosophy, and it is a potentially more attractive and persuasive form of liberalism for nations that have tended to resist it.

Devoted to counterparts of classical structures of mathematical analysis in analysis over local fields of positive characteristic, this book treats positive characteristic phenomena from an analytic viewpoint. Building on the basic objects introduced by L. Carlitz - such as the Carlitz factorials, exponential and logarithm, and the orthonormal system of Carlitz polynomials - the author develops a kind of differential and integral calculi. He also expands on the basics of an analytic theory of (Carlitz's) differential equations, providing a useful foundation for the study of various special functions. The differential calculus is extended to a type of Rota's umbral calculus, and an investigation is made of the corresponding rings of differential operators. A theory of quasi-holonomic modules over these rings, having some common features with holonomic modules in the sense of Bernstein, is also connected to some special functions in the spirit of Zeilberger's theory.

This rigourous and self-contained book describes mathematical and, in particular, stochastic methods to assess the performance of networked systems. It consists of three parts. The first part is a review on probability theory. Part two covers the classical theory of stochastic processes (Poisson, renewal, Markov and queuing theory), which are considered to be the basic building blocks for performance evaluation studies. Part three focuses on the relatively new field of the physics of networks. This part deals with the recently obtained insights that many very different large complex networks - such as the Internet, World Wide Web, proteins, utility infrastructures, social networks - evolve and behave according to more general common scaling laws. This understanding is useful when assessing the end-to-end quality of communications services, for example, in Internet telephony, real-time video and interacting games. Containing problems and solutions, this book is ideal for graduate studen

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.

Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book, first published in 2006, are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe results of Smirnov in conformal invariance, and outline the proof that the critical probability for random Voronoi percolation in the plane is 1/2. Throughout, the presentation is streamlined, with elegant and straightforward proofs requiring minimal background in probability and graph theory. Numerous examples illustrate the important concepts and enrich the arguments. All-in-all, it will be an essential purchase for mathematicians, physicists, electrical engineers and computer scientists working in this exciting area.

Liberal political philosophy and natural law theory are not contradictory, but - properly understood - mutually reinforcing. Contemporary liberalism (as represented by Rawls, Guttman and Thompson, Dworkin, Raz, and Macedo) rejects natural law and seeks to diminish its historical contribution to the liberal political tradition, but it is only one, defective variant of liberalism. A careful analysis of the history of liberalism, identifying its core principles, and a similar examination of classical natural law theory (as represented by Thomas Aquinas and his intellectual descendants), show that a natural law liberalism is possible and desirable. Natural law theory embraces the key principles of liberalism, and it also provides balance in resisting some of its problematic tendencies. Natural law liberalism is the soundest basis for American public philosophy, and it is a potentially more attractive and persuasive form of liberalism for nations that have tended to resist it.

This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-conta

Corings and comodules are fundamental algebraic structures, which can be thought of as both dualisations and generalisations of rings and modules. Introduced by Sweedler in 1975, only recently they have been shown to have far reaching applications ranging from the category theory including differential graded categories through classical and Hopf-type module theory to non-commutative geometry and mathematical physics. This is the first extensive treatment of the theory of corings and their comodules. In the first part, the module-theoretic aspects of coalgebras over commutative rings are described. Corings are then defined as coalgebras over non-commutative rings. Topics covered include module-theoretic aspects of corings, such as the relation of comodules to special subcategories of the category of modules (sigma-type categories), connections between corings and extensions of rings, properties of new examples of corings associated to entwining structures, generalisations of bialgebras

This book contains eight expository articles by well-known authors of the theory of Galois groups and fundamental groups. They focus on presenting developments, avoiding classical aspects which have already been described at length in the standard literature. The volume grew from the special semester held at the MSRI in Berkeley in 1999 and many of the results are due to work accomplished during that program. Among the subjects covered are elliptic surfaces, Grothendieck's anabelian conjecture, fundamental groups of curves and differential Galois theory in positive characteristic. Although the articles contain fresh results, the authors have striven to make them as introductory as possible, making them accessible to graduate students as well as researchers in algebraic geometry and number theory. The volume also contains a lengthy overview by Leila Schneps that sets the individual articles into the broader context of contemporary research in Galois groups.

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.

Quantum field theory forms the present theoretical framework for our understanding of the fundamental interactions of particle physics. This up-dated and expanded text examines gauge theories and their symmetries with an emphasis on their physical and technical aspects. Beginning with a new chapter giving a systematic introduction to classical field theories and a short discussion of their canonical quantization and the discrete symmetries C, P and T, the book provides a brief exposition of perturbation theory, the renormalization programme, and the use of the renormalization group equation. It then explores topics of current research interest including chiral symmetry and its breaking, anomalies, and low energy effective lagrangians and some basics of supersymmetry. A chapter on basics of the electroweak theory is now included. Professor Pokorski, a distinguished theoretical physicist, has presented here a self-contained text for graduate courses in physics; the only prerequisite is s

Every form of behaviour is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realised how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centred not on the concept of rational players but on the population dynamics of behavioural programmes. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behaviour, and of the closely related interactions between species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions which can alter the basis of their success, i.e. to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions which punctuate evolution. In short, evolutionary

This is a self-contained introduction to the classical theory of homoclinic bifurcation theory, as well as its generalizations and more recent extensions to higher dimensions. It is also intended to stimulate new developments, relating the theory of fractal dimensions to bifurcations, and concerning homoclinic bifurcations as generators of chaotic dynamics. To this end the authors finish the book with an account of recent research and point out future prospects. The book begins with a review chapter giving background material on hyperbolic dynamical systems. The next three chapters give a detailed treatment of a number of examples, Smale's description of the dynamical consequences of transverse homoclinic orbits and a discussion of the subordinate bifurcations that accompany homoclinic bifurcations, including Hénon-like families. The core of the work is the investigation of the interplay between homoclinic tangencies and non-trivial basic sets. The fractal dimensions of these basic set

Many of the fundamental questions in social science entail an examination of the role played by social institutions. Why do we have so many social institutions? Why do they take one form in one society and quite different ones in others? In what ways do these institutions develop? When and why do they change? Institutions and Social Conflict addresses these questions in two ways. First it offers a thorough critique of a wide range of theories of institutional change, from the classical accounts of Smith, Hume, Marx and Weber to the contemporary approaches of evolutionary theory, the theory of social conventions and the new institutionalism. Secondly, it develops a new theory of institutional change that emphasises the distributional consequences of social institutions. The emergence of institutions is explained as a by-product of distributional conflict in which asymmetries of power in a society generate institutional solutions to conflicts.

Network flow theory has been used across a number of disciplines, including theoretical computer science, operations research, and discrete math, to model not only problems in the transportation of goods and information, but also a wide range of applications from image segmentation problems in computer vision to deciding when a baseball team has been eliminated from contention. This graduate text and reference presents a succinct, unified view of a wide variety of efficient combinatorial algorithms for network flow problems, including many results not found in other books. It covers maximum flows, minimum-cost flows, generalized flows, multicommodity flows, and global minimum cuts and also presents recent work on computing electrical flows along with recent applications of these flows to classical problems in network flow theory.