Constructive Approximation

This book offers key insights into how to manage software development across international boundaries. It is based on a series of case studies looking at the relationships between firms from North America, the UK, Japan and Korea with Indian software houses. In these case studies, which have typically been compiled over a 3-4 year timespan, the authors analyse the multi-faceted challenges encountered in managing these Global Software Alliances (GSAs). These challenges range from the conflicts that managers face when dealing with distance, to the tensions of transferring knowledge across time and space, to issues in trying to establish universal standards in a context of constant change, and the problems of identity that developers and clients experience in having to deal with different organizations and countries. Throughout the book, the authors draw on their extensive research and experience to offer constructive advice on how to manage GSAs more effectively.

Robben Island prison in South Africa held thousands of black political prisoners, including Nelson Mandela, who opposed apartheid. This book reconstructs the inmates' resistance strategies to show how these men created a political and social order behind bars. Survival was their first goal; challenging apartheid was their true aim. So although Robben Island was designed to repress, it was continually transformed by its political inmates into a site of resistance. The book theorizes that, where material conditions permit, the most far-reaching and effective forms of resistance involve constructive political action which seeks to remake existing power relationships. This theory is demonstrated in three focuses of the book: the activism of Robben Islanders, the effects of political prisoner resistance on the apartheid state machinery, and in comparative cases which illustrate various international instances of political prisoners shaping both prisons and political orders.

Robben Island prison in South Africa held thousands of black political prisoners, including Nelson Mandela, who opposed apartheid. This book reconstructs the inmates' resistance strategies to show how these men created a political and social order behind bars. Survival was their first goal; challenging apartheid was their true aim. So although Robben Island was designed to repress, it was continually transformed by its political inmates into a site of resistance. The book theorizes that, where material conditions permit, the most far-reaching and effective forms of resistance involve constructive political action which seeks to remake existing power relationships. This theory is demonstrated in three focuses of the book: the activism of Robben Islanders, the effects of political prisoner resistance on the apartheid state machinery, and in comparative cases which illustrate various international instances of political prisoners shaping both prisons and political orders.

May we speak, in the present age, of holy scripture? And what validation of that claim can be offered, robust enough to hold good for both religious practice and intellectual enquiry? John Webster argues that while any understanding of scripture must subject it to proper textual and historical interrogation, it is necessary at the same time to acknowledge the special character of scriptural writing. His 2003 book is an exercise in Christian dogmatics, a loud reaffirmation of the triune God at the heart of a scripture-based Christianity. But it is written with intellectual rigour by a theologian who understands the currents of modern secular thought and is able to work from them towards a constructive position on biblical authority. It will resonate with anyone who has wondered or worried about the grounds on which we may validly regard the Bible as God's direct communication with humanity.

Famous mathematical constants include the ratio of circular circumference to diameter, pi=3.14 …, and the natural logarithmic base, e=2.178 … Students and professionals usually can name at most a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. Topics covered include the statistics of continued fractions, chaos in nonlinear systems, prime numbers, sum-free sets, isoperimetric problems, approximation theory, self-avoiding walks and the Ising model (from statistical physics), binary and digital search trees (from theoretical computer science), the Prouhet-Thue-Morse sequence, complex analysis, geometric probability and the traveling salesman problem. This book will be helpful both to readers seeking information about a specific constant, and to readers

Book 1 of De Natura Deorum exhibits in a nutshell Cicero's philosophical method, with the prior part stating the case for Epicurean theology, the latter (rather longer) part refuting it. Thus the reader observes Cicero at work in both constructive and skeptical modes as well as his art of characterizing speakers. Prefaced to the Book is Cicero's most elaborate justification of his philosophical writing. The Book thus makes an ideal starting point for the study of Cicero's philosophica or indeed of any philosophical writing in Latin, since it delineates the problems such a project raised in the minds of Roman readers and shows how Cicero thought they could be met. There is also a systematic and detailed doxography of ancient views about the deity, an important document in itself, presented from an Epicurean perspective. The volume's Introduction situates this text within Cicero's intellectual development and ancient reflection about the gods.

Designed for one-semester courses at the senior undergraduate level, this 2003 book will appeal to mathematics undergraduates, to mathematics teachers, and to others who need to learn some mathematical analysis for use in other areas such as engineering, physics, biology or finance. Topics such as completeness and compactness are approached initially through convergence of sequences in metric space, and the emphasis remains on this approach. However, the alternative topological approach is described in a separate chapter. This gives the book more flexibility, making it especially useful as an introduction to more advanced areas such as functional analysis. Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for what further developments might look like. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, nu

In many areas of mathematics, science and engineering, from computer graphics to inverse methods to signal processing, it is necessary to estimate parameters, usually multidimensional, by approximation and interpolation. Radial basis functions are a powerful tool which work well in very general circumstances and so are becoming of widespread use as the limitations of other methods, such as least squares, polynomial interpolation or wavelet-based, become apparent. The author's aim is to give a thorough treatment from both the theoretical and practical implementation viewpoints. For example, he emphasises the many positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence and provides a careful classification of the radial basis functions into types that have different convergence. A comprehensive bibliography rounds off what will prove a very valuable work.

Designed for one-semester courses at the senior undergraduate level, this 2003 book will appeal to mathematics undergraduates, to mathematics teachers, and to others who need to learn some mathematical analysis for use in other areas such as engineering, physics, biology or finance. Topics such as completeness and compactness are approached initially through convergence of sequences in metric space, and the emphasis remains on this approach. However, the alternative topological approach is described in a separate chapter. This gives the book more flexibility, making it especially useful as an introduction to more advanced areas such as functional analysis. Nominal divisions of pure and applied mathematics have been merged, leaving enough for students of either inclination to have a feeling for what further developments might look like. Applications have been included from such fields as differential and integral equations, systems of linear algebraic equations, approximation theory, nu

This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical n

This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half introduces probability based on measure theory, including laws of large numbers, ergodic theorems, the central limit theorem, conditional expectations and martingale's convergence. A chapter on stochastic processes introduces Brownian motion and the Brownian bridge. The edition has been made even more self-contained than before; it now includes a foundation of the real number system and the Stone-Weierstrass theorem on uniform approximation in algebras of functions. Several other sections have been revised and improved, and the comprehensive historical n

Using her experience of living under apartheid and witnessing its downfall and the subsequent creation of new governments in South Africa, the author examines and compares gender inequality in societi

This book provides a thorough introduction to one of the most efficient approximation methods for the analysis and solution of problems in theoretical physics and applied mathematics. It is written with practical needs in mind and contains a discussion of 50 problems with solutions, of varying degrees of difficulty. The problems are taken from quantum mechanics, but the method has important applications in any field of science involving second order ordinary differential equations. The power of the asymptotic solution of second order differential equations is demonstrated, and in each case the authors clearly indicate which concepts and results of the general theory are needed to solve a particular problem. This book will be ideal as a manual for users of the phase-integral method, as well as a valuable reference text for experienced research workers and graduate students.

Revelation and the God of Israel explores the concept of revelation as it emerges from the Hebrew Scriptures and is interpreted in Jewish philosophy and theology. The first part is a study in intellectual history that attempts to answer the question, what is the best possible understanding of revelation. The second part is a study in constructive theology and attempts to answer the question, is it reasonable to affirm belief in revelation. Here Norbert M. Samuelson focuses on the challenges given from a variety of contemporary academic disciplines, including evolutionary psychology, political ethics, analytic philosophy of religion, and source critical studies of the Bible. This important book offers a unique approach to theological questions and fresh solutions to them and will appeal to those interested in the history of philosophy, religious thought, and Judaism.

Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs results from ordinary integration theory, for instance previsible envelopes and an algorithm computing stochastic integrals of càglàd integrands pathwise. Full proofs are given for all results, and motivation is stressed throughout. A large appendix contains most of the analysis that readers will need as a prerequisite. This will be an invaluable reference for graduate students and researchers in mathematics, physics, electrical en

Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This 2002 book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not ju

Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This 2002 book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not ju

Corporate loggers have damaged much of the tropical forest throughout the Asia-Pacific over the last four decades. Despite a steady rise in global and local concern, few firms have changed their practices. Loggers and Degradation in the Asia-Pacific examines why and how loggers have resisted and ignored calls for environmental reforms. Concentrating on the period after 1990, the book explains what is happening on the ground and highlights the structures within which firms and governments operate. Within this broader context the author considers a range of factors including: the science of tropical forest management, the capacity of states to regulate and enforce rules, the relative power of environmental reformers, and the 1997–9 Asian financial crisis. This is a constructive, insightful approach to a depressing, yet urgent, problem. It will be accessible to academic and student readers as well as those in corporations, government and NGOs.

Corporate loggers have damaged much of the tropical forest throughout the Asia-Pacific over the last four decades. Despite a steady rise in global and local concern, few firms have changed their practices. Loggers and Degradation in the Asia-Pacific examines why and how loggers have resisted and ignored calls for environmental reforms. Concentrating on the period after 1990, the book explains what is happening on the ground and highlights the structures within which firms and governments operate. Within this broader context the author considers a range of factors including: the science of tropical forest management, the capacity of states to regulate and enforce rules, the relative power of environmental reformers, and the 1997–9 Asian financial crisis. This is a constructive, insightful approach to a depressing, yet urgent, problem. It will be accessible to academic and student readers as well as those in corporations, government and NGOs.

Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of

Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of

Threats to fungi and fungal diversity throughout the world have prompted debates about whether and how fungi can be conserved. Should it be the site, or the habitat, or the host that is conserved? All of these issues are addressed in this volume, but coverage goes beyond mere debate with constructive guidance for management of nature in ways beneficial to fungi. Different parts of the world experience different problems and a range of examples are presented; from Finland in the North to Kenya in the South, and from Washington State, USA in the West to Fujian Province, China in the East. Equally wide-ranging solutions, are put forward, from voluntary agreements, through land management techniques, to primary legislation. Taken together, these provide useful suggestions about how fungi can be included in conservation projects in a range of circumstances.

The Society for the Foundations of Computational Mathematics supports fundamental research in a wide spectrum of computational mathematics and its application areas. As part of its endeavour to promote research in computational mathematics, the society regularly organises conferences and workshops which bring together leading researchers in the diverse fields impinging on all aspects of computation. This book presents thirteen papers written by plenary speakers from the 1999 conference, all of whom are the foremost figures in their respective fields. Topics covered include complexity theory, approximation theory, optimisation, computational geometry, stochastic systems and the computation of partial differential equations. The wide range of topics covered illustrates the diversity of contemporary computational mathematics and the intricate web of its interaction with pure mathematics and application areas. This book will be of interest to researchers and graduate students in all areas

This 2001 book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of 'natural number' and 'set'. This leads to an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, as well as in the analysis of proof by induction and definition by recursion. The subject matter of the book falls on the borderline between philosophy and mathematics, and should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics.

Animal Traditions maintains that the assumption that the selection of genes supplies both a sufficient explanation of the evolution and a true description of its course is, despite its almost universal acclaim, wrong. Eytan Avital and Eva Jablonka contend that evolutionary explanations must take into account the well-established fact that in mammals and birds, the transfer of learnt information is both ubiquitous and indispensable. The introduction of the behavioural inheritance system into the Darwinian explanatory scheme enables the authors to offer new interpretations for common behaviours such as maternal behaviours, behavioural conflicts within families, adoption and helping. This approach offers a richer view of heredity and evolution, integrates developmental and evolutionary processes, suggests new lines for research, and provides a constructive alternative to both the selfish gene and meme views of the world. It will make stimulating reading for all those interested in evoluti

The seven original essays included in this volume from 2000, written by some of the world's most distinguished moral and legal philosophers, offer a sophisticated perspective on issues about the objectivity of legal interpretation and judicial decision-making. They examine objectivity from both metaphysical and epistemological perspectives and develop a variety of approaches, constructive and critical, to the fundamental problems of objectivity in morality. One of the key issues explored is that of the alleged 'domain-specificity' of conceptions of objectivity, i.e. whether there is a conception of objectivity appropriate for ethics that is different in kind from the conception of objectivity appropriate for other areas of study. This volume considers the intersection between objectivity in ethics and objectivity in law. It presents a survey of live issues in metaethics, and examines their relevance to theorizing about law and adjudication.

This book tests the explanatory and descriptive power of the doctrine of sin in relation to two concrete situations: sexual abuse of children and the holocaust. Taking seriously the explanatory power of secular discourses for analysing and regulating therapeutic action in relation to such situations, the book asks whether the theological language of sin can offer further illumination by speaking of God and the world together. Through its discussion of abuse and the holocaust, an engagement with Augustine, original sin and feminism, a fresh and sometimes surprising perspective is offered, both on the theology of sin and on the pathologies under consideration. The understanding of sin that emerges is centred on joyful worship of the trinitarian God. This essay is more systematic and more theological than most practical, pastoral or applied theology and more practical and concrete than most systematic or constructive theology. It is a genuinely concrete, systematic theology.

This book tests the explanatory and descriptive power of the doctrine of sin in relation to two concrete situations: sexual abuse of children and the holocaust. Taking seriously the explanatory power of secular discourses for analysing and regulating therapeutic action in relation to such situations, the book asks whether the theological language of sin can offer further illumination by speaking of God and the world together. Through its discussion of abuse and the holocaust, an engagement with Augustine, original sin and feminism, a fresh and sometimes surprising perspective is offered, both on the theology of sin and on the pathologies under consideration. The understanding of sin that emerges is centred on joyful worship of the trinitarian God. This essay is more systematic and more theological than most practical, pastoral or applied theology and more practical and concrete than most systematic or constructive theology. It is a genuinely concrete, systematic theology.

In this book Jonathan Hall seeks to demonstrate that the ethnic groups of ancient Greece, like many ethnic groups throughout the world today, were not ultimately racial, linguistic, religious or cultural groups, but social groups whose 'origins' in extraneous territories were just as often imagined as they were real. Adopting an explicitly anthropological point of view, he examines the evidence of literature, archaeology and linguistics to elucidate the nature of ethnic identity in ancient Greece. Rather than treating Greek ethnic groups as 'natural' or 'essential' - let alone 'racial' - entities, he emphasises the active, constructive and dynamic role of ethnography, genealogy, material culture and language in shaping ethnic consciousness. An introductory chapter outlines the history of the study of ethnicity in Greek antiquity.

Thinking quantitatively about physiology is something many students find difficult. However, it is fundamentally important to a proper understanding of many of the concepts involved. In this enlarged second edition of his popular textbook, Richard Burton gives the reader the opportunity to develop a feel for values such as ion concentrations, lung and fluid volumes, blood pressures etc. through the use of calculations which require little more than simple arithmetic for their solution. Much guidance is given on how to avoid errors and the usefulness of approximation and 'back-of-envelope sums'. Energy metabolism, nerve and muscle, blood and the cardiovascular system, respiration, renal function, body fluids and acid-base balance are all covered, making this book essential reading for students (and teachers) of physiology everywhere, both those who shy away from numbers and those who revel in them.

Thinking quantitatively about physiology is something many students find difficult. However, it is fundamentally important to a proper understanding of many of the concepts involved. In this enlarged second edition of his popular textbook, Richard Burton gives the reader the opportunity to develop a feel for values such as ion concentrations, lung and fluid volumes, blood pressures etc. through the use of calculations which require little more than simple arithmetic for their solution. Much guidance is given on how to avoid errors and the usefulness of approximation and 'back-of-envelope sums'. Energy metabolism, nerve and muscle, blood and the cardiovascular system, respiration, renal function, body fluids and acid-base balance are all covered, making this book essential reading for students (and teachers) of physiology everywhere, both those who shy away from numbers and those who revel in them.

Systems of conservation laws arise naturally in physics and chemistry. Following on from the previous volume, the author considers the maximum principle from the viewpoints of both viscous approximation and numerical schemes. Convergence is studied through compensated compactness. This tool is applied to the description of large amplitude wave propagation. Small waves are studied through geometrical optics. Special structures are presented in chapters on Rich and Temple systems. Finally, Serre explains why the initial-boundary value problem is far from trivial, with descriptions of the Kreiss–Lopatinski condition for well-posedness, with applications to shock wave stability, and certain problems in boundary layer theory. Throughout the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.

Developments in sensor and processor sophistication have created a need for effective estimation and control algorithms for hybrid, nonlinear systems. This book presents an effective, flexible family of estimation algorithms that can be used in estimating or controlling a variety of nonlinear plants. Several applications are studied, including tracking a manoeuvring aircraft, automatic target recognition, and the decoding of signals transmitted across a wireless communications link. The authors begin by setting out the necessary theoretical background and then develop a practical, finite-dimensional approximation to an optimal estimator. Throughout the book, they illustrate theoretical results by simulation of control and estimation in real-world hybrid systems, drawn from a variety of engineering fields. The book will be of great interest to graduate students and researchers in electrical and computer engineering. It will also be a useful reference for practising engineers involved in

This book describes theoretical advances in the study of artificial neural networks. It explores probabilistic models of supervised learning problems, and addresses the key statistical and computational questions. Research on pattern classification with binary-output networks is surveyed, including a discussion of the relevance of the Vapnik–Chervonenkis dimension, and calculating estimates of the dimension for several neural network models. A model of classification by real-output networks is developed, and the usefulness of classification with a 'large margin' is demonstrated. The authors explain the role of scale-sensitive versions of the Vapnik–Chervonenkis dimension in large margin classification, and in real prediction. They also discuss the computational complexity of neural network learning, describing a variety of hardness results, and outlining two efficient constructive learning algorithms. The book is self-contained and is intended to be accessible to researchers and gradua

This 1997 book offers a major reassessment of the philosophy of Peter Abelard (1079–1142) which argues that he was not, as usually presented, a predominantly critical thinker but a constructive one. By way of evidence the author offers analyses of frequently discussed topics in Abelard's philosophy, and examines other areas such as the nature of substances and accidents, cognition, the definition of 'good' and 'evil', virtues and merit, and practical ethics in detail. Part I discusses Abelard's life and works, and considers problems of chronology and canon (including the question of the authenticity of the correspondence with Heloise). Part II analyses Abelard's ontology, epistemology and semantics, showing how he tried to reconstruct the ideas he had learned from Aristotle, Porphyry and Boethius to fit his presumption that there is nothing which is not a particular. Part III analyses Abelard's ethical theory, showing that it is far wider and more sophisticated than has been believed.

Semiclassical approximation addresses the important relationship between quantum and classical mechanics. There has been a very strong development in the mathematical theory, mainly thanks to methods of microlocal analysis. This book develops the basic methods, including the WKB-method, stationary phase and h-pseudodifferential operators. The applications include results on the tunnel effect, the asymptotics of eigenvalues in relation to classical trajectories and normal forms, plus slow perturbations of periodic Schrödinger operators appearing in solid state physics. No previous specialized knowledge in quantum mechanics or microlocal analysis is assumed, and only general facts about spectral theory in Hilbert space, distributions, Fourier transforms and some differential geometry belong to the prerequisites. This book is addressed to researchers and graduate students in mathematical analysis, as well as physicists who are interested in rigorous results. A fairly large fraction can be

At the time of this book's first publication in 1999, orthodoxy interpreted the Georgics as a statement of profound ambivalence towards Octavian and his claim to be Rome's saviour after the catastrophe of the civil wars. This book takes issue with the model of the subtly subversive poet. It argues that in the turbulent political circumstances which obtained at the time of the poem's composition, Virgil's preoccupation with violent conflict has a highly optimistic import. Octavian's brutal conduct in the civil wars is subjected to a searching analysis, but is ultimately vindicated, refigured as a paradoxically constructive violence analogous to blood sacrifice or Romulus' fratricide of Remus. The vindication of Octavian also has strictly literary implications for Virgil. The close of the poem sees Virgil asserting his mastery of the Homeric mode of poetry and the providential world-view it was thought to embody.

This book aims to give a self-contained presentation of a number of results, which relate the volume of convex bodies in n-dimensional Euclidean space and the geometry of the corresponding finite-dimensional normed spaces. The methods employ classical ideas from the theory of convex sets, probability theory, approximation theory and the local theory of Banach spaces. The book is in two parts. The first presents self-contained proofs of the quotient of the subspace theorem, the inverse Santalo inequality and the inverse Brunn-Minkowski inequality. The second part gives a detailed exposition of the recently introduced classes of Banach spaces of weak cotype 2 or weak type 2, and the intersection of the classes (weak Hilbert space). The book is based on courses given in Paris and in Texas.

Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject. The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth. Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.

This eagerly awaited book by David F. Ford makes a unique and important contribution to the debate about the Christian doctrine of salvation. Using the pivotal image of the face, Professor Ford offers a constructive and contemporary account of the self being transformed. He engages with three modern thinkers (Levinas, Jüngel and Ricoeur) in order to rethink and reimagine the meaning of self. Developing the concept of a worshipping self, he explores the dimensions of salvation through the lenses of scripture, worship practices, the life, death and resurrection of Christ, and the lives of contemporary saints. He uses different genres and traditions to show how the self flourishes through engagement with God, other people, and the responsibilities and joys of ordinary living. The result is a habitable theology of salvation immersed in Christian faith, thought and practice while also being deeply involved with modern life in a pluralist world.