Mathematics of Discrete Structures for Computer Science

A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on s

When The Concept of Nature by Alfred North Whitehead was first published in 1920 it was declared to be one of the most important works on the relation between philosophy and science for many years, and several generations later it continues to deserve careful attention. Whitehead explores the fundamental problems of substance, space and time, and offers a criticism of Einstein's method of interpreting results while developing his own well-known theory of the four-dimensional 'space-time manifold'. With a specially commissioned new preface written by Michael Hampe, this book is presented in a fresh series livery for the twenty-first century for a new generation of readers.

When The Concept of Nature by Alfred North Whitehead was first published in 1920 it was declared to be one of the most important works on the relation between philosophy and science for many years, and several generations later it continues to deserve careful attention. Whitehead explores the fundamental problems of substance, space and time, and offers a criticism of Einstein's method of interpreting results while developing his own well-known theory of the four-dimensional 'space-time manifold'. With a specially commissioned new preface written by Michael Hampe, this book is presented in a fresh series livery for the twenty-first century for a new generation of readers.

First published in 1880, this study of the biology and geography of islands investigates some of the most pressing questions of nineteenth-century natural science. Why do countries as far-flung as Britain and Japan share similar flora and fauna when those of neighbouring islands in Malaysia are utterly unalike? What is the origin of life in New Zealand? And why do the geological formations of Scotland and Wales appear to be the result of glaciers when those countries lie in the temperate zone? Dismissing popular theories of submerged continents and 'special creation', Alfred Russel Wallace (1823–1913) presents extensive evidence of the mass migration of species, and of drastic and repeated climatic changes across the globe. Drawing on a vast range of sources and the newest ocean soundings to support his theories, Wallace wrote the text for the intelligent general reader. It remains a fascinating introduction to the subject matter today.

Digital methodologies, new forms of data visualization and computer-based learning and assessment are creating new challenges as well as opportunities for scholars in educational research. The World Y

Drawing on political science, economics, philosophy, theology, social anthropology, history, management studies, law, and other subject areas, In Search of Good Energy Policy brings together leading academics from across the social sciences and humanities to offer an innovative look at why science and technology, and the type of quantification they champion, cannot alone meet the needs of energy policy making in the future. Featuring world-class researchers from the University of Cambridge and other leading universities around the world, this innovative book presents an interdisciplinary dialogue in which scientists and practitioners reach across institutional divides to offer their perspectives on the relevance of multi-disciplinary research for 'real world' application. This work should be read by anyone interested in understanding how multidisciplinary research and collaboration is essential to crafting good energy policy.

Drawing on political science, economics, philosophy, theology, social anthropology, history, management studies, law, and other subject areas, In Search of Good Energy Policy brings together leading academics from across the social sciences and humanities to offer an innovative look at why science and technology, and the type of quantification they champion, cannot alone meet the needs of energy policy making in the future. Featuring world-class researchers from the University of Cambridge and other leading universities around the world, this innovative book presents an interdisciplinary dialogue in which scientists and practitioners reach across institutional divides to offer their perspectives on the relevance of multi-disciplinary research for 'real world' application. This work should be read by anyone interested in understanding how multidisciplinary research and collaboration is essential to crafting good energy policy.

The main theme of this book is micromagnetism and microstructure as well as the analysis of the relations between characteristic properties of the hysteresis loop and microstructure. Also presented is an analysis of the role of microstructure in the fundamental magnetic properties (for example, magnetorestriction or critical behaviour) of crystalline and amorphous alloys. The authors apply the theory of micromagnetism to all aspects of advanced magnetic materials including domain patterns and magnetization processes under the influence of defect structures. Coverage includes modern developments in computational micromagnetism and its application to spin structures of small particles and platelets. It will be of interest to researchers and graduate students in condensed matter, physics, electrical engineering and materials science, as well as to industrial researchers working in the electrotechnical and recording industry.

The main theme of this book is micromagnetism and microstructure as well as the analysis of the relations between characteristic properties of the hysteresis loop and microstructure. Also presented is an analysis of the role of microstructure in the fundamental magnetic properties (for example, magnetorestriction or critical behaviour) of crystalline and amorphous alloys. The authors apply the theory of micromagnetism to all aspects of advanced magnetic materials including domain patterns and magnetization processes under the influence of defect structures. Coverage includes modern developments in computational micromagnetism and its application to spin structures of small particles and platelets. It will be of interest to researchers and graduate students in condensed matter, physics, electrical engineering and materials science, as well as to industrial researchers working in the electrotechnical and recording industry.

This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such 'fully developed turbulence' is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.

The basis of this graduate-level textbook is a careful survey of a wide range of problems affecting the solution of linear partial differential equations. The book begins with a fairly elementary introduction to the theory of Fourier series of continuous functions and goes on to describe the fundamental theory of linear partial differential equations of elliptic and hyperbolic types, equations of evolution, semi-linear hyperbolic equations and selected topics on Green's functions and spectra of some special operators. The book is intended for use by pure mathematicians in functional analysis. The selection of material is interesting and differs from existing literature in European languages. This paperback edition will make it particularly attractive to graduate students in pure and applied mathematics.

The tithe surveys of the early Victorian Age, after the great Domesday Book of the eleventh century, represent the most detailed and important national inventory to be taken before our own times. This 1986 book reconstructs elements of mid-nineteenth-century rural landscapes and farming systems by analysing the wealth of quantitative data which these tithe surveys contain, communicated cartographically by a set of 582 computer-generated maps, and statistically by a series of tables. The book also reveals the richness and variety of written evidence which the 14,829 parish tithe files (P.R.O. Class IR 18) contain, by means of analytical place and subject indexes for each English and Welsh county (some 200,000 entries in all) and by essays in which themes commonly encountered in the tithe file papers of each county are described. These sections of the book will be an essential tool for historians and historical geographers.

This book is a definitive reference source for the growing, increasingly more important, and interdisciplinary field of computational cognitive modeling, that is, computational psychology. It combines breadth of coverage with definitive statements by leading scientists in this field. Research in computational cognitive modeling explores the essence of cognition and various cognitive functionalities through developing detailed, process-based understanding by specifying computational mechanisms, structures, and processes. Given the complexity of the human mind and its manifestation in behavioral flexibility, process-based computational models may be necessary to explicate and elucidate the intricate details of the mind. The key to understanding cognitive processes is often in fine details. Computational models provide algorithmic specificity: detailed, exactly specified, and carefully thought-out steps, arranged in precise yet flexible sequences. These models provide both conceptual clar

This book is a definitive reference source for the growing, increasingly more important, and interdisciplinary field of computational cognitive modeling, that is, computational psychology. It combines breadth of coverage with definitive statements by leading scientists in this field. Research in computational cognitive modeling explores the essence of cognition and various cognitive functionalities through developing detailed, process-based understanding by specifying computational mechanisms, structures, and processes. Given the complexity of the human mind and its manifestation in behavioral flexibility, process-based computational models may be necessary to explicate and elucidate the intricate details of the mind. The key to understanding cognitive processes is often in fine details. Computational models provide algorithmic specificity: detailed, exactly specified, and carefully thought-out steps, arranged in precise yet flexible sequences. These models provide both conceptual clar

In this book Craig, Kinney and their collaborators confront the main unsolved mysteries in Shakespeare's canon through computer analysis of Shakespeare's and other writers' styles. In some cases their analysis confirms the current scholarly consensus, bringing long-standing questions to something like a final resolution. In other areas the book provides more surprising conclusions: that Shakespeare wrote the 1602 additions to The Spanish Tragedy, for example, and that Marlowe along with Shakespeare was a collaborator on Henry VI, Parts 1 and 2. The methods used are more wholeheartedly statistical, and computationally more intensive, than any that have yet been applied to Shakespeare studies. The book also reveals how word patterns help create a characteristic personal style. In tackling traditional problems with the aid of the processing power of the computer, harnessed through computer science, and drawing upon large amounts of data, the book is an exemplar of the new domain of digita

In this book Craig, Kinney and their collaborators confront the main unsolved mysteries in Shakespeare's canon through computer analysis of Shakespeare's and other writers' styles. In some cases their analysis confirms the current scholarly consensus, bringing long-standing questions to something like a final resolution. In other areas the book provides more surprising conclusions: that Shakespeare wrote the 1602 additions to The Spanish Tragedy, for example, and that Marlowe along with Shakespeare was a collaborator on Henry VI, Parts 1 and 2. The methods used are more wholeheartedly statistical, and computationally more intensive, than any that have yet been applied to Shakespeare studies. The book also reveals how word patterns help create a characteristic personal style. In tackling traditional problems with the aid of the processing power of the computer, harnessed through computer science, and drawing upon large amounts of data, the book is an exemplar of the new domain of digita

Since its inception some fifty years ago, cognitive science has seen a number of sea changes. Perhaps the best known is the development of connectionist models of cognition as an alternative to classical, symbol-based approaches. A more recent - and increasingly influential - trend is that of dynamical-systems-based, ecologically oriented models of the mind. Researchers suggest that a full understanding of the mind will require systematic study of the dynamics of interaction between mind, body, and world. Some argue that this new orientation calls for a revolutionary new metaphysics of mind, according to which mental states and processes, and even persons, literally extend into the environment. This book is a guide to this movement in cognitive science. Each chapter tackles either a specific area of empirical research or specific sector of the conceptual foundation underlying this research.

Since its inception some fifty years ago, cognitive science has seen a number of sea changes. Perhaps the best known is the development of connectionist models of cognition as an alternative to classical, symbol-based approaches. A more recent - and increasingly influential - trend is that of dynamical-systems-based, ecologically oriented models of the mind. Researchers suggest that a full understanding of the mind will require systematic study of the dynamics of interaction between mind, body, and world. Some argue that this new orientation calls for a revolutionary new metaphysics of mind, according to which mental states and processes, and even persons, literally extend into the environment. This book is a guide to this movement in cognitive science. Each chapter tackles either a specific area of empirical research or specific sector of the conceptual foundation underlying this research.

In American criminal law, if a defendant demonstrates that they lack certain psychological capabilities, they may be excused of blame and punishment for wrongdoing. However, criminal defense law often fails to consider the developmental science of individual differences in ability and functioning that may inform jurisprudential issues of rational capacity and responsibility in criminal law. This book discusses the excusing nature of a range of both traditional and non-traditional criminal law defenses and questions the structure of these defenses based on scientific findings from social and developmental psychology. This book explores how research on individual differences in the development of social perception, judgment and decision making explain why some youths and adults develop psychological tendencies that favor criminal behavior, and considers how developmental science can guide the understanding of criminal excuses and affirmative defense law.

During development cells and tissues undergo changes in pattern and form that employ a wider range of physical mechanisms than at any other time in an organism's life. This book shows how physics can be used to analyze these biological phenomena. Written to be accessible to both biologists and physicists, major stages and components of the biological development process are introduced and then analyzed from the viewpoint of physics. The presentation of physical models requires no mathematics beyond basic calculus. Physical concepts introduced include diffusion, viscosity and elasticity, adhesion, dynamical systems, electrical potential, percolation, fractals, reaction-diffusion systems, and cellular automata. With full-color figures throughout, this comprehensive textbook teaches biophysics by application to developmental biology and is suitable for graduate and upper-undergraduate courses in physics and biology.

This textbook is ideal for a course in engineering systems dynamics and controls. The work is a comprehensive treatment of the analysis of lumped parameter physical systems. Starting with a discussion of mathematical models in general, and ordinary differential equations, the book covers input/output and state space models, computer simulation and modeling methods and techniques in mechanical, electrical, thermal and fluid domains. Frequency domain methods, transfer functions and frequency response are covered in detail. The book concludes with a treatment of stability, feedback control (PID, lead-lag, root locus) and an introduction to discrete time systems. This new edition features many new and expanded sections on such topics as: solving stiff systems, operational amplifiers, electrohydraulic servovalves, using Matlab with transfer functions, using Matlab with frequency response, Matlab tutorial and an expanded Simulink tutorial. The work has 40% more end-of-chapter exercises and 3

This textbook is ideal for a course in engineering systems dynamics and controls. The work is a comprehensive treatment of the analysis of lumped parameter physical systems. Starting with a discussion of mathematical models in general, and ordinary differential equations, the book covers input/output and state space models, computer simulation and modeling methods and techniques in mechanical, electrical, thermal and fluid domains. Frequency domain methods, transfer functions and frequency response are covered in detail. The book concludes with a treatment of stability, feedback control (PID, lead-lag, root locus) and an introduction to discrete time systems. This new edition features many new and expanded sections on such topics as: solving stiff systems, operational amplifiers, electrohydraulic servovalves, using Matlab with transfer functions, using Matlab with frequency response, Matlab tutorial and an expanded Simulink tutorial. The work has 40% more end-of-chapter exercises and 3

The use of behavioural science to inform policy is one of the main developments in the social sciences over the last several decades. In this book, Adam Oliver offers an accessible introduction to the development of behavioural public policy, examining how behavioural economics might be used to inform the design of a broad spectrum of policy frameworks, from nudges, to bans on certain individual behaviours, to the regulation of the commercial sector. He also considers how behavioural economics can explain and predict phenomena as a challenge to economists' assumptions around how people perceive time, utility and money. The book offers an intellectual foundation for all those concerned with behavioural public policy, from academics, undergraduate and postgraduate students with a diverse range of disciplinary perspectives, such as economics, political science, sociology and anthropology, to policy makers and practitioners working directly with behavioural public policy in their everyday

The use of behavioural science to inform policy is one of the main developments in the social sciences over the last several decades. In this book, Adam Oliver offers an accessible introduction to the development of behavioural public policy, examining how behavioural economics might be used to inform the design of a broad spectrum of policy frameworks, from nudges, to bans on certain individual behaviours, to the regulation of the commercial sector. He also considers how behavioural economics can explain and predict phenomena as a challenge to economists' assumptions around how people perceive time, utility and money. The book offers an intellectual foundation for all those concerned with behavioural public policy, from academics, undergraduate and postgraduate students with a diverse range of disciplinary perspectives, such as economics, political science, sociology and anthropology, to policy makers and practitioners working directly with behavioural public policy in their everyday

The common cause principle says that every correlation is either due to a direct causal effect linking the correlated entities or is brought about by a third factor, a so-called common cause. The principle is of central importance in the philosophy of science, especially in causal explanation, causal modeling and in the foundations of quantum physics. Written for philosophers of science, physicists and statisticians, this book contributes to the debate over the validity of the common cause principle, by proving results that bring to the surface the nature of explanation by common causes. It provides a technical and mathematically rigorous examination of the notion of common cause, providing an analysis not only in terms of classical probability measure spaces, which is typical in the available literature, but in quantum probability theory as well. The authors provide numerous open problems to further the debate and encourage future research in this field.

Why does matter stick together? Why do gases condense to liquids, and liquids to solids? This book provides a detailed historical account of how some of the leading scientists of the past three centuries have tried to answer these questions. The topic of cohesion and the study of intermolecular forces has been an important component of physical science research for hundreds of years. This book is organised into four broad periods of advances in our understanding. The first three are associated with Newton, Laplace and van der Waals. The final section gives an account of the successful use in the twentieth century of quantum mechanics and statistical mechanics to resolve most of the remaining problems. The book will be of primary interest to physical chemists and physicists, as well as historians of science interested in the historical origins of our modern day understanding of cohesion.

Originally published in Italian in 1976, this book describes the methods scientists use to investigate the physical world. It is ideal for students and teachers of science and the philosophy of science. It is both a high-level popularization and a critical appraisal of these methods, describing important advances in physics and analyzing the historical development, value, reliability and philosophical implications of the way physicists approach the problems confronting them. The introductory chapter on the meaning of physical theories and the mathematical tools used to develop them is followed by a general discussion on the foundations of physics under four major headings: the physics of the reversible, the physics of the irreversible, microphysics, and cosmology. Throughout, the subject matter of physical theories is linked to discussion of the attendant philosophical and epistemological implications, such as the validity of the theories, inductive inference, causal explanation, proba

George Frederick Charles Searle (1864–1954) was a British physicist who worked at the Cavendish Laboratory in Cambridge for 55 years. In this book, which was first published in 1934, Searle presents details on a selection of experiments relating to mechanics, elasticity, surface tension, viscosity, heat and sound. Illustrative figures and textual notes are incorporated throughout. This book will be of value to anyone with an interest in physics, the history of education and the history of science.

This essential reference for graduate students and researchers provides a unified treatment of earthquakes and faulting as two aspects of brittle tectonics at different timescales. The intimate connection between the two is manifested in their scaling laws and populations, which evolve from fracture growth and interactions between fractures. The connection between faults and the seismicity generated is governed by the rate and state dependent friction laws - producing distinctive seismic styles of faulting and a gamut of earthquake phenomena including aftershocks, afterslip, earthquake triggering, and slow slip events. The third edition of this classic treatise presents a wealth of new topics and new observations. These include slow earthquake phenomena; friction of phyllosilicates, and at high sliding velocities; fault structures; relative roles of strong and seismogenic versus weak and creeping faults; dynamic triggering of earthquakes; oceanic earthquakes; megathrust earthquakes in

在 Ends of the Earth 中，Neil Shubin 從南北兩極出發，描繪人類如何在冰雪、寒風與孤立中，持續探索地球的運作方式。極地並非世界的邊緣，而是影響氣候穩定、海洋健康與生命演化的重要核心。本書透過與多位極地研究者的對話，介紹最新的北極與南極科學成果，也呈現這些研究背後的耐心、幽默與冒險精神。作者擅長將專業知識轉化為具體場景，讓讀者理解極端環境如何成為科學突破的起點。本書兼具旅行記的畫面感與自然科學的扎實內容，閱讀時既能感受現場氛圍，也能逐步累積對地球系統的理解。榮獲《The Economist》年度選書，並入圍 2025 年 Royal Society Trivedi Science Book Prize，是適合關心環境、科學與未來議題讀者的一本作品。Meet the scientists uncovering the secrets of Earth's harshest environments – the polar regionsSHORTLISTED FOR THE ROYAL SOCIETY TRIVEDI SCIENCE BOOK PRIZE 2025AN ECONOMIST BOOK OF THE YEAR'Thrilling... This book is a reminder of how incredibly "cool" our planet can be, and how we must fight to protect it.' Nick MohammedFrigid, remote and inhospitable – the polar regions seem far removed from our everyday lives. But these seemingly isolated ice realms shape life on our planet far more than we realise, influencing everything from the climate to ocean health.They may even hold the secrets to the origins of the Earth. Taking an epic journey of discovery

This book is a self-contained introduction to the theory of atomic motion in proteins and nucleic acids. An understanding of such motion is essential because it plays a crucially important role in biological activity. The authors, both of whom are well known for their work in this field, describe in detail the major theoretical methods that are likely to be useful in the computer-aided design of drugs, enzymes and other molecules. A variety of theoretical and experimental studies is described and these are critically analyzed to provide a comprehensive picture of dynamic aspects of biomolecular structure and function. The book will be of interest to graduate students and research workers in structural biochemistry (X-ray diffraction and NMR), theoretical chemistry (liquids and polymers), biophysics, enzymology, molecular biology, pharmaceutical chemistry, genetic engineering and biotechnology.

Citizenship is the common language for expressing aspirations to democratic and egalitarian ideals of inclusion, participation and civic membership. However, there continues to be a significant gap between formal commitments to gender equality and equal citizenship - in the laws and constitutions of many countries, as well as in international human rights documents - and the reality of women's lives. This volume presents a collection of original works that examine this persisting inequality through the lens of citizenship. Distinguished scholars in law, political science and women's studies investigate the many dimensions of women's equal citizenship, including constitutional citizenship, democratic citizenship, social citizenship, sexual and reproductive citizenship and global citizenship. Gender Equality takes stock of the progress toward - and remaining impediments to - securing equal citizenship for women, develops strategies for pursuing that goal and identifies new questions that

Understanding the changing role of central banks and their recent novel policies is essential for analysing many economic and financial issues, ranging from financial regulation and crisis, to exchange rate dynamics and regime changes, and QE and prolonged low interest rates. This book features contributions by the world's leading experts on central banking, providing in accessible essays a fascinating review of today's key issues for central banks. Luminaries including Stephen Cecchetti, Takatoshi Ito, Anil Kashyap, Mervyn King, Donald Kohn, Otmar Issing and Hyun Shin are joined by Charles Goodhart of the London School of Economics and Political Science, whose many achievements in the field of central banking are honoured as the inspiration for this book. The Changing Fortunes of Central Banking discusses the developing role of central banks in seeking monetary and financial stabilisation, while also giving suggestions for model strategies. This comprehensive review will appeal to cen

Understanding the changing role of central banks and their recent novel policies is essential for analysing many economic and financial issues, ranging from financial regulation and crisis, to exchange rate dynamics and regime changes, and QE and prolonged low interest rates. This book features contributions by the world's leading experts on central banking, providing in accessible essays a fascinating review of today's key issues for central banks. Luminaries including Stephen Cecchetti, Takatoshi Ito, Anil Kashyap, Mervyn King, Donald Kohn, Otmar Issing and Hyun Shin are joined by Charles Goodhart of the London School of Economics and Political Science, whose many achievements in the field of central banking are honoured as the inspiration for this book. The Changing Fortunes of Central Banking discusses the developing role of central banks in seeking monetary and financial stabilisation, while also giving suggestions for model strategies. This comprehensive review will appeal to cen

Fluid dynamics plays a crucial role in many cellular processes, including the locomotion of cells such as bacteria and spermatozoa. These organisms possess flagella, slender organelles whose time periodic motion in a fluid environment gives rise to motility. Sitting at the intersection of applied mathematics, physics and biology, the fluid dynamics of cell motility is one of the most successful applications of mathematical tools to the understanding of the biological world. Based on courses taught over several years, it details the mathematical modelling necessary to understand cell motility in fluids, covering phenomena ranging from single-cell motion to instabilities in cell populations. Each chapter introduces mathematical models to rationalise experiments, uses physical intuition to interpret mathematical results, highlights the history of the field and discusses notable current research questions. All mathematical derivations are included for students new to the field, and end-of-

Fluid dynamics plays a crucial role in many cellular processes, including the locomotion of cells such as bacteria and spermatozoa. These organisms possess flagella, slender organelles whose time periodic motion in a fluid environment gives rise to motility. Sitting at the intersection of applied mathematics, physics and biology, the fluid dynamics of cell motility is one of the most successful applications of mathematical tools to the understanding of the biological world. Based on courses taught over several years, it details the mathematical modelling necessary to understand cell motility in fluids, covering phenomena ranging from single-cell motion to instabilities in cell populations. Each chapter introduces mathematical models to rationalise experiments, uses physical intuition to interpret mathematical results, highlights the history of the field and discusses notable current research questions. All mathematical derivations are included for students new to the field, and end-of-

The striking theorems showcased in this book are among the most profound results of twentieth-century analysis. The authors' original approach combines rigorous mathematical proofs with commentary on the underlying ideas to provide a rich insight into these landmarks in mathematics. Results ranging from the proof of Littlewood's conjecture to the Banach–Tarski paradox have been selected for their mathematical beauty as well as educative value and historical role. Placing each theorem in historical perspective, the authors paint a coherent picture of modern analysis and its development, whilst maintaining mathematical rigour with the provision of complete proofs, alternative proofs, worked examples, and more than 150 exercises and solution hints. This edition extends the original French edition of 2009 with a new chapter on partitions, including the Hardy–Ramanujan theorem, and a significant expansion of the existing chapter on the Corona problem.

The striking theorems showcased in this book are among the most profound results of twentieth-century analysis. The authors' original approach combines rigorous mathematical proofs with commentary on the underlying ideas to provide a rich insight into these landmarks in mathematics. Results ranging from the proof of Littlewood's conjecture to the Banach–Tarski paradox have been selected for their mathematical beauty as well as educative value and historical role. Placing each theorem in historical perspective, the authors paint a coherent picture of modern analysis and its development, whilst maintaining mathematical rigour with the provision of complete proofs, alternative proofs, worked examples, and more than 150 exercises and solution hints. This edition extends the original French edition of 2009 with a new chapter on partitions, including the Hardy–Ramanujan theorem, and a significant expansion of the existing chapter on the Corona problem.

One of the greatest challenges in fundamental physics is to reconcile quantum mechanics and general relativity in a theory of quantum gravity. A successful theory would have profound consequences for our understanding of space, time, and matter. This collection of essays written by eminent physicists and philosophers discusses these consequences and examines the most important conceptual questions among philosophers and physicists in their search for a quantum theory of gravity. Comprising three parts, the book explores the emergence of classical spacetime, the nature of time, and important questions of the interpretation, metaphysics, and epistemology of quantum gravity. These essays will appeal to both physicists and philosophers of science working on problems in foundational physics, specifically that of quantum gravity.

For hundreds of years, we thought we knew what happened during Jesus' last days. Holy Thursday, Good Friday and Easter Sunday are not only observed by Christians around the world, but are also recognized in calendars and by non-practitioners as commemorating the true timeline of events in the life of Christ. But apparent inconsistencies in the gospel accounts of Jesus' final week have puzzled Bible scholars for centuries. In The Mystery of the Last Supper, Colin Humphreys uses science to reveal the truth about Jesus' final days. Reconciling conflicting Gospel accounts and scientific evidence, Humphreys reveals the exact date of the Last Supper in a definitive new timeline of Holy Week.