Mathematics of Discrete Structures for Computer Science

Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains the quality of earlier editions while at the same time seeing numerous minor improvements and major additions. The latter include: a new chapter on singular values and singular vectors, including ways to analyze a matrix of data; a revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages; a new section on linear algebra and cryptography; and a new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (e.g. practice problems, exams, development of textbook examples), plus codes in MATLAB, Julia, and Python.

A concise yet elementary introduction to measure and integration theory, which are vital in many areas of mathematics, including analysis, probability, mathematical physics and finance. In this highly successful textbook, core ideas of measure and integration are explored, and martingales are used to develop the theory further. Other topics are also covered such as Jacobi's transformation theorem, the Radon–Nikodym theorem, differentiation of measures and Hardy–Littlewood maximal functions. In this second edition, readers will find newly added chapters on Hausdorff measures, Fourier analysis, vague convergence and classical proofs of Radon–Nikodym and Riesz representation theorems. All proofs are carefully worked out to ensure full understanding of the material and its background. Requiring few prerequisites, this book is suitable for undergraduate lecture courses or self-study. Numerous illustrations and over 400 exercises help to consolidate and broaden knowledge. Full solutions to a

This undergraduate textbook is a rigorous mathematical introduction to dynamical systems and an accessible guide for students transitioning from calculus to advanced mathematics. It has many student-friendly features, such as graded exercises that range from straightforward to more difficult with hints, and includes concrete applications of real analysis and metric space theory to dynamical problems. Proofs are complete and carefully explained, and there is opportunity to practice manipulating algebraic expressions in an applied context of dynamical problems. After presenting a foundation in one-dimensional dynamical systems, the text introduces students to advanced subjects in the latter chapters, such as topological and symbolic dynamics. It includes two-dimensional dynamics, Sharkovsky's theorem, and the theory of substitutions, and takes special care in covering Newton's method. Mathematica code is available online, so that students can see implementation of many of the dynamical a

Christiane L. Joost-Gaugier offers the first systematic study of Pythagoras and his influence on mathematics, astronomy, philosophy, religion, medicine, music, the occult, and social life - as well as on architecture and art - in the late medieval and early modern eras. Following the threads of admiration for this ancient Greek sage from the fourteenth century to Kepler and Galileo in the seventeenth, this book demonstrates that Pythagoras's influence in intellectual circles - Christian, Jewish, and Arab - was more widespread than has previously been acknowledged. Joost-Gaugier shows how this admiration was reflected in ideas that were applied to the visual arts by a number of well known architects and artists who sought, through the use of a visual language inspired by the memory of Pythagoras, to obtain perfect harmony in their creations. Among these were Alberti, Bramante, Leonardo da Vinci, Michelangelo, and Raphael.

Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.

Temperature is probably the most influential of all climatic variables. Our only direct, quantitative knowledge of global temperatures comes from instruments operated over the last 150 or so years. Yet as crucial and as central as these data are to our understanding of the climate, they are largely taken for granted, even by many of those using them. Measuring Global Temperatures will fill this gap by explaining how global temperatures are measured, how the data are analysed, what the potential errors are, and what needs to be done to improve temperature measurement in the future. The book is of great interest to all meteorologists, climatologists, and hydrologists, and especially those concerned with climate change and global warming. It is written in accessible language with little mathematics, and so will appeal to students and amateur meteorologists with a strong interest in weather and climate.

Christiane L. Joost-Gaugier offers the first systematic study of Pythagoras and his influence on mathematics, astronomy, philosophy, religion, medicine, music, the occult, and social life - as well as on architecture and art - in the late medieval and early modern eras. Following the threads of admiration for this ancient Greek sage from the fourteenth century to Kepler and Galileo in the seventeenth, this book demonstrates that Pythagoras's influence in intellectual circles - Christian, Jewish, and Arab - was more widespread than has previously been acknowledged. Joost-Gaugier shows how this admiration was reflected in ideas that were applied to the visual arts by a number of well known architects and artists who sought, through the use of a visual language inspired by the memory of Pythagoras, to obtain perfect harmony in their creations. Among these were Alberti, Bramante, Leonardo da Vinci, Michelangelo, and Raphael.

Functional Magnetic Resonance Imaging (fMRI) has become a standard tool for mapping the working brain's activation patterns, both in health and in disease. It is an interdisciplinary field and crosses the borders of neuroscience, psychology, psychiatry, radiology, mathematics, physics and engineering. Developments in techniques, procedures and our understanding of this field are expanding rapidly. In this second edition of Introduction to Functional Magnetic Resonance Imaging, Richard Buxton – a leading authority on fMRI – provides an invaluable guide to how fMRI works, from introducing the basic ideas and principles to the underlying physics and physiology. He covers the relationship between fMRI and other imaging techniques and includes a guide to the statistical analysis of fMRI data. This book will be useful both to the experienced radiographer, and the clinician or researcher with no previous knowledge of the technology.

The most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications where algebraic varieties appear in mathematics and the sciences, we see rational ones emerging as the most interesting examples. The authors have given an elementary treatment of rationality questions using a mix of classical and modern methods. Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational and nearly rational varieties at a level that will particularly suit graduate students. There are numerous examples and exercises, all of which are accompanied by fully worked out solutions, that will make this book ideal as the basis of a graduate course. It will act as a valuable reference for researchers whilst helping graduate students to reach the point where they can begin to tackle contemporary research problems.

It is not uncommon to be frustrated by the outcome of an election or a decision in voting, law, economics, engineering, and other fields. Does this 'bad' result reflect poor data or poorly informed voters? Or does the disturbing conclusion reflect the choice of the decision/election procedure? Nobel Laureate Kenneth Arrow's famed theorem has been interpreted to mean 'no decision procedure is without flaws'. Similarly, Nobel Laureate Amartya Sen dashes hope for individual liberties by showing their incompatibility with societal needs. This highly accessible book offers a new, different interpretation and resolution of Arrow's and Sen's theorems. Using simple mathematics, it shows that these negative conclusions arise because, in each case, some of their assumptions negate other crucial assumptions. Once this is understood, not only do the conclusions become expected, but a wide class of other phenomena can also be anticipated.

Life is a compelling addition to the Darwin College Lecture Series, in which eight distinguished authors each present an essay from their area of expertise devoted to the theme of 'life'. The book forges connections between art, science and the humanities in a vibrant and thought-provoking collection that exposes both conventional and unconventional views on the meaning of life, the enigmatic boundaries between the living and the dead, and what may or may not follow afterwards. This collection arises from the Darwin College Lecture Series of 2012 and includes contributions from eight distinguished scholars, all of whom are held in esteem not only for their research, but also for their ability to communicate their subject to popular audiences.

The scope of the detection techniques in particle detectors is very wide, depending on the aim of the measurement. Detectors cover the measurement of energies from the very low to the highest of energies observed in cosmic rays. Describing the instrumentation for experiments in high energy physics and astroparticle physics, this edition describes track detectors, calorimeters, particle identification, neutrino detectors, momentum measurement, electronics, and data analysis. It also discusses applications of these detectors in other fields such as nuclear medicine, radiation protection and environmental science. Problem sets have been added to each chapter and additional instructive material has been provided, making this an excellent reference for graduate students and researchers in particle physics.

The scope of the detection techniques in particle detectors is very wide, depending on the aim of the measurement. Detectors cover the measurement of energies from the very low to the highest of energies observed in cosmic rays. Describing the instrumentation for experiments in high energy physics and astroparticle physics, this edition describes track detectors, calorimeters, particle identification, neutrino detectors, momentum measurement, electronics, and data analysis. It also discusses applications of these detectors in other fields such as nuclear medicine, radiation protection and environmental science. Problem sets have been added to each chapter and additional instructive material has been provided, making this an excellent reference for graduate students and researchers in particle physics.

Climate change is one of the great challenges of modern politics. In this volume, leading political theorists and historians investigate how the history of political ideas can help us make sense of it. The contributors add a historical perspective to contemporary debates in political theory. They also show that the history of political thought offers new directions for thinking about the environment today. By situating the relationship between humans and nature within a wider history of ideas, the essays provide alternative ways of thinking about the most intractable problems of environmental politics - the status of science in modern democracies, problems of collective action, and the challenges of fatalism. This volume will create new avenues of research for scholars and students in the history of political thought. It is essential reading for undergraduate students interested in environmental challenges: both those in politics seeking a historical perspective, and those in history w

This 1996 volume reviewed advances in the field of human tumour immunology, particularly in relation to the potential for immune intervention in preventing or treating tumours. The editors and contributors, all prominent workers in the field, survey advances in the understanding of the relationship between the cancer cell and the immune response at the time of publication. Chapters review in depth the function of immune surveillance and mechanisms of tumour immunity, the role of T lymphocytes and oncogenes in the immune response to cancer, and the potential for immunotherapy of cancer. Areas of tumour immunology that were new at the time of this book's publication are presented, including progress in the development of tumour vaccines with particular reference to melanoma. The volumes in this series are intended for a wide audience of clinicians and researchers with an interest in the applications of biomedical science to the understanding and management of cancer.

How genomics reveals deep histories of inequality, going back many thousands of years. Inequality is an urgent global concern, with pundits, politicians, academics, and best-selling books all taking up its causes and consequences. In Inequality, Carles Lalueza-Fox offers an entirely new perspective on the subject, examining the genetic marks left by inequality on humans throughout history. Lalueza-Fox describes genetic studies, made possible by novel DNA sequencing technologies, that reveal layers of inequality in past societies, manifested in patterns of migration, social structures, and funerary practices. Through their DNA, ancient skeletons have much to tell us, yielding anonymous stories of inequality, bias, and suffering. Lalueza-Fox, a leader in paleogenomics, offers the deep history of inequality. He explores the ancestral shifts associated with migration and describes the gender bias unearthed in these migrations―the brutal sexual asymmetries, for example, between male Euro

This book deals with a key feature of globalization: the rise of regulation beyond the state. It examines the emergence of transnational regulatory cooperation between public and private actors and pursues an inquiry that is at once legal, empirical and theoretical. It asks why a private actor and an international organization would regulate cooperatively and what this tells us about the material meaning of concepts such as 'expertise', 'authority' and 'legitimacy' in specific domains of global governance. Additionally, the book addresses the structures and patterns in which cooperation evolves and how this affects the broader global order. It does so through an investigation of two public-private cooperative agreements: one between the International Standards Organization, the Organisation for Economic Co-operation and Development, the Global Compact and the International Labor Organization and one between the International Olympic Committee and the United Nations Environment Programm

This book deals with a key feature of globalization: the rise of regulation beyond the state. It examines the emergence of transnational regulatory cooperation between public and private actors and pursues an inquiry that is at once legal, empirical and theoretical. It asks why a private actor and an international organization would regulate cooperatively and what this tells us about the material meaning of concepts such as 'expertise', 'authority' and 'legitimacy' in specific domains of global governance. Additionally, the book addresses the structures and patterns in which cooperation evolves and how this affects the broader global order. It does so through an investigation of two public-private cooperative agreements: one between the International Standards Organization, the Organisation for Economic Co-operation and Development, the Global Compact and the International Labor Organization and one between the International Olympic Committee and the United Nations Environment Programm

The book is a comprehensive study of India's relationship with the non-proliferation regime, and its transformative evolution from a perennial outlier to one seeking greater integration with the regime and its normative structures. The highlight of this study is its incisive conceptual analysis of the regime as a functional system and its structural complexities, which brings forth new insights on the regime's core ideas like non-proliferation and counter-proliferation. The book also provides an extensive non-Western narrative on the concept of counter-proliferation and its conceivable role and influence in the regime. It breaks new ground in explaining India's quest for an anti-proliferation strategy, which could determine its status and future in the emerging global nuclear order. It will be a substantial contribution to the literature on India's approach towards non-proliferation, counter-proliferation and disarmament, and will enhance the understanding of the impact of the regime's

Who marched in religious processions and why? How were blood sacrifice and communal feasting related to identities in the ancient Greek city? With questions such as these, current scholarship aims to demonstrate the ways in which religion maps on to the socio-political structures of the Greek polis ('polis religion'). In this book Dr Kindt explores a more comprehensive conception of ancient Greek religion beyond this traditional paradigm. Comparative in method and outlook, the book invites its readers to embark on an interdisciplinary journey touching upon such diverse topics as religious belief, personal religion, magic and theology. Specific examples include the transformation of tyrant property into ritual objects, the cultural practice of setting up dedications at Olympia, and a man attempting to make love to Praxiteles' famous statue of Aphrodite. The book will be valuable for all students and scholars seeking to understand the complex phenomenon of ancient Greek religion.

Who marched in religious processions and why? How were blood sacrifice and communal feasting related to identities in the ancient Greek city? With questions such as these, current scholarship aims to demonstrate the ways in which religion maps on to the socio-political structures of the Greek polis ('polis religion'). In this book Dr Kindt explores a more comprehensive conception of ancient Greek religion beyond this traditional paradigm. Comparative in method and outlook, the book invites its readers to embark on an interdisciplinary journey touching upon such diverse topics as religious belief, personal religion, magic and theology. Specific examples include the transformation of tyrant property into ritual objects, the cultural practice of setting up dedications at Olympia, and a man attempting to make love to Praxiteles' famous statue of Aphrodite. The book will be valuable for all students and scholars seeking to understand the complex phenomenon of ancient Greek religion.

While much has been written on asymmetric aspects of sentence structure, symmetric aspects have been largely ignored, or claimed to be non-existent. Does symmetry in syntax exist, and if it does, how do we account for it? In this book, Barbara Citko sets out to tackle these questions and offers a unified approach to a number of phenomena that have so far been studied only in isolation. Focusing on three core minimalist mechanisms: merge, move and labeling, she advances a new theory of these mechanisms, by showing that under certain well-defined circumstances merge can create symmetric structures, move can target either of two potentially moveable objects, and labels can be constructed symmetrically from the features of two objects. This book is aimed at researchers and graduate students interested in minimalist syntax, the structure of questions, relative clauses, coordination, double object constructions and copular sentences.

In the tenth century AD, a remarkable cultural development took place in the harsh and forbidding San Juan Basin of northwestern New Mexico. From small-scale, simply organised, prehistoric Pueblo societies, a complex and socially differentiated political system emerged which has become known as the Chaco Phenomenon. The origins, evolution, and decline of this system have long been the subject of intense archaeological debate. Lynne Sebastian examines the transition of the Chaco system from an acephalous society, in which leadership was situational and most decision making carried out within kinship structures, to a hierarchically organised political structure with institutional roles of leadership. She argues that harsh environmental factors were not the catalyst for the transition, as has previously been thought. Rather, the increasing political complexity was a consequence of improved rainfall in the region which permitted surplus production, thus allowing those farming the best land

Writing and the Ancient State explores the early development of writing and its relationship to the growth of political structures. The first part of the book focuses on the contribution of writing to the state's legitimating project. The second part deals with the state's use of writing in administration, analyzing both textual and archaeological evidence to reconstruct how the state used bookkeeping to allocate land, police its people, and extract taxes from them. The third part focuses on education, the state's system for replenishing its staff of scribe-officials. The first half of each part surveys evidence from Mesopotamia, Egypt, the Maya lowlands, Central Mexico, and the Andes; against this background the second half examines the evidence from China. The chief aim of this book is to shed new light on early China (from the second millennium BC through the end of the Han period, ca. 220 AD) while bringing to bear the lens of cross-cultural analysis on each of the civilizations un

Thomas Hobbes (1588–1679) is recognized as one of the fathers of modern philosophy and political theory. In his own time he was as famous for his work in physics, geometry, and religion. He associated with some of the greatest writers, scientists, and politicians of his age. Martinich has written a complete and accessible biography of Hobbes. The book takes full account of the historical and cultural context in which Hobbes lived, drawing on both published and unpublished sources. It will be a great resource for philosophers, political theorists and historians of ideas. The clear, crisp prose style will also ensure that the book appeals to general readers with an interest in the history of philosophy, the rise of modern science and the English Civil War.

Thomas Hobbes (1588–1679) is recognized as one of the fathers of modern philosophy and political theory. In his own time he was as famous for his work in physics, geometry, and religion. He associated with some of the greatest writers, scientists, and politicians of his age. Martinich has written a complete and accessible biography of Hobbes. The book takes full account of the historical and cultural context in which Hobbes lived, drawing on both published and unpublished sources. It will be a great resource for philosophers, political theorists and historians of ideas. The clear, crisp prose style will also ensure that the book appeals to general readers with an interest in the history of philosophy, the rise of modern science and the English Civil War.

WINNER OF The Hugo and Nebula Awards for Best Novella, the Reddit Stabby Award for Best Novella AND The British Science Fiction Association Award for Best NovellaSHORTLISTED FOR2020 Theodore Sturgeon Memorial AwardThe Ray Bradbury PrizeKitschies Red Tentacle AwardKitschies Inky TentacleBrave New Words AwardCo-written by two award-winning writers, This Is How You Lose the Time War is an epic love story spanning time and space. Among the ashes of a dying world, an agent of the Commandant finds a letter. It reads: Burn before reading.Thus begins an unlikely correspondence between two rival agents hellbent on securing the best possible future for their warring factions. Now, what began as a taunt, a battlefield boast, grows into something more. Something epic.Something romantic. Something that could change the past and the future. Except the discovery of their bond would mean death for each of them.There's still a war going on, after all. And someone has to win that war. That's how war wor

This new addition to the highly successful Core Topics in Anaesthesia series provides a clinically relevant text for both trainees and consultants, covering the entire sub-specialty of obstetric anaesthesia. In-depth coverage of pregnancy-related physiology and pharmacology makes this book an excellent revision tool for basic science examinations. It is also a troubleshooting guide for anaesthetists when managing parturients suffering with concurrent medical conditions including obesity, sepsis, hypertensive, renal, respiratory, neurological, haematological and endocrine diseases. Chapters provide recommended management plans for specific conditions such as HIV and neuropraxia following regional anaesthesia, and include algorithms to guide clinical decision-making. Guidance on the required infrastructure for setting up services such as antenatal clinics is also included. Experts in their fields have contributed sections including allergy testing and immunology, the immunocompromised p

For many years, planetary science has been taught as part of the astronomy curriculum, from a very physics-based perspective, and from the framework of a tour of the Solar System - body by body. Over the past decades, however, spacecraft exploration and related laboratory research on extraterrestrial materials have given us a new understanding of planets and how they are shaped by geological processes. Based on a course taught at the University of Tennessee, Knoxville, this is the first textbook to focus on geologic processes, adopting a comparative approach that demonstrates the similarities and differences between planets, and the reasons for these. Profusely illustrated, and with a wealth of pedagogical features, this book provides an ideal capstone course for geoscience majors - bringing together aspects of mineralogy, petrology, geochemistry, volcanology, sedimentology, geomorphology, tectonics, geophysics and remote sensing.

In a world facing multiple crises, our foundational institutions are failing to offer effective solutions. Drawing on the emerging consilience of knowledge, Michael Pirson debunks the fundamental yet outdated assumptions of human nature that guide twentieth-century management theory and practice - as captured in the 'economistic' paradigm - and instead provides an urgently needed conceptual and practical 'humanistic' framework, based on the protection of human dignity and the promotion of well-being. By outlining the science-based pillars of this innovative system, Pirson provides a twenty first-century model for the responsible twenty first-century leader seeking sustainable ways to organize in a world of crisis. Highlighting relevant applications for research, practice, teaching and policy, this book is ideal for graduate students and professionals seeking to develop their understanding of responsible business, business ethics and corporate responsibility.

In a world facing multiple crises, our foundational institutions are failing to offer effective solutions. Drawing on the emerging consilience of knowledge, Michael Pirson debunks the fundamental yet outdated assumptions of human nature that guide twentieth-century management theory and practice - as captured in the 'economistic' paradigm - and instead provides an urgently needed conceptual and practical 'humanistic' framework, based on the protection of human dignity and the promotion of well-being. By outlining the science-based pillars of this innovative system, Pirson provides a twenty first-century model for the responsible twenty first-century leader seeking sustainable ways to organize in a world of crisis. Highlighting relevant applications for research, practice, teaching and policy, this book is ideal for graduate students and professionals seeking to develop their understanding of responsible business, business ethics and corporate responsibility.

Many research problems in cryospheric science, such as global warming-induced permafrost degradation, require information about the subsurface, which can be imaged using geophysical methods. This book is a practical guide to the application of geophysical techniques in mountainous and polar terrain, where the harsh environment and nature of the subsurface pose particular challenges. It starts with an introduction to the main geophysical methods and then demonstrates their application in periglacial environments through various case studies - written by a team of international experts. The final part of the book presents a series of reference tables with typical values of geophysical parameters for periglacial environments. This handbook is a valuable resource for glaciologists, geomorphologists and geologists requiring an introduction to geophysical techniques, as well as for geophysicists lacking experience of planning and conducting field surveys in cold regions.

According to the Institute of Medicine (IOM) and U.S. Food and Drug Administration (FDA), 'developing new scientific approaches to detecting, understanding, predicting and preventing adverse events' was a critical path to the future of drug safety. This book brings together a collection of state-of-the-art chapters, written by experts in the drug safety field. It provides information on the present knowledge of drug side effects and their mitigation strategy during drug discovery, gives guidance for risk assessment and promotes evidence-based toxicology. Each specific area of toxicology relevant for drug discovery is discussed in detail, including theory, experimental approaches and data interpretation supported by comprehensive up-to-date references. Many chapters provide fascinating case studies, which are of general interest for those who have basic science training and are interested in how chemicals interact with the human body.

Many research problems in cryospheric science, such as global warming-induced permafrost degradation, require information about the subsurface, which can be imaged using geophysical methods. This book is a practical guide to the application of geophysical techniques in mountainous and polar terrain, where the harsh environment and nature of the subsurface pose particular challenges. It starts with an introduction to the main geophysical methods and then demonstrates their application in periglacial environments through various case studies - written by a team of international experts. The final part of the book presents a series of reference tables with typical values of geophysical parameters for periglacial environments. This handbook is a valuable resource for glaciologists, geomorphologists and geologists requiring an introduction to geophysical techniques, as well as for geophysicists lacking experience of planning and conducting field surveys in cold regions.

For over 40 years, satellites have been orbiting the Earth quietly monitoring the state of our planet. Unseen by most of us, they are providing information on the many changes taking place, from movements in the land and volcanic eruptions, to human-caused changes such as the growth of cities, deforestation and the spread of pollutants in the atmosphere and oceans. Led by four editors with support from a production team at NASA Goddard Space Flight Center, many of the world's top remote sensing scientists showcase some spectacular and beautiful satellite imagery along with informed essays on the science behind these images and the implications of what is shown. This is a stunningly attractive and informative book for anyone interested in environmental issues and the beauty of our home planet, providing inspiration for students, teachers, environmentalists and the general public alike.

This unique text uses Microsoft Excel® workbooks to instruct students. In addition to explaining fundamental concepts in microeconomic theory, readers acquire a great deal of sophisticated Excel skills and gain the practical mathematics needed to succeed in advanced courses. In addition to the innovative pedagogical approach, the book features explicitly repeated use of a single central methodology, the economic approach. Students learn how economists think and how to think like an economist. With concrete, numerical examples and novel, engaging applications, interest for readers remains high as live graphs and data respond to manipulation by the user. Finally, clear writing and active learning are features sure to appeal to modern practitioners and their students. The website accompanying the text is found at www.depauw.edu/learn/microexcel.

Beginning in Italy, the Renaissance was a cultural movement that spread throughout Europe and affected art, science, technology, politics, and thought. From the 1300s to the beginning of the 1600s, scholars started to question what they knew and looked to literature and historical texts to develop new ideas for why things were the way they were. In just a short amount of time, the foundations for European life were uprooted and examined, leading people, including Leonardo da Vinci and Michelangelo, to explore new ways of thinking and being.Readers will learn why the Reinassance was such a pivotal time in European history and how it still influences us.

This new, up-to-date, concise revision guide for the MRCS Part B examination equips candidates with the essential knowledge and armamentarium required to tackle the exam. Written in a model question-and-answer format to aid the breakdown of information, candidates can practise some of the most common exam questions they can expect to face. Including subdivisions on applied surgical science and critical care, anatomy and surgical pathology, surgical skills and patient safety and a section on clinical examinations of the limbs and spine, this guide will increase candidates' confidence in both exam technique and key concepts. MRCS Revision Guide: Limbs and Spine is a concise, handy pocket book; a 'must have' quick reference guide for busy surgical trainees studying for the MRCS examination.

Einstein's general theory of relativity is widely considered to be one of the most elegant and successful scientific theories ever developed, and it is increasingly being taught in a simplified form at advanced undergraduate level within both physics and mathematics departments. Due to the increasing interest in gravitational physics, in both the academic and the public sphere, driven largely by widely-publicised developments such as the recent observations of gravitational waves, general relativity is also one of the most popular scientific topics pursued through self-study. Modern General Relativity introduces the reader to the general theory of relativity using an example-based approach, before describing some of its most important applications in cosmology and astrophysics, such as gamma-ray bursts, neutron stars, black holes, and gravitational waves. With hundreds of worked examples, explanatory boxes, and end-of-chapter problems, this textbook provides a solid foundation for unde

The atmosphere and ocean are two of the most important components of the climate system, and fluid dynamics is central to our understanding of both. This book provides a unified and comprehensive treatment of the field that blends classical results with modern interpretations. It takes the reader seamlessly from the basics to the frontiers of knowledge, from the equations of motion to modern theories of the general circulation of the atmosphere and ocean. These concepts are illustrated throughout the book with observations and numerical examples. As well as updating existing chapters, this full-color second edition includes new chapters on tropical dynamics, El Niño, the stratosphere and gravity waves. Supplementary resources are provided online, including figures from the book and problem sets, making this new edition an ideal resource for students in the atmospheric, oceanic and climate sciences, as well as in applied mathematics and engineering.