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This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research--- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer.This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A fewnew topics have been added, notably Sard’s theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures.Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.

Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the University of California at Berkeley. He is the author of "Residues and Duality" (1966), "Foundations of Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles. His current research interest is the geometry of projective varieties and vector bundles. He has been a visiting professor at the College de France and at Kyoto University, where he gave lectures in French and in Japanese, respectively. Professor Hartshorne is married to Edie Churchill, educator and psychotherapist, and has two sons. He has travelled widely, speaks several foreign languages, and is an experienced mountain climber. He is also an accomplished amateur musician: he has played the flute for many years, and during his last visit to Kyoto he began studying the shakuhachi.

This richly illustrated textbook covers modern statistical methods with applications in medicine, epidemiology and biology. Firstly, it discusses the importance of statistical models in applied quantitative research and the central role of the likelihood function, describing likelihood-based inference from a frequentist viewpoint, and exploring the properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic. In the second part of the book, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. It includes a separate chapter on modern numerical techniques for Bayesian inference, and also addresses advanced topics, such as model choice and prediction from frequentist and Bayesian perspectives. This revised edition of the book “Applied Statistical Inference” has been expanded to include new material on Markov models for time series analysis. It also features a comprehensive appendix covering the prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis, and each chapter is complemented by exercises. The text is primarily intended for graduate statistics and biostatistics students with an interest in applications.

A half-century ago, advanced calculus was a well-de?ned subject at the core of the undergraduate mathematics curriulum. The classic texts of Taylor [19], Buck [1], Widder [21], and Kaplan [9], for example, show some of the ways it was approached. Over time, certain aspects of the course came to be seen as more signi?cant—those seen as giving a rigorous foundation to calculus—and they - came the basis for a new course, an introduction to real analysis, that eventually supplanted advanced calculus in the core. Advanced calculus did not, in the process, become less important, but its role in the curriculum changed. In fact, a bifurcation occurred. In one direction we got c- culus on n-manifolds, a course beyond the practical reach of many undergraduates; in the other, we got calculus in two and three dimensions but still with the theorems of Stokes and Gauss as the goal. The latter course is intended for everyone who has had a year-long introduction to calculus; it often has a name like Calculus III. In my experience, though, it does not manage to accomplish what the old advancedcalculus course did. Multivariable calculusnaturallysplits intothreeparts:(1)severalfunctionsofonevariable,(2)one function of several variables, and (3) several functions of several variables. The ?rst two are well-developed in Calculus III, but the third is really too large and varied to be treated satisfactorily in the time remaining at the end of a semester. To put it another way: Green’s theorem ?ts comfortably; Stokes’ and Gauss’ do not.

For a brief period during the latter part of World War II, Nevill F. Mott led a theoretical group at Fort Halstead in the United Kingdom that tackled scientific issues related to pressing war-time concerns. Among later awards and honors, Mott was knighted and a recipient of the Nobel Prize. While at Fort Halstead, he undertook an effort to theoretically describe the statistical fragmentation of munitions subjected to intense explosive loading. Mott`s original internal reports contain seminal theoretical concepts on the physics and statistics of dynamic fracture and fragmentation, which have provided the inspiration for numerous later modeling efforts and engineering formulae. Some of his most forward-looking thoughts on the micromechanical and molecular aspects of fracture are included in these publications. The present book surveys the theoretical analysis put forth by Mott with particular focus on his efforts to characterize the size and distribution of fragments resulting from a dynamic fragmentation event. Copies of the original internal reports of Mott and his co-workers are included. The book also pursues additional theoretical analysis with the intent of delving further into the physical ideas and unfinished analysis implicit in Mott`s original studies. This book will be of interest to all scientists and engineers concerned with the dynamic fracture and fragmentation of solid bodies subject to intense transient loads imparted by explosive detonation and high-velocity impact from both the historical and modern perspective.

Stung by the pioneering space successes of the Soviet Union - in particular, Gagarin being the first man in space, the United States gathered the best of its engineers and set itself the goal of reaching the Moon within a decade. In an expanding 2nd edition of How Apollo Flew to the Moon, David Woods tells the exciting story of how the resulting Apollo flights were conducted by following a virtual flight to the Moon and its exploration of the surface. From launch to splashdown, he hitches a ride in the incredible spaceships that took men to another world, exploring each step of the journey and detailing the enormous range of disciplines, techniques, and procedures the Apollo crews had to master. While describing the tremendous technological accomplishment involved, he adds the human dimension by calling on the testimony of the people who were there at the time. He provides a wealth of fascinating and accessible material: the role of the powerful Saturn V, the reasoning behind trajectories, the day-to-day concerns of human and spacecraft health between two worlds, the exploration of the lunar surface and the sheer daring involved in traveling to the Moon and the mid-twentieth century. Given the tremendous success of the original edition of How Apollo Flew to the Moon, the second edition will have a new chapter on surface activities, inspired by reader's comment on Amazon.com. There will also be additional detail in the existing chapters to incorporate all the feedback from the original edition, and will include larger illustrations.

Imagine that we had some way to look directly at the molecules in a living organism. An x-ray microscope would do the trick, or since we’re dreaming, perhaps an Asimov-style nanosubmarine (unfortunately, neither is currently feasible). Think of the wonders we could witness firsthand: antibodies atta- ing a virus, electrical signals racing down nerve fibers, proteins building new strands of DNA. Many of the questions puzzling the current cadre of sci- tists would be answered at a glance. But the nanoscale world of molecules is separated from our everyday world of experience by a daunting million-fold difference in size, so the world of molecules is completely invisible. I created the illustrations in this book to help bridge this gulf and allow us to see the molecular structure of cells, if not directly, then in an artistic rendition. I have included two types of illustrations with this goal in mind: watercolor paintings which magnify a small portion of a living cell by one million times, showing the arrangement of molecules inside, and comput- generated pictures, which show the atomic details of individual molecules. In this second edition of The Machinery of Life, these illustrations are presented in full color, and they incorporate many of the exciting scientific advances of the 15 years since the first edition.

Pro Git (Second Edition) is your fully-updated guide to Git and its usage in the modern world. Git has come a long way since it was first developed by Linus Torvalds for Linux kernel development. It has taken the open source world by storm since its inception in 2005, and this book teaches you how to use it like a pro. Effective and well-implemented version control is a necessity for successful web projects, whether large or small. With this book you’ll learn how to master the world of distributed version workflow, use the distributed features of Git to the full, and extend Git to meet your every need. Written by Git pros Scott Chacon and Ben Straub, Pro Git (Second Edition) builds on the hugely successful first edition, and is now fully updated for Git version 2.0, as well as including an indispensable chapter on GitHub. It’s the best book for all your Git needs.

The world is undergoing unprecedented changes in many of the factors that determine its fundamental properties and their in- ence on society. These changes include climate; the chemical c- position of the atmosphere; the demands of a growing human population for food and ?ber; and the mobility of organisms, ind- trial products, cultural perspectives, and information ?ows. The magnitude and widespread nature of these changes pose serious challenges in managing the ecosystem services on which society depends. Moreover, many of these changes are strongly in?uenced by human activities, so future patterns of change will continue to be in?uenced by society’s choices and governance. The purpose of this book is to provide a new framework for n- ural resource management—a framework based on stewardship of ecosystems for human well-being in a world dominated by unc- tainty and change. The goal of ecosystem stewardship is to respond to and shape change in social-ecological systems in order to s-tain the supply and opportunities for use of ecosystem services by society. The book links recent advances in the theory of resilience, sustainability, and vulnerability with practical issues of ecosystem management and governance. The book is aimed at advanced undergraduates and beginning graduate students of natural resource management as well as professional managers, community leaders, and policy makers with backgrounds in a wide array of d- ciplines, including ecology, policy studies, economics, sociology, and anthropology.

This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden’s permanent conjecture, as well as additional, highly original and delightful proofs in other chapters.From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition"“… It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. […] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty.”From the Reviews"... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... "Notices of the AMS, August 1999"... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..."LMS Newsletter, January 1999"Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ..." SIGACT News, December 2011

Die Beobachtungsmöglichkeiten der modernen Astrophysik werden immer zahlreicher. Sie reichen von optischen Teleskopen über Weltraumteleskope im Infraroten bis zu Radioteleskopen und von Gravitationswellendetektoren bis hin zu Neutrinoobservatorien. Während die einen im Weltraum ein Augenmerk auf das Licht werfen, nehmen andere unter Wasser kleinste Teilchen unter die Lupe oder messen Störungen der Raumzeit, die kleiner sind als der Durchmesser eines Protons. Das Buch bietet einen spannenden umfassenden Überblick über unsere technischen Möglichkeiten, das Universum zu erforschen. Als Grundlage für eine Vorlesung in Astronomie bzw. Astrophysik ist es ebenso geeignet wie als Lektüre für naturwissenschaftlich Interessierte.

Understanding and employing cryptography has become central for securing virtually any digital application, whether user app, cloud service, or even medical implant.Heavily revised and updated, the long-awaited second edition of Understanding Cryptography follows the unique approach of making modern cryptography accessible to a broad audience, requiring only a minimum of prior knowledge. After introducing basic cryptography concepts, this seminal textbook covers nearly all symmetric, asymmetric, and post-quantum cryptographic algorithms currently in use in applications—ranging from cloud computing and smart phones all the way to industrial systems, block chains, and cryptocurrencies.Topics and features:Opens with a foreword by cryptography pioneer and Turing Award winner, Ron RivestHelps develop a comprehensive understanding of modern applied cryptographyProvides a thorough introduction to post-quantum cryptography consisting of the three standardized cipher familiesIncludes for every chapter a comprehensive problem set, extensive examples, and a further-reading discussionCommunicates, using a unique pedagogical approach, the essentials about foundations and use in practice, while keeping mathematics to a minimumSupplies up-to-date security parameters for all cryptographic algorithmsIncorporates chapter reviews and discussion on such topics as historical and societal contextThis must-have book is indispensable as a textbook for graduate and advanced undergraduate courses, as well as for self-study by designers and engineers.The authors have more than 20 years’ experience teaching cryptography at various universities in the US and Europe. In addition to being renowned scientists, they have extensive experience with applying cryptography in industry, fromwhich they have drawn important lessons for their teaching.

Linear algebra is the branch of mathematics that has grown from a care­ ful study of the problem of solving systems of linear equations. The ideas that developed in this way have become part of the language of much of higher mathematics. They also provide a framework for appli­ cations of linear algebra to many problems in mathematics, the natural sciences, economics, and computer science. This book is the revised fourth edition of a textbook designed for upper division courses in linear algebra. While it does not presuppose an earlier course, many connections between linear algebra and under­ graduate analysis are worked into the discussion, making it best suited for students who have completed the calculus sequence. For many students, this may be the first course in which proofs of the main results are presented on an equal footing with methods for solving numerical problems. The concepts needed to understand the proofs are shown to emerge naturally from attempts to solve concrete problems. This connection is illustrated by worked examples in almost every section. Many numerical exercises are included, which use all the ideas, and develop important techniques for problem-solving. There are also theoretical exercises, which provide opportunities for students to discover interesting things for themselves, and to write mathematical explanations in a convincing way. Answers and hints for many of the problems are given in the back. Not all answers are given, however, to encourage students to learn how to check their work.

TheclassicaltheoryofFourierseriesandintegrals,aswellasLaplacetra- forms, is of great importance for physical and technical applications, and its mathematical beauty makes it an interesting study for pure mathema- cians as well. I have taught courses on these subjects for decades to civil engineeringstudents,andalsomathematicsmajors,andthepresentvolume can be regarded as my collected experiences from this work. There is, of course, an unsurpassable book on Fourier analysis, the tr- tise by Katznelson from 1970. That book is, however, aimed at mathem- ically very mature students and can hardly be used in engineering courses. Ontheotherendofthescale,thereareanumberofmore-or-lesscookbo- styled books, where the emphasis is almost entirely on applications. I have felt the need for an alternative in between these extremes: a text for the ambitious and interested student, who on the other hand does not aspire to become an expert in the ?eld. There do exist a few texts that ful?ll these requirements (see the literature list at the end of the book), but they do not include all the topics I like to cover in my courses, such as Laplace transforms and the simplest facts about distributions.

The purpose of this book is to provide the reader with a solid background and understanding of the basic results and methods in probability theory before entering into more advanced courses (in probability and/or statistics). The presentation is fairly thorough and detailed with many solved examples. Several examples are solved with di erent methods in order to illustrate their di erent levels of sophistication, their pros, and their cons. The motivation for this style of exposition is that experience has proved that the hard part in courses of this kind usually is the application of the results and methods; to know how, when, and where to apply what; and then, technically, to solve a given problem once one knows how to proceed. Exercises are spread out along the way, and every chapter ends with a large selection of problems. Chapters 1 through 6 focus on some central areas of what might be called pure probability theory: multivariate random variables, conditioning, tra- forms, order variables, the multivariate normal distribution, and convergence.

There has been a convergence in recent years of people from the physical and biological sciences and from various engineering disciplines who are interested in analyzing the electrical activity of nerve and muscle quantita­ tively. Various courses have been established at the graduate level or final-year undergraduate level in many universities to teach this subject matter, yet no satisfactory short text has existed. The present book is an attempt to fill this gap, and arises from my experience in teaching this material over the past fifteen years to students on both sides of the Atlantic. Although covering a wide range of biophysi­ cal topics from the level of single molecules to that of complex systems, I have attempted to keep the text relatively short by considering only examples of the most general interest. Problems are included whenever possible at the end of each chapter so the reader may test his understand­ ing of the material presented and consider other examples which have not been included in the text.

From the reviews of the second edition:"This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here."(David Parrott, Australian Mathematical Society)This third edition includes new chapters on simple groups and combinatorics, and new sections on several topics, including the Poincare conjecture. The book has also been enriched by added exercises.

​This book both summarizes the basic theory of evolutionary games and explains their developing applications, giving special attention to the 2-player, 2-strategy game. This game, usually termed a "2×2 game” in the jargon, has been deemed most important because it makes it possible to posit an archetype framework that can be extended to various applications for engineering, the social sciences, and even pure science fields spanning theoretical biology, physics, economics, politics, and information science. The 2×2 game is in fact one of the hottest issues in the field of statistical physics. The book first shows how the fundamental theory of the 2×2 game, based on so-called replicator dynamics, highlights its potential relation with nonlinear dynamical systems. This analytical approach implies that there is a gap between theoretical and reality-based prognoses observed in social systems of humans as well as in those of animal species. The book explains that this perceived gap is theresult of an underlying reciprocity mechanism called social viscosity. As a second major point, the book puts a sharp focus on network reciprocity, one of the five fundamental mechanisms for adding social viscosity to a system and one that has been a great concern for study by statistical physicists in the past decade. The book explains how network reciprocity works for emerging cooperation, and readers can clearly understand the existence of substantial mechanics when the term "network reciprocity" is used. In the latter part of the book, readers will find several interesting examples in which evolutionary game theory is applied. One such example is traffic flow analysis. Traffic flow is one of the subjects that fluid dynamics can deal with, although flowing objects do not comprise a pure fluid but, rather, are a set of many particles. Applying the framework of evolutionary games to realistic traffic flows, the book reveals that social dilemma structures lie behind traffic flow.

This book elucidates how Finite Element methods look like from the perspective of Green’s functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Green’s functions  and how approximating of Green’s functions. It discusses in detail the discretization error and shows that are coherent with the strategy of “goal oriented refinement”. The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.

This chapter briefly describes the general goals of the book, introduces the most fundamental features of the methodology that is employed to achieve these goals, and gives an outline of the structure of the book. A more detailed account of the goals and methodology is presented in chapters 2 and 3, respectively. What the Book Is About The main objective of this study is to attempt to answer the question: How do people understand their emotions? As we shall see in the next chapter, a large number of scholars have tried to provide answers to this question. The interest in the way people understand their emotions has led scholars to the issue of the nature of emotion concepts and emotional meaning. Since the notion of understanding involves or presupposes the notions of concept and meaning, it was only natural for scholars with an interest in the way people understand their emotions to tum their attention to emo­ tion concepts and the meaning associated with emotion terms. So the broader issue has often become more specific. For example, Davitz in his The Language of Emotion formulated the central question in the following way: "What does a person mean when he says someone is happy or angry or sad?" (Davitz 1969: 1).

Although Rock Mechanics addresses many of the rock mechanics issues which arise in underground mining engineering, it is not a text exclusively for mining applications. It consists of five categories of topics on the science and practice of rock engineering: basic engineering principles relevant to rock mechanics; mechanical properties of rock and rock masses; design of underground excavations in various rock mass conditions; mining methods and their implementation; and guidelines on rock mechanics practice. Throughout the text, and particularly in those sections concerned with excavation design and design of mining layouts, reference is made to computational methods of analysis of stress and displacement in a rock mass. The principles of various computational schemes, such as boundary element, finite element and distinct element methods, are considered. This new edition has been completely revised to reflect the notable innovations in mining engineering and the remarkable developments in the science of rock mechanics and the practice of rock engineering that have taken place over the last two decades.Based on extensive professional, research and teaching experience, this book will provide an authoritative and comprehensive text for final year undergraduates and commencing postgraduate students. For professional practitioners, not only will it be of interest to mining and geological engineers but also to civil engineers, structural and mining geologists and geophysicists as a standard work for professional reference purposes.B.H.G. Brady is Emeritus Professor and former Dean of the Faculty of Engineering, Computing and Mathematics at The University of Western Australia, and a consulting rock mechanics engineer. E.T. Brown is Senior Consultant, Golder Associates Pty Ltd, Brisbane, Australia and formerly Senior Deputy Vice-Chancellor of The University of Queensland, Australia.

High-performance process improvement takes process improvement to the next ambition level. The kernel of the substance is a generic process improvement process that operates under the strictest time, quality and cost constraints. Thanks to a modular composition and robust methods the scope may range from one single person to networks with hundreds of companies. This is realized via three high-class phases:network and company analysis and synthesis, process analysis and synthesis, the implementation, including process improvement education and training and the practical realization of the improvement potential.The presented methods contain mass customization features and a very advanced logic for optimizing the interaction of people, technology, information and material both in the process improvement process itself and the focus process.The book is based on an extensive R&D effort and thorough practical verifications in more than 75 companies in almost any business and in all sizes.

Enterprise resource planning (ERP), supply chain management (SCM), customer relationship management (CRM), business intelligence (BI), and big data analytics are business tasks and processes that are implemented using standardized software solutions. Artificial intelligence methods such as machine learning and generative AI influence and support these processes. This textbook allows students to learn, from a business perspective, how these methods are interconnected, how they influence one another, and what their limitations are. It teaches management-oriented thinking and acting, which are essential for computer scientists who work with business-process-oriented IT solutions.The third edition of this textbook introduces artificial intelligence methods for the ERP, SCM, CRM, BI, and Big Data process chain. These business tasks and processes, implemented with standardized software systems, are increasingly linked to artificial intelligence methods with varying degrees of success. Human cognitive abilities are identified as suitability criteria for evaluating and selecting AI methods for operational business areas such as procurement, production, sales, asset management, finance and accounting, human resources, etc. The fundamentals of machine learning and neural networks are supplemented by general topics related to AI. The chapters on ERP, SCM, CRM, BI, and Big Data have been largely taken from the second edition. Errors have been corrected, and additions or updates have been made to single chapters. Extensive and confusing derivations and theoretical sections have been moved to the Appendix, and a case study for a virtual company has been included to be used throughout the book. Each chapter finishes with an online true/false quiz. With at least 80% passed, it grants access to supplementary online exercises, including cognitive skill assessments, inventory management optimization, backpropagation, and supplemental online materials (videos, documents) on the author’s Web page. This book is aimed at business informatics students and industry professionals, who deal with business-oriented standardized software solutions.

This book offers readers an essential introduction to the fundamentals of digital image processing. Pursuing a signal processing and algorithmic approach, it makes the fundamentals of digital image processing accessible and easy to learn. It is written in a clear and concise manner with a large number of 4 x 4 and 8 x 8 examples, figures and detailed explanations. Each concept is developed from the basic principles and described in detail with equal emphasis on theory and practice. The book is accompanied by a companion website that provides several MATLAB programs for the implementation of image processing algorithms. The book also offers comprehensive coverage of the following topics: Enhancement, Transform processing, Restoration, Registration, Reconstruction from projections, Morphological image processing, Edge detection, Object representation and classification, Compression, and Color processing.

Itisaspecialpleasureformetowritethisforewordforaremarkablebookbya remarkableauthor.MarcoPettiniisadeepthinker,whohasspentmanyyears probing the foundations of Hamiltonian chaos and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. Itisinparticularthequalityofmindoftheauthorandhisdeepphysical,as well as mathematical insights which make this book so special and inspiring. It is a “must” for those who want to venture into a new approach to old problems or want to use new tools for new problems. Although topology has penetrated a number of ?elds of physics, a broad participationoftopologyintheclari?cationandprogressoffundamentalpr- lems in the above-mentioned ?elds has been lacking. The new perspectives topology gives to the above-mentioned problems are bound to help in their clari?cation and to spread to other ?elds of science. The sparsity of geometric thinking and of its use to solve fundamental problems, when compared with purely analytical methods in physics, could be relieved and made highly productive using the material discussed in this book. It is unavoidable that the physicist reader may have then to learn some new mathematics and be challenged to a new way of thinking, but with the author as a guide, he is assured of the best help in achieving this that is presently available.

This account is an introduction to mathematical knot theory, the theory of knots and links of simple closed curves in three-dimensional space. Knots can be studied at many levels and from many points of view. They can be admired as artifacts of the decorative arts and crafts, or viewed as accessible intimations of a geometrical sophistication that may never be attained. The study of knots can be given some motivation in terms of applications in molecular biology or by reference to paral­ lels in equilibrium statistical mechanics or quantum field theory. Here, however, knot theory is considered as part of geometric topology. Motivation for such a topological study of knots is meant to come from a curiosity to know how the ge­ ometry of three-dimensional space can be explored by knotting phenomena using precise mathematics. The aim will be to find invariants that distinguish knots, to investigate geometric properties of knots and to see something of the way they interact with more adventurous three-dimensional topology. The book is based on an expanded version of notes for a course for recent graduates in mathematics given at the University of Cambridge; it is intended for others with a similar level of mathematical understanding. In particular, a knowledge of the very basic ideas of the fundamental group and of a simple homology theory is assumed; it is, after all, more important to know about those topics than about the intricacies of knot theory.

In this edition two new chapters, 9 and 10, on mathematical finance are added. They are written by Dr. Farid AitSahlia, ancien eleve, who has taught such a course and worked on the research staff of several industrial and financial institutions. The new text begins with a meticulous account of the uncommon vocab­ ulary and syntax of the financial world; its manifold options and actions, with consequent expectations and variations, in the marketplace. These are then expounded in clear, precise mathematical terms and treated by the methods of probability developed in the earlier chapters. Numerous graded and motivated examples and exercises are supplied to illustrate the appli­ cability of the fundamental concepts and techniques to concrete financial problems. For the reader whose main interest is in finance, only a portion of the first eight chapters is a "prerequisite" for the study of the last two chapters. Further specific references may be scanned from the topics listed in the Index, then pursued in more detail.

The aim of stochastic programming is to find optimal decisions in problems  which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. At the same time, it is now being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems.In this extensively updated new edition there is more material on methods and examples including several new approaches for discrete variables, new results on risk measures in modeling and Monte Carlo sampling methods, a new chapter on relationships to other methods including approximate dynamic programming, robust optimization and online methods.The book is highly illustrated with chapter summaries and many examples and exercises. Students, researchers and practitioners in operations research and the optimization area will find it particularly of interest. Review of First Edition:"The discussion on modeling issues, the large number of examples used to illustrate the material, and the breadth of the coverage make 'Introduction to Stochastic Programming' an ideal textbook for the area." (Interfaces, 1998)

This book provides a unified mechanics and materials perspective on polymers: both the mathematics of viscoelasticity theory as well as the physical mechanisms behind polymer deformation processes. Introductory material on fundamental mechanics is included to provide a continuous baseline for readers from all disciplines. Introductory material on the chemical and molecular basis of polymers is also included, which is essential to the understanding of the thermomechanical response. This self-contained text covers the viscoelastic characterization of polymers including constitutive modeling, experimental methods, thermal response, and stress and failure analysis. Example problems are provided within the text as well as at the end of each chapter.New to this edition:·         One new chapter on the use of nano-material inclusions for structural polymer applications and applications such as fiber-reinforced polymers and adhesively bonded structures·         Brings up-to-date polymer production and sales data and equipment and procedures for evaluating polymer characterization and classification·         The work serves as a comprehensive reference for advanced seniors seeking graduate level courses, first and second year graduate students, and practicing engineers