Mathematics Books

Book SynopsisThis book presents topics in a single source format using unified spectral theory of computing. With developments of DNS and LES, practitioners are rediscovering waves as important in fluid flows, and capturing these numerically is central to high accuracy computing. Analysis of waves and its use in numerical methods in propagating energy at the right velocity (dispersion effects) and with right amplitude (dissipation) are essential. Most industrial codes using Reynolds-averaged NavierStokes equations with turbulence models cannot conceive of capturing waves. The new themes covered in this book are: Correct error propagation analysis Practical compact schemes and global analysis tool Aliasing error and its alleviation Spurious upstream propagating q-waves Explanation of the Gibbs phenomenon New 1D and 2D filters for LES/DNS without SGS modelling Anisotropic skewed wave propagation Development and analysis of dispersion relation preservation (DRP) schemes Flow instabilities andTable of ContentsForeword; Preface; 1. Introduction to scientific computing; 2. Governing equations of fluid mechanics; 3. Classification of quasi-linear partial differential equations; 4. Waves and space-time dependence in computing; 5. Spatial and temporal discretizations of partial differential equations; 6. Solution methods for parabolic partial differential equations; 7. Solution methods for elliptic partial differential equations; 8. Solution of hyperbolic PDEs: signal and error propagation; 9. Curvilinear coordinates and grid generation; 10. Spectral analysis of numerical schemes and aliasing error; 11. Higher accuracy and higher order methods; 12. Introduction to finite volume and finite element methods; 13. Solution of Navier–Stokes equations; 14. Recent developments in discrete computing; Exercises; References.

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Book SynopsisIn Measuring and Reasoning, Fred L. Bookstein examines the way ordinary arithmetic and numerical patterns are translated into scientific understanding, showing how the process relies on two carefully managed forms of argument: Abduction: the generation of new hypotheses to accord with findings that were surprising on previous hypotheses, and Consilience: the confirmation of numerical pattern claims by analogous findings at other levels of measurement. These profound principles include an understanding of the role of arithmetic and, more importantly, of how numerical patterns found in one study can relate to numbers found in others. More than 200 figures and diagrams illuminate the text. The book can be read with profit by any student of the empirical nature or social sciences and by anyone concerned with how scientists persuade those of us who are not scientists why we should credit the most important claims about scientific facts or theories.Table of ContentsPart I. The Basic Structure of a Numerical Inference: 1. Getting started; 2. Consilience as a rhetorical strategy; 3. Abduction and strong inference; Part II. A Sampler of Strategies: 4. The undergraduate course; Part III. Numerical Inference for General Systems: 5. Abduction and consilience in more complicated systems; 6. The singular value decomposition: a family of pattern engines for organized systems; 7. Morphometrics, and other examples; Part IV. What Is to Be Done?: 8. Retrospect and prospect.

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Book SynopsisSpectral analysis is widely used to interpret time series collected in diverse areas. This book covers the statistical theory behind spectral analysis and provides data analysts with the tools needed to transition theory into practice. Actual time series from oceanography, metrology, atmospheric science and other areas are used in running examples throughout, to allow clear comparison of how the various methods address questions of interest. All major nonparametric and parametric spectral analysis techniques are discussed, with emphasis on the multitaper method, both in its original formulation involving Slepian tapers and in a popular alternative using sinusoidal tapers. The authors take a unified approach to quantifying the bandwidth of different nonparametric spectral estimates. An extensive set of exercises allows readers to test their understanding of theory and practical analysis. The time series used as examples and R language code for recreating the analyses of the series are aTrade Review'Percival and Walden have written an excellent text for anyone who analyzes or wants to learn how to analyze time series data in the frequency domain. The aims and scope of the text are broad and require the skills that one would acquire in a basic course on mathematical statistics. The authors take a data analysis approach and relegate theoretical material to special sections or problems, and give ample references to the more theoretical details. The authors give philosophical as well as practical guidance in applying spectral techniques to time series data. This book is one of the best texts on the topic and would be useful as a reference for researchers. In addition, the book would be great as a textbook for a one semester/quarter course on the spectral analysis of time series.' David Stoffer, University of Pittsburgh'I used Spectral Analysis for Physical Applications several times for my spectral analysis courses. It was an excellent addition to the literature. This new book, considerably enlarged, will certainly have the same impact. The authors should be congratulated for a most valuable book.' Pedro A. Morettin, Universidade de São Paulo'Spectral Analysis for Univariate Time Series is an excellent step-by-step introduction to using Fourier methods in the statistical analysis of time series. The in-depth material, extensive exercises, practical advice, and illustrative data analyses provide valuable insights to readers of varied backgrounds.' Peter F. Craigmile, Ohio State University'This book will serve scientists and engineers in many fields with a general toolbox for spectral analysis. The fundamentals of non-parametric and parametric methods are presented, together with convincing examples and exercises. I especially appreciate the extensive chapter on combining direct spectral estimators, as todays standard toolbox definitely should include multitaper based spectral analysis.' Maria Sandsten, Lunds universitet'The book constitutes a lot more than an update of the authors' 1993 book Spectral Analysis for Physical Applications. The stand-out features are still the examples and exercises, but all data analysis has been done in R and considerable effort has gone into explanation, and how the methods fit in with alternatives. There is also a new chapter on simulation. The book is suitable not just as a reference for statisticians, engineers and physicists, but also as a graduate level text, particularly because of the chapter summaries and the thought-provoking comments at the section ends.' Barry Quinn, Macquarie University, Sydney'The excellent new textbook by Percival and Walden is an important source of information for anyone interested in time series analysis. Theoretical rigour combined with practical analysis of interesting real world data gives the reader a pedagogical journey into the world of spectral analysis and time series analysis. Highly recommended!' Alfred Hanssen, Universitetet i Tromsø – Norges arktiske universitetTable of Contents1. Introduction to spectral analysis; 2. Stationary stochastic processes; 3. Deterministic spectral analysis; 4. Foundations for stochastic spectral analysis; 5. Linear time-invariant filters; 6. Periodogram and other direct spectral estimators; 7. Lag window estimators; 8. Combining direct spectral estimators; 9. Parametric spectral estimators; 10. Harmonic analysis; 11. Simulation of time series.

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Book SynopsisProviding the latest results and color images from the Cassini space mission, this up-to-date edition is an important resource for students and professionals in planetary science. Revised highlighted topics include Saturn's F ring, Uranus' rings and moons, Neptune's partial rings, dusty rings, and Jupiter's ring-moon system after the New Horizons mission.Trade Review'Supported by an online collection of beautiful NASA images, this is a critical resource for anyone interested in planetary sciences.' ChoiceTable of ContentsPreface: a personal view of planetary rings; 1. Introduction: the allure of the ringed planets; 2. Studies of planetary rings 1610–2013; 3. Diversity of planetary rings; 4. Individual ring particles and their collisions; 5. Large-scale ring evolution; 6. Moons confine and sculpt rings; 7. Explaining ring phenomena; 8. N-body simulations; 9. Stochastic models; 10. Age and evolution of rings; 11. Saturn's mysterious F ring; 12. Uranus' rings and moons; 13. Neptune's partial rings; 14. Jupiter's ring-moon system after Galileo and New Horizons; 15. Ring photometry; 16. Dusty rings; 17. Concluding remarks; Afterword; Glossary; References; Index.

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Book SynopsisThe field of mathematical psychology began in the 1950s and includes both psychological theorizing, in which mathematics plays a key role, and applied mathematics motivated by substantive problems in psychology. Central to its success was the publication of the first Handbook of Mathematical Psychology in the 1960s. The psychological sciences have since expanded to include new areas of research, and significant advances have been made in both traditional psychological domains and in the applications of the computational sciences to psychology. Upholding the rigor of the original Handbook, the New Handbook of Mathematical Psychology reflects the current state of the field by exploring the mathematical and computational foundations of new developments over the last half-century. The second volume focuses on areas of mathematics that are used in constructing models of cognitive phenomena and decision making, and on the role of measurement in psychology.Trade Review'This Handbook contains review articles by leaders of the field. It will be a valuable reference for all who are interested in mathematical psychology.' Brian Skyrms, University of California, Irvine'This volume is the second in a series devoted to presenting a very readable, yet broad and deep, up-to-date perspective on mathematical psychology. It will be of interest to graduate students and experienced researchers who are concerned with modeling and measurement in the psychological and cognitive sciences.' Thomas S. Wallsten, University of Maryland'These two volumes are a valuable contribution to mathematical psychology; partly representing important summaries of special branches, partly pushing the forefront of research towards new horizons. They should be read by all working in special fields, but also by students who are striving for a general point of view. We are looking forward to the third volume.' Reinhard Suck, Journal of Mathematical PsychologyTable of Contents1. Stochastic methods for modeling decision making Adele Diederich and Keivan Mallahi-kara; 2. The diffusion model of speeded choice, from a rational perspective Matt Jones; 3. Stochastic foundations of elementary mental architectures Joseph W. Haupt, James T. Townsend and Brett Jefferson; 4. Identifiability of probabilistic models, with examples from knowledge structure theory Jean-Paul Doignon, Jurgen Heller and Luca Stefanutti; 5. Quantum models of cognition and decision Jerome R. Busemeyer and Peter D. Kvam; 6. Computational cognitive neuroscience F. Gregory Ashby; 7. Discovering aggregation properties via voting Donald G. Saari; 8. Categorization based on similarity and features: the Reproducing Kernel Banach Space (RKBS) approach Jun Zhang and Haizhang Zhang; 9. The axiom of meaningfulness in science and geometry Jean-Claude Falmagne, Louis Narens and Christopher Doble.

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Book SynopsisThis book provides thorough and comprehensive coverage of most of the new and important quantitative methods of data analysis for graduate students and practitioners. In recent years, data analysis methods have exploded alongside advanced computing power, and it is critical to understand such methods to get the most out of data, and to extract signal from noise. The book excels in explaining difficult concepts through simple explanations and detailed explanatory illustrations. Most unique is the focus on confidence limits for power spectra and their proper interpretation, something rare or completely missing in other books. Likewise, there is a thorough discussion of how to assess uncertainty via use of Expectancy, and the easy to apply and understand Bootstrap method. The book is written so that descriptions of each method are as self-contained as possible. Many examples are presented to clarify interpretations, as are user tips in highlighted boxes.Trade Review'This text is suitable for undergraduates and graduates, as well as seasoned scientists and engineers seeking to broaden their statistical skills. It will have lasting value as it is comprehensive, containing detailed explanations of a wide range of statistical methods. The book is clearly written by a meticulous scientist who is an expert in the field and an award winning teacher.' James Hays, Columbia University, New York'At last: a guide for getting the most out of your data analysis while avoiding the many pitfalls, hazards and common mistakes. This book is an invaluable and inspired opus on the fundamentals of quantitative data analysis. It is both comprehensive and illuminating, with many a nugget of enlightened wisdom, as well as succinctly summarized 'take-home' points in each and every section. A very accessible must-have guide for exploring data in the most informed way, and a gem of a textbook for students, teachers and practitioners alike.' Sharon Stammerjohn, University of Colorado, Boulder'Coherent book-length treatments are so valuable in the Data Age: the internet is full of algorithms - but described flatly, and in myriad notations and nomenclatures. This long-time teacher's lucid text expresses the spirit and strategy of data analysis, as well as the details. Boxes set off optional advanced derivations, appendices survey matrix algebra and uncertainty analysis, and the chapters aim for standalone readability, making this a valuable reference as well as a flexible textbook (with questions). Spectral estimation is especially well covered.' Brian Mapes, University of Miami'This is a competent development of many data analysis methods … Overall, the book is the outgrowth of teaching the subject for 30 years, which shows in the well-developed, clear narrative descriptions accompanying the theory.' D. A. Vaccari, ChoiceTable of ContentsPart I. Fundamentals: 1. The nature of data and analysis; 2. Probability theory; 3. Statistics; Part II. Fitting Curves to Data; 4. Interpolation; 5. Smoothed curve fitting; 6. Special curve fitting; Part III. Sequential Data Fundamentals: 7. Serial products; 8. Fourier series; 9. Fourier transform; 10. Fourier sampling theory; 11. Spectral analysis; 12. Cross spectral analysis; 13. Filtering and deconvolution; 14. Linear parametric models; 15. Empirical orthogonal function (EOF) analysis; A1. Overview of matrix algebra; A2. Uncertainty analysis; References; Index.

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Book SynopsisOffering a comprehensive treatment of adhesive particle flows, this book adopts a particle-level approach oriented toward directly simulating the various fluid, electric field, collision, and adhesion forces and torques acting on the particles, within the framework of a discrete-element model. It is ideal for professionals and graduate students working in engineering and atmospheric and condensed matter physics, materials science, environmental science, and other disciplines where particulate flows have a significant role. The presentation is applicable to a wide range of flow fields, including aerosols, colloids, fluidized beds, and granular flows. It describes both physical models of the various forces and torques on the particles as well as practical aspects necessary for efficient implementation of these models in a computational framework.Table of Contents1. Introduction; 2. Modeling viewpoints and approaches; 3. Contact mechanics without adhesion; 4. Adhesion forces; 5. Fluid forces on particles; 6. Particle dispersion in turbulent flows; 7. Ellipsoidal particles; 8. Particle interactions with electric and magnetic fields; 9. Nanoscale particle dynamics; 10. Computer implementation and data analysis; 11. Applications.

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Book SynopsisSurveying the last sixty years of research, this book describes the physical properties of DNA in the context of its biological functioning. It is designed to enable both students and researchers of molecular biology, biochemistry and physics to better understand the biophysics of DNA, addressing key questions and facilitating further research. The chapters integrate theoretical and experimental approaches, emphasising throughout the importance of a quantitative knowledge of physical properties in building and analysing models of DNA functioning. For example, the book shows how the relationship between DNA mechanical properties and the sequence specificity of DNA-protein binding can be analyzed quantitatively by using our current knowledge of the physical and structural properties of DNA. Theoretical models and experimental methods in the field are critically considered to enable the reader to engage effectively with the current scientific literature on the physical properties of DNA.Table of ContentsPreface; 1. DNA structures; 2. Conformational transitions; 3. Equilibrium large-scale conformational properties of DNA; 4. DNA dynamics; 5. DNA-protein interaction; 6. Circular DNA; Index.

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Book SynopsisThis modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to long-range dependence and self-similarity; central and non-central limit theorems for long-range dependent series, and the limiting Hermite processes; fractional Brownian motion and its stochastic calculus; several celebrated decompositions of fractional Brownian motion; multidimensional models for long-range dependence and self-similarity; and maximum likelihood estimation methods for long-range dependent time series. Designed for graduate students and researchers, each chapter of the book is supplemented by numerous exercises, some designed to test the reader''s understanding, while others invite the reader to consider some of the open research problems in the field today.Trade Review'This is a marvelous book that brings together both classical background material and the latest research results on long-range dependence. The book is written so that it can be used as a main source by a graduate student, including all the essential proofs. I highly recommend this book.' Mark M. Meerschaert, Michigan State University'This volume lays a rock-solid foundation for the subjects of long-range dependence and self-similarity. It also provides an up-to-date survey of more specialized topics at the center of this research area. The text is very readable and suitable for graduate courses, as it is self-contained and does not require more than an introductory course on stochastic calculus and time series. It is also written with the necessary level of mathematical detail to make it suitable for self-study. I particularly enjoyed the very nice introduction to fractional Brownian motion, its different representations, its stochastic calculus, and the connection to fractional calculus. I strongly recommend this book, which is a welcome addition to the literature and useful for a large audience.' Eric Moulines, Centre de Mathématiques Appliquées, École Polytechnique, Paris'This book provides a modern, rigorous introduction to long-range dependence and self-similarity. The authors write with wonderful clarity, covering fundamental as well as selected specialized topics. The book can be highly recommended to anybody interested in mathematical foundations of long memory and self-similar processes.' Jan Beran, University of Konstanz, Germany'This is the most readable and lucid account I have seen on long-range dependence and self-similarity. Pipiras and Taqqu present a time-series-centric view of this subject that should appeal to both practitioners and researchers in stochastic processes and statistics. I was especially enamored by the insightful comments on the history of the subject that conclude each chapter. This alone is worth the price of the book!' Richard Davis, Columbia University, New YorkTable of ContentsList of abbreviations; Notation; Preface; 1. A brief overview of times series and stochastic processes; 2. Basics of long-range dependence and self-similarity; 3. Physical models for long-range dependence and self-similarity; 4. Hermite processes; 5. Non-central and central limit theorems; 6. Fractional calculus and integration of deterministic functions with respect to FBM; 7. Stochastic integration with respect to fractional Brownian motion; 8. Series representations of fractional Brownian motion; 9. Multidimensional models; 10. Maximum likelihood estimation methods; Appendix A. Auxiliary notions and results; Appendix B. Integrals with respect to random measures; Appendix C. Basics of Malliavin calculus; Appendix D. Other notes and topics; Bibliography; Index.

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Book SynopsisA modern introduction to synchronization phenomena, this text presents recent discoveries and the current state of research in the field, from low-dimensional systems to complex networks. The book describes some of the main mechanisms of collective behaviour in dynamical systems, including simple coupled systems, chaotic systems, and systems of infinite-dimension. After introducing the reader to the basic concepts of nonlinear dynamics, the book explores the main synchronized states of coupled systems and describes the influence of noise and the occurrence of synchronous motion in multistable and spatially-extended systems. Finally, the authors discuss the underlying principles of collective dynamics on complex networks, providing an understanding of how networked systems are able to function as a whole in order to process information, perform coordinated tasks, and respond collectively to external perturbations. The demonstrations, numerous illustrations and application examples will Table of ContentsPreface; 1. Introduction and main concepts; 2. Low-dimensional systems; 3. Multistable systems, coupled neurons and applications; 4. High-dimensional systems; 5. Complex networks; References; Index.

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Book SynopsisFocusing on simple models, this book describes methods for studying the quantitative aspects of life through physical modelling, using E. coli and phage lambda as key examples. It encompasses fields such as quantitative molecular biology, systems biology and biophysics, providing a tool for students from both biological and physical science backgrounds.Trade Review'Models of Life is an insight of a physicist into biological regulatory mechanisms. It provides a quantitative basis of how many of the biological systems work. Using simple logic and mathematics, Kim Sneppen, a world renowned scientist and thinker, has created a must-read for investigators in quantitative biology. The book provides a clear explanation of triumphant experiments in a lucid way with crisp figures. The brilliance of the author's analytical mind is on display when one sees how he explains some of the exciting paradigmatic regulatory systems, beginning with the basics of molecular biology. The book is also replete with intellectually challenging problem questions for readers, making the book an excellent text for students as well.' Sankar Adhya, National Cancer Institute, Maryland'Kim Sneppen's insightful book covers lots of ground in describing biological systems at different time and length scales and levels of resolution. Its different chapters unified by the author's modeling philosophy are sure to be of interest to a very diverse group of readers … Readers interested in agent-based modeling will find it applies to systems as diverse as epigenetics, propagation of information and evolutionary patterns in fossil records. Dedicated chapters combine biophysics and systems biology of gene regulation and protein-protein interactions. The book provides especially deep coverage of biology of phages, bacteria and their interactions within ecosystems. It would make an excellent textbook for one or even several university courses on systems or evolutionary biology. In fact when teaching these courses I will use it heavily myself and recommend it to my students.' Sergei Maslov, Brookhaven National Laboratory, New York'Sneppen has written a wonderfully friendly and readable book on the principles of biological cells for physicists. He presents concepts and models at a level that is sufficiently deep to convey powerful insights, while keeping the math to the absolutely minimal level that is needed to be clear and informative. This book is pioneering in covering scientific terrain that is largely not covered much elsewhere, but will be in the future - including feedback, regulation, networks, bistability in the lambda-phage switch, DNA looping, diffusion in cells, epigenetic regulation and cellular evolution. I highly recommend it as a deeply insightful book about the principles of biology and a great read.' Ken Dill, Laufer Center, Stony Brook UniversityTable of ContentsPreface; 1. Life from a physics perspective; 2. E. coli as a model system; 3. Dynamics of regulatory links; 4. Statistical mechanics of phage λ; 5. Diffusion and randomness in transcription; 6. Stochastic genes and persistent decisions; 7. Gene regulation and epigenetics in cis; 8. Feedback circuits; 9. Networks; 10. Signalling and metabolic networks; 11. Agent-based models of signalling and selection; 12. Competition and diversity; 13. Evolution and extinction; Appendix; References; Index.

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Book SynopsisSpectroscopy is the study of electromagnetic radiation and its interaction with solid, liquid, gas and plasma. It is one of the widely used analytical techniques to study the structure of atoms and molecules. The technique is also employed to obtain information about atoms and molecules as a result of their distinctive spectra. The fast-spreading field of spectroscopic applications has made a noteworthy influence on many disciplines, including energy research, chemical processing, environmental protection and medicine. This book aims to introduce students to the topic of spectroscopy. The author has avoided the mathematical aspects of the subject as far as possible; they appear in the text only when inevitable. Including topics such as time-dependent perturbation theory, laser action and applications of Group Theory in interpretation of spectra, the book offers a detailed coverage of the basic concepts and applications of spectroscopy.Table of ContentsList of figures; List of tables; List of abbreviations; Preface; Acknowledgement; 1. Fundamentals of spectroscopy; 2. Theoretical principles; 3. Atomic spectroscopy; 4. Pure rotational spectroscopy; 5. Vibrational spectroscopy of diatomics; 6. Vibrational spectroscopy of polyatomic molecules; 7. The Raman effect; 8. Electronic spectroscopy of diatomic molecules; 9. Electronic spectroscopy of polyatomic molecules; Appendices; Select bibliography; Index; About the author.

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Book SynopsisCosmology is in crisis. In this book, philosopher Roberto Mangabeira Unger and physicist Lee Smolin, world-renowned for their radical ideas in their fields, argue for a revolution in our cosmological ideas. The book is readily accessible to non-scientists as well as to the physicists and cosmologists whom it challenges.Trade Review'It might be one of the most important books of our time … Right or wrong, this book is an event.' Bryan Appleyard, The Sunday Times'A hefty explication setting out clear agendas for research into quantum foundations, explanations for the 'arrow of time' and other parts of this puzzle.' Nature'Any serious intellectual rebellion is worth watching. This one is ambitious: it seeks to root out one of the oldest impulses in the western imagination.' The Spectator'Is time, after all, real? Two mavericks take an axe to the established theories of cosmology.' The Guardian'… an admirable restatement of cosmological ambition.' The Times Higher Education Supplement'Anyone that wants to thoroughly deliberate over the question of cosmology should read this book.' Peter Eisenhardt, translated from Physik JournalTable of ContentsIntroduction; Part I. Roberto Mangabeira Unger: 1. The science of the one universe in time; 2. The context and consequences of the argument; 3. The singular existence of the universe; 4. The inclusive reality of time; 5. The mutability of the laws of nature; 6. The selective realism of mathematics; Part II. Lee Smolin: 1. Cosmology in crisis; 2. Principles for a cosmological theory; 3. The setting: the puzzles of contemporary cosmology; 4. Hypotheses for a new cosmology; 5. Mathematics; 6. Approaches to solving the metalaw dilemma; 7. Implications of temporal naturalism for philosophy of mind; 8. An agenda for science; 9. Concluding remarks; A note concerning disagreements between our views.

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Book SynopsisProbability comes of age with this, the first dictionary of probability and its applications in English, which supplies a guide to the concepts and vocabulary of this rapidly expanding field. Besides the basic theory of probability and random processes, applications covered here include financial and insurance mathematics, operations research (including queueing, reliability, and inventories), decision and game theory, optimization, time series, networks, and communication theory, as well as classic problems and paradoxes. The dictionary is reliable, stable, concise, and cohesive. Each entry provides a rigorous definition, a sketch of the context, and a reference pointing the reader to the wider literature. Judicious use of figures makes complex concepts easier to follow without oversimplifying. As the only dictionary on the market, this will be a guiding reference for all those working in, or learning, probability together with its applications.Trade Review'To construct a dictionary about such an enormous field is a daunting task, and David Stirzaker deserves high praise, first for even attempting to do so, and second for the success he has achieved. A dictionary's usefulness depends on its organisation as well as on the quality of the individual entries, and this book's structure is simple and logical: two initial pages list the abbreviations and symbols, then the main body of 3000-odd entries with easy-to-use cross-referencing, ending with an appendix of probability distributions … I shall be delighted to possess this authoritative tome. It will sit alongside Abramowitz and Steguns' Handbook of Mathematical Functions as a reliable source of enlightenment.' John Haigh, University of SussexTable of ContentsPreface; Table of distributions; The dictionary.

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Book SynopsisAs researchers try to predict the effects of human modification at all trophic levels and mediate the impact of rapid environmental change, it has become clear it is no longer a matter of agreeing that both bottom-up and top-down forces play important roles in diverse ecosystems. Rather, the question is: how do these forces interact across aquatic and terrestrial systems? Written by leading experts in the field, this book presents a unique synthesis of trophic relationships within and across ecosystems that is a valuable foundation for the development of cross-system, multidisciplinary research. It also provides new insights into population biology and community ecology and examines the interactive effects of bottom-up and top-down forces on biodiversity at each trophic level. A one-stop resource for learning about bottom-up and top-down interactions, this book encourages discussion and collaboration among researchers to identify similarities and differences in trophic interactions acrTable of ContentsList of contributors; Preface; Part I. Theory: 1. Theoretical perspectives on bottom-up and top-down interactions across ecosystems Shawn J. Leroux and Michel Loreau; Part II. Ecosystems: 2. The spatio-temporal dynamics of trophic control in large marine ecosystems Kenneth T. Frank, Jonathan A. D. Fisher and William C. Leggett; 3. Top-down and bottom-up interactions in freshwater ecosystems: emerging complexities Jason M. Taylor, Michael J. Vanni and Alexander S. Flecker; 4. Top-down and bottom-up interactions determine tree and herbaceous layer dynamics in savannah grasslands A. Carla Staver and Sally Koerner; 5. Bottom-up and top-down forces shaping wooded ecosystems: lessons from a cross-biome comparison Dries P. J. Kuijper, Mariska te Beest, Marcin Churski and Joris P. G. M. Cromsigt; 6. Dynamic systems of exchange link trophic dynamics in freshwater and terrestrial food webs John L. Sabo and David Hoekman; 7. Bottom-up and top-down interactions in coastal interface systems Jan P. Bakker, Karina J. Nielsen, Juan Alberti, Francis Chan, Sally D. Hacker, Oscar O. Iribarne, Dries P. J. Kuijper, Bruce A. Menge, Maarten Schrama and Brian R. Silliman; Part III. Patterns and Processes: 8. Influence of plant defences and nutrients on trophic control of ecosystems Karin T. Burghardt and Oswald J. Schmitz; 9. Interactive effects of plants, decomposers, herbivores, and predators on nutrient cycling Sarah E. Hobbie and Sébastien Villéger; 10. The role of bottom-up and top-down interactions in determining microbial and fungal diversity and function Thomas W. Crowther and Hans-Peter Grossart; 11. The question of scale in trophic ecology Lee A. Dyer, Tara J. Massad and Matthew L. Forister; 12. The role of species diversity in bottom-up and top-down interactions Jerome J. Weis; 13. Plant and herbivore evolution within the trophic sandwich Luis Abdala-Roberts and Kailen A. Mooney; 14. Bottom-up and top-down interactions across ecosystems in an era of global change Kimberly J. La Pierre and Torrance C. Hanley; Index.

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Book SynopsisThis authoritative work provides an in-depth treatment of state space methods, with a range of applications in neural and clinical data. Advanced and state-of-the-art research topics are detailed, including topics in state space analyses, maximum likelihood methods, variational Bayes, sequential Monte Carlo, Markov chain Monte Carlo, nonparametric Bayesian, and deep learning methods. Details are provided on practical applications in neural and clinical data, whether this is characterising time series data from neural spike trains recorded from the rat hippocampus, the primate motor cortex, or the human EEG, MEG or fMRI, or physiological measurements of heartbeats or blood pressures. With real-world case studies of neuroscience experiments and clinical data sets, and written by expert authors from across the field, this is an ideal resource for anyone working in neuroscience and physiological data analysis.Table of Contents1. Introduction Z. Chen; 2. Inference and learning in latent Markov models D. Barber and S. Chiappa; Part I. State Space Methods for Neural Data: 3. State space methods for MEG source reconstruction M. Fukushima, O. Yamashita and M. Sato; 4. Autoregressive modeling of fMRI time series: state space approaches and the general linear model A. Galka, M. Siniatchkin, U. Stephani, K. Groening, S. Wolff, J. Bosch-Bayard and T. Ozaki; 5. State space models and their spectral decomposition in dynamic causal modeling R. Moran; 6. Estimating state and parameters in state space models of spike trains J. H. Macke, L. Buesing and M. Sahani; 7. Bayesian inference for latent stepping and ramping models of spike train data K. W. Latimer, A. C. Huk and J. W. Pillow; 8. Probabilistic approaches to uncover rat hippocampal population codes Z. Chen, F. Kloosterman and M. A. Wilson; 9. Neural decoding in motor cortex using state space models with hidden states W. Wu and S. Liu; 10. State-space modeling for analysis of behavior in learning experiments A. C. Smith; Part II. State Space Methods for Clinical Data: 11. Bayesian nonparametric learning of switching dynamics in cohort physiological time series: application in critical care patient monitoring L. H. Lehman, M. J. Johnson, S. Nemati, R. P. Adams and R. G. Mark; 12. Identifying outcome-discriminative dynamics in multivariate physiological cohort time series S. Nemati and R. P. Adams; 13. A dynamic point process framework for assessing heartbeat dynamics and cardiovascular functions Z. Chen and R. Barbieri; 14. Real-time segmentation and tracking of brain metabolic state in ICU EEG recordings of burst suppression M. B. Westover, S. Ching, M. M. Shafi, S. S. Cash and E. N. Brown; 15. Signal quality indices for state-space electrophysiological signal processing and vice versa J. Oster and G. D. Clifford.

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Book SynopsisBased on a course taught by the author, this book combines the theoretical underpinnings of statistics with the practical analysis of Earth sciences data using MATLAB. The book is organized to introduce the underlying concepts, and then extends these to the data, covering methods that are most applicable to Earth sciences. Topics include classical parametric estimation and hypothesis testing, and more advanced least squares-based, nonparametric, and resampling estimators. Multivariate data analysis, not often encountered in introductory texts, is presented later in the book, and compositional data is treated at the end. Datasets and bespoke MATLAB scripts used in the book are available online, as well as additional datasets and suggested questions for use by instructors. Aimed at entering graduate students and practicing researchers in the Earth and ocean sciences, this book is ideal for those who want to learn how to analyse data using MATLAB in a statistically-rigorous manner.Trade Review'One of the main strengths of this book is the combination of mathematical rigor with extensive examples, allowing readers to work through case studies to better understand the concepts presented. The tool used for this purpose is MATLAB, which is widely used in the earth science community. Examples are drawn from geophysics, astrophysics, and anthropology (among others). Both the scripts and the data examples used in the book are available for download from the publisher's website. … This book is an ideal guide for graduate students seeking a comprehensive and rigorous understanding of statistical methods in earth sciences. For the more mature earth scientist (and I include myself in that number), it provides a useful reference to widely used statistical concepts that many of us regularly encounter.' Lucy MacGregor, The Leading Edge'… this book will be a welcome and invaluable addition to any earth scientist's library.' Sven Treitel, The Leading EdgeTable of ContentsPreface; 1. Probability concepts; 2. Statistical concepts; 3. Statistical distributions; 4. Characterization of data; 5. Point, interval and ratio estimators; 6. Hypothesis testing; 7. Nonparametric methods; 8. Resampling methods; 9. Linear regression; 10. Multivariate statistics; 11. Compositional data; Appendix: MATLAB functions to produce ternary diagrams; References; Index.

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Book SynopsisOver the past three decades there has been a total revolution in the classic branch of mathematics called 3-dimensional topology, namely the discovery that most solid 3-dimensional shapes are hyperbolic 3-manifolds. This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal proofs. The book is heavily illustrated with pictures, mostly in color, that help explain the manifold properties described in the text. Each chapter ends with a set of exercises and explorations that both challenge the reader to prove assertions made in the text, and suggest further topics to explore that bring additional insight. There is an extensive index and bibliography.Trade Review'The diagrams, over 60 in number and for the most part highly intricate computer-generated graphics, will leave the reader craving for more.' Tushar Das, MAA Reviews'With its plenitude of exercises, both closed- and open-ended, and its extensive index and bibliography, this book merits what a reviewer wrote of the first edition: its 'topic's central importance and the author's singular viewpoint earn this book a place in all academic libraries.' Summing Up: Recommended. Upper-division undergraduates and above; faculty and professionals.' F. E. J. Linton, CHOICE'… the book provides an excellent overview of the developments of recent decades in the theory of hyperbolic 3-manifolds.' Thilo Kuessner, Mathematical ReviewsTable of ContentsList of illustrations; Preface; 1. Hyperbolic space and its isometries; 2. Discrete groups; 3. Properties of hyperbolic manifolds; 4. Algebraic and geometric convergence; 5. Deformation spaces and the ends of manifolds; 6. Hyperbolization; 7. Line geometry; 8. Right hexagons and hyperbolic trigonometry; Bibliography; Index.

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Book SynopsisThis book provides a rigorous yet accessible introduction to the scientific study of sociology and other social sciences. It is designed to provide students with the basic tools needed to be both critical consumers and beginning producers of scholarly social science research.Trade Review'Kellstedt, Whitten, and Tuch provide an accessible, sophisticated text. With well-chosen examples, they show why a full understanding of research design, theory construction, and causal inference is essential for effective use of our modern toolkit of data analysis techniques.' Stephen L. Morgan, Johns Hopkins University'A comprehensive and well-written introduction to the techniques and logic of social research. The logic and application of a wide range of methodological techniques are explained eloquently and clearly, and the examples used cut across social science disciplines. This book should be widely used in methods courses across the social sciences.' George Wilson, University of Miami'This valuable textbook is unique for two reasons: first, it seamlessly integrates theory, research design, and data analysis, providing students with the foundation required to develop empirically grounded research projects that can make theoretical progress in social science. Second, it is accessible and engaging, drawing students in and showing them how stimulating and exciting social research can be.' Michael Hughes, Virginia TechTable of ContentsList of Figures; List of Tables; Preface; Acknowledgments; 1. The Scientific Study of Society; 2. The Art of Theory Building; 3. Evaluating Causal Relationships; 4. Research Design; 5. Survey Research; 6. Measuring Concepts of Interest; 7. Getting to Know Your Data; 8. Probability and Statistical Inference; 9. Bivariate Hypothesis Testing; 10. Two-Variable Regression Models; 11. Multiple Regression; 12. Putting it all Together to Produce Effective Research; Appendix A. Critical Values of Chi-square; Appendix B. Critical Values of t; Appendix C. The Λ Link Function for Binomial Logit Models; Appendix D. The Φ Link Function for Binomial Probit Models; References; Index.

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Book SynopsisExploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exerciseTrade Review'Wonderful list of topics, entertaining presentation, well-chosen problems - this is the way I want my grandchildren to engage with the beauty of mathematics. Too many students enter college with tools from calculus but no concept of how mathematicians think, and hardly any exposure to sets, logic, numbers, groups, or probability. How can we expect them to decide about continuing with mathematics, without a glimpse of the wonders ahead? A marvelous world lies at your students' doorstep, and Exploring Mathematics makes them players, not just observers, in that world. You'll want all your math majors, and perhaps your computer science majors as well, to have this experience.' Peter Winkler, Dartmouth College, New Hampshire'Meier and Smith have written a wonderful introduction to higher mathematics, showing both the thrill of abstraction and the beauty in discovering proofs.' Tom Garrity, Williams College, Massachusetts'I think that this is an excellent book. It is playful and serious at the same time. The book takes the unusual step of explaining not just mathematical topics but also what math is about and how to do it. The book is full of interesting topics, exercises, and examples. I think that this book could really fire up the imagination of a student wanting to get a start in real mathematics.' Richard Schwartz, Brown University, Rhode Island'The biggest step in studying mathematics is learning to write proofs. After calculus, students discover that truth is not a matter of a calculation, but a careful argument, juggling concepts within formal logic. Exploring Mathematics is a guide to this new level. Rich with exercises and projects, the book provides a well-grounded introduction to proof. 'Then the fun begins'. The reader participates by doing what mathematicians do, experimenting, formulating conjectures, exploring foundations for the basis of a proof. This book engages the reader fully to reach the goal of learning to fashion real mathematics. A valuable addition to every undergraduate library.' John McCleary, Vassar College, New YorkTable of Contents1. Let's play!; 2. Discovering and presenting mathematics; 3. Sets; 4. The integers and the fundamental theorem of arithmetic; 5. Functions; 6. Relations; 7. Cardinality; 8. The real numbers; 9. Probability and randomness; 10. Algebra and symmetry; 11. Projects; Appendix A. Solutions, answers, or hints to in-text exercises; Index; Bibilography.

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Book SynopsisExploration seismology uses seismic imaging to form detailed images of the Earth''s interior, enabling the location of likely petroleum targets. Due to the size of seismic datasets, sophisticated numerical algorithms are required. This book provides a technical guide to the essential algorithms and computational aspects of data processing, covering the theory and methods of seismic imaging. The first part introduces an extensive online library of MATLAB seismic data processing codes maintained by the CREWES project at the University of Calgary. Later chapters then focus on digital signal theory and relevant aspects of wave propagation and seismic modelling, followed by deconvolution and seismic migration methods. Presenting a rigorous explanation of how to construct seismic images, it provides readers with practical tools and codes to pursue research projects and analyses. It is ideal for advanced students and researchers in applied geophysics, and for practicing exploration geoscientiTrade Review'This book is a masterpiece in scope and content. It explains the essential algorithms and computational aspects of data processing, covering the theory and methods of seismic imaging. A particularly outstanding feature is that it gives useful methods and tools to pursue research projects and analyses - representing the way that things should be taught in the computer age. For this reason, it should be adopted in the undergraduate curriculum and will be a wonderful resource for graduate students and researchers in applied geophysics. Practicing geoscientists will also welcome this book as it will make their daily tasks easier and more productive.' Enders Robinson, Columbia University, New York City'The authors are to be commended for putting together this valuable resource which will instantly be highly useful to many geophysicists in the academic and industrial communities. The book is a pleasing and unusual mixture of rigorous geophysical signal processing theory and practical concepts, algorithms and code snippets. The MATLAB library functions and scripts that are provided or available for download will prove indispensable to all readers.' Peter Cary, Chief Geophysicist, TGS Canada'… Numerical Methods of Exploration Seismology and its elegant MATLAB codes are a must for explorationists' bookshelves.' Sven Treitel, The Leading EdgeTable of ContentsPreface; 1. Introduction to MATLAB and seismic data; 2. Signal theory – continuous; 3. Signal theory – discrete; 4. Wave propagation and seismic modelling; 5. Deconvolution – the estimation of reflectivity; 6. Velocity measures and ray tracing; 7. Elementary migration methods; References; Index.

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Book SynopsisThe theory of Hardy spaces is a cornerstone of modern analysis. It combines techniques from functional analysis, the theory of analytic functions and Lesbesgue integration to create a powerful tool for many applications, pure and applied, from signal processing and Fourier analysis to maximum modulus principles and the Riemann zeta function. This book, aimed at beginning graduate students, introduces and develops the classical results on Hardy spaces and applies them to fundamental concrete problems in analysis. The results are illustrated with numerous solved exercises that also introduce subsidiary topics and recent developments. The reader''s understanding of the current state of the field, as well as its history, are further aided by engaging accounts of important contributors and by the surveys of recent advances (with commented reference lists) that end each chapter. Such broad coverage makes this book the ideal source on Hardy spaces.Trade Review'This is a beautiful introduction to a beautiful subject. The author does a masterful job of choosing topics that give a solid introduction to Hardy spaces without overwhelming the reader with too much too soon. Every student of mathematics should enjoy this book.' John McCarthy, Washington University, St Louis'This is an excellent, highly-recommendable book by a leading expert in the field. Describing in a self-contained way the classical approach to Hardy spaces and their applications - with emphasis on the invariant subspace point of view - it also offers an entertaining journey into the history of twentieth-century analysis.' Joaquim Bruna, Universitat Autònoma de Barcelona'The author has created a very interesting text that will serve as a source of basic material and an introduction for those interested in the interactions between harmonic analysis, complex analysis, and operator theory. Any researcher who masters the material in this text is well placed to read the more intensive monographs that further develop the interactions of these subjects.' Brett Wick, Washington University, St Louis'From the high stand due to a lifelong affinity for the subject, Nikolaï Nikolski delineates and recounts the fascinating history of Hardy space with style. His inviting text is sparkled with biographical snapshots, colorful anecdotes, and insightful remarks, conveying a vivid picture of the field. The mathematical discourse is light, yet rigorous and self-contained. Carefully selected problems offer the earnest reader perspectives into current research. The apogee chapter is devoted to the immersion of the daunting Riemann hypothesis into Hardy space framework … Nikolski's text is a truly masterful piece of scholarship.' Mihai Putinar, University of California, Santa Barbara'This is a comfortably paced introduction to the theory of Hardy spaces, starting at a level of advanced graduate students in analysis … Historical context and biographical details of the main researchers of the field is discussed more deeply than in comparable books.' M. Bona, Choice'To help the reader through this material, Nikolski is both an experienced educator and writer and knows how to present the material, efficiently … so the student can learn as well as appreciate the subject. Nikolski also gives us plenty of historical vignettes of the main figures in the development of Hardy spaces and, especially for the student, gives several appendices for those needing some gentle reminders of measure theory, complex analysis, Hilbert spaces, Banach spaces, and operator theory.' William T. Ross, Bulletin of the American Mathematical SocietyTable of ContentsThe origins of the subject; 1. The space H^2(T). An archetypal invariant subspace; 2. The H^p(D) classes. Canonical factorization and first applications; 3. The Smirnov class D and the maximum principle; 4. An introduction to weighted Fourier analysis; 5. Harmonic analysis and stationary filtering; 6. The Riemann hypothesis, dilations, and H^2 in the Hilbert multi-disk; Appendix A. Key notions of integration; Appendix B. Key notions of complex analysis; Appendix C. Key notions of Hilbert spaces; Appendix D. Key notions of Banach spaces; Appendix E. Key notions of linear operators; References; Notation; Index.

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Book SynopsisNonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.Trade Review'This book has been written by a well-established researcher in the field. His expertise is evidenced by the deft exposition of relatively challenging material. In that regard, one of the very useful functions of this book is its provision of a number of background mathematical techniques in Hamiltonians systems, symplectic geometry, Noether theory and Lagrangian field theory.' K. Alan Shore, Contemporary Physics'The book is clearly written, and only the most basic knowledge of Hamiltonian and Lagrangian theories is required.' Wen-Xiu Ma, MathSciNetTable of Contents1. Introduction; 2. Hamiltonian ODEs and relative equilibria; 3. Modulation of relative equilibria; 4. Revised modulation near a singularity; 5. Introduction to Whitham Modulation Theory – the Lagrangian viewpoint; 6. From Lagrangians to Multisymplectic PDEs; 7. Whitham Modulation Theory – the multisymplectic viewpoint; 8. Phase modulation and the KdV equation; 9. Classical view of KdV in shallow water; 10. Phase modulation of uniform flows and KdV; 11. Generic Whitham Modulation Theory in 2+1; 12. Phase modulation in 2+1 and the KP equation; 13. Shallow water hydrodynamics and KP; 14. Modulation of three-dimensional water waves; 15. Modulation and planforms; 16. Validity of Lagrangian-based modulation equations; 17. Non-conservative PDEs and modulation; 18. Phase modulation – extensions and generalizations; Appendix A. Supporting calculations – 4th and 5th order terms; Appendix B. Derivatives of a family of relative equilibria; Appendix C. Bk and the spectral problem; Appendix D. Reducing dispersive conservation laws to KdV; Appendix E. Advanced topics in multisymplecticity; References; Index.

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Book SynopsisMajor shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact of model theory on contemporary algebraic geometry, number theory, combinatorics, and differential equations. This comprehensive and detailed book will interest logicians and mathematicians as well as those working on the history and philosophy of mathematics.Trade Review'The book under review has a lot to offer at many levels. First of all, it may serve as a guide to recent advances in pure and applied model theory. Such a guide may be useful not only to novices, but also to old hands. Secondly, Baldwin summarizes several trends in contemporary philosophy of mathematics, and his insights should be of interest to philosophers as well as to mathematicians.' Roman Kossak, The Mathematical IntelligencerTable of ContentsPart I. Refining the Notion of Categoricity: 1. Formalization; 2. The context of formalization; 3. Categoricity; Part II. The Paradigm Shift: 4. What was model theory about?; 5. What is contemporary model theory about?; 6. Isolating tame mathematics; 7. Infinitary logic; 8. Model theory and set theory; Part III. Geometry: 9. Axiomatization of geometry; 10. π, area, and circumference of circles; 11. Complete: the word for all seasons; Part IV. Methodology: 12. Formalization and purity in geometry; 13. On the nature of definition: model theory; 14. Formalism-freeness; 15. Summation.

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Book SynopsisProbing and controlling electrons and nuclei in matter at the attosecond timescale became possible with the generation of attosecond pulses by few-cycle intense lasers, and has revolutionized our understanding of atomic structure and molecular processes. This book provides an intuitive approach to this emerging field, utilizing simplified models to develop a clear understanding of how matter interacts with attosecond pulses of light. An introductory chapter outlines the structure of atoms and molecules and the properties of a focused laser beam. Detailed discussion of the fundamental theory of attosecond and strong-field physics follows, including the molecular tunnelling ionization model (MO-ADK theory), the quantitative rescattering (QRS) model, and the laser induced electronic diffraction (LIED) theory for probing the change of atomic configurations in a molecule. Highlighting the cutting-edge developments in attosecond and strong field physics, and identifying future opportunities Trade Review'This is the book we were waiting for…Definitely a must-have!' Jens Biegert, The Institute of Photonic Sciences (ICFO)'… a very accessible introduction to the emerging fields of attosecond science and strong field laser physics … This book will be a valuable resource for both new students and experienced researchers in the field.' Mark Vrakking, Max Born Institute, Berlin'The first reference in the attosecond and strong field community.' Katsumi Midorikawa, Director, RIKEN Center for Advanced Photonics'This is a textbook dedicated to graduate students who wish to understand strong laser fields and attosecond physics. The book is very clearly written and beautifully illustrated, the majority of figures being in color. Exercises and references are found at the end of all chapters … Since attosecond pulses are a booming area of research, with many applications, this book is a must for university libraries and can be read easily by students and experts in the field. Daniela Dragoman, Optics & Photonics NewsTable of ContentsPreface; 1. Elements of atoms, molecules and wave propagation; 2. Basic formulation of interactions between an intense laser pulse and atoms; 3. Strong field ionization and low-energy electron spectra of atoms and molecules; 4. Rescattering and laser-induced electron diffraction; 5. Fundamentals of high-order harmonic generation; 6. Applications of high-order harmonics: HHG spectroscopy and optimization of harmonics; 7. Generation and characterization of attosecond pulses; 8. Probing electron dynamics with isolated attosecond pulses; List of books; Solutions to selected problems; Index.

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Book SynopsisFrom Measures to Itô Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Itô integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure theory. This text is ideal preparation for graduate-level courses in mathematical finance and perfect for any reader seeking a basic understanding of the mathematics underpinning the various applications of Itô calculus.Table of ContentsPreface; 1. Probability and measure; 2. Measures and distribution functions; 3. Measurable functions/random variables; 4. Integration and expectation; 5. Lp-spaces and conditional expectation; 6. Discrete-time martingales; 7. Brownian motion; 8. Stochastic integrals; Bibliography; Index.

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Book SynopsisState-of-the-art analysis of geological structures has become increasingly quantitative but traditionally, graphical methods are used in teaching. This innovative lab book provides a unified methodology for problem-solving in structural geology using linear algebra and computation. Assuming only limited mathematical training, the book begins with classic orientation problems and progresses to more fundamental topics of stress, strain and error propagation. It introduces linear algebra methods as the foundation for understanding vectors and tensors, and demonstrates the application of geometry and kinematics in geoscience without requiring students to take a supplementary mathematics course. All algorithms are illustrated with a suite of online MATLAB functions, allowing users to modify the code to solve their own structural problems. Containing 20 worked examples and over 60 exercises, this is the ideal lab book for advanced undergraduates or beginning graduate students. It will also pTrade Review'I like this book. The material covered, the level of detail and the inclusion of MATLAB scripts make this a timely, relevant and very useful textbook … [it] will help structural geologists - of all levels - make that critical leap from purely geometrical analyses, through kinematics and into the underlying continuum mechanics of rock deformation. A worthy addition to your bookshelf.' Geological Magazine'I highly recommend this book to all structural geology students and practitioners, as well as to earth scientists from a wide range of fields, who will benefit from this clear introduction of the principles and application of linear algebra in the analysis of commonly encountered vector and tensor quantities.' Roland Bürgmann, University of California, Berkeley'The book is suitable for numerate researchers and advanced undergraduates who are reasonably comfortable with mathematics … it is essential in the twenty-first century that we have numerate geoscientists trained in quantitative techniques of structural geology … The authors take care to describe the basics of tensor algebra as well as its application; this book is a solid foundation for understanding the mathematical analysis of how the Earth deforms.' John Wheeler, American MineralogistTable of ContentsPreface; 1. Problem solving in structural geology; 2. Coordinate systems, scalars and vectors; 3. Transformations of coordinate axes and vectors; 4. Matrix operations and indicial notation; 5. Tensors; 6. Stress; 7. Introduction to deformation; 8. Infinitesimal strain; 9. Finite strain; 10. Progressive strain histories and kinematics; 11. Velocity description of deformation; 12. Error analysis; References; Index.

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Book SynopsisRandom set theory is a fascinating branch of mathematics that amalgamates techniques from topology, convex geometry, and probability theory. Social scientists routinely conduct empirical work with data and modelling assumptions that reveal a set to which the parameter of interest belongs, but not its exact value. Random set theory provides a coherent mathematical framework to conduct identification analysis and statistical inference in this setting and has become a fundamental tool in econometrics and finance. This is the first book dedicated to the use of the theory in econometrics, written to be accessible for readers without a background in pure mathematics. Molchanov and Molinari define the basics of the theory and illustrate the mathematical concepts by their application in the analysis of econometric models. The book includes sets of exercises to accompany each chapter as well as examples to help readers apply the theory effectively.Trade Review'The book builds upon and greatly elaborates on the pioneering, fundamental work that Arie Beresteanu, Ilya Molchanov, and Francesca Molinari did on connecting econometric models with missing data and set-valued responses - such as games with multiple equilibria - to the theory of random sets, a beautiful field of mathematics, probability theory, and mathematical economics. It should be of equal interest to students and researchers in mathematical statistics, econometrics, and machine learning, particularly in problems where set-valued predictions arise, in either observational or counterfactual settings.' V. Chernozhukov, Economics Department and Center for Statistics and Data Science, Massachusetts Institute of Technology'This book will be very useful to graduate students, faculty, and other researchers interested in the exciting new area of partial identification. Partial identification analysis has become important in empirical economics, largely motivated by revealed preference ideas. Random sets provide a useful and important way of approaching these problems. They are particularly helpful in obtaining sharp identified sets, e.g. ones that are as small as possible. This book is timely and useful in providing an introduction to this new area that is clear and gives the necessary mathematical background for a good understanding of and research on these methods.' Whitney Newey, Ford Professor of Economics, Massachusetts Institute of Technology'Random set theory provides the natural abstract mathematical language for study of partial identification. Molchanov and Molinari, a brilliant collaboration of mathematician and econometrician, present the fundamentals meticulously and describe the fruitful applications to date. Their book provides the foundation for much more to come.' Charles F. Manski, Board of Trustees Professor in Economics, Northwestern University, Illimois'Molchanov and Molinari define the basics of the theory and illustrate the mathematical concepts by their application in the analysis of econometric models. The book includes sets of exercises to accompany each chapter as well as examples to help readers apply the theory effectively.' Hans-Jürgen Schmidt, ZB Math ReviewsTable of Contents1. Basic concepts; 2. Selections; 3. Expectation of random sets; 4. Limit theorems for Minkowski sums; 5. Estimation and interference.

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Book SynopsisThis textbook provides an introduction to the scientific study of sociology and other social sciences. It offers the basic tools necessary for readers to become both critical consumers and beginning producers of scientific research on society. The authors present an integrated approach to research design and empirical analyses in which researchers can develop and test causal theories. They use examples from social science research that students will find engaging and inspiring and that will help them to understand key concepts. The book makes technical materials accessible to students who might otherwise be intimidated by mathematical examples. This new text, with the addition of sociologist Steven A. Tuch to the author team, follows the successful format, approach, and pedagogical features in Paul M. Kellstedt and Guy D. Whitten''s bestselling text, The Fundamentals of Political Science Research, now in its third edition. Workbooks in Stata, SPSS, and R, three of the most popular statTrade Review'Kellstedt, Whitten, and Tuch provide an accessible, sophisticated text. With well-chosen examples, they show why a full understanding of research design, theory construction, and causal inference is essential for effective use of our modern toolkit of data analysis techniques.' Stephen L. Morgan, Johns Hopkins University'A comprehensive and well-written introduction to the techniques and logic of social research. The logic and application of a wide range of methodological techniques are explained eloquently and clearly, and the examples used cut across social science disciplines. This book should be widely used in methods courses across the social sciences.' George Wilson, University of Miami'This valuable textbook is unique for two reasons: first, it seamlessly integrates theory, research design, and data analysis, providing students with the foundation required to develop empirically grounded research projects that can make theoretical progress in social science. Second, it is accessible and engaging, drawing students in and showing them how stimulating and exciting social research can be.' Michael Hughes, Virginia TechTable of ContentsList of Figures; List of Tables; Preface; Acknowledgments; 1. The Scientific Study of Society; 2. The Art of Theory Building; 3. Evaluating Causal Relationships; 4. Research Design; 5. Survey Research; 6. Measuring Concepts of Interest; 7. Getting to Know Your Data; 8. Probability and Statistical Inference; 9. Bivariate Hypothesis Testing; 10. Two-Variable Regression Models; 11. Multiple Regression; 12. Putting it all Together to Produce Effective Research; Appendix A. Critical Values of Chi-square; Appendix B. Critical Values of t; Appendix C. The Λ Link Function for Binomial Logit Models; Appendix D. The Φ Link Function for Binomial Probit Models; References; Index.

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Book SynopsisThis volume contains a selection of survey articles and original research papers concerned with the rigorous mathematical theory of fluid mechanics, written by leading researchers. The book serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.Table of ContentsPreface; List of contributors; 1. Towards fluid equations by approximate deconvolution models L. C. Berselli; 2. On flows of fluids described by an implicit constitutive equation characterized by a maximal monotone graph M. Bulíček, P. Gwiazda, J. Málek, K. R. Rajagopal and A. Świerczewska-Gwiazda; 3. A continuous model for turbulent energy cascade A. Cheskidov, R. Shvydkoy and S. Friedlander; 4. Remarks on complex fluid models P. Constantin; 5. A naive parametrization for the vortex-sheet problem A. Castro, D. Córdoba and F. Gancedo; 6. Sharp and almost-sharp fronts for the SQG equation C. L. Fefferman; 7. Feedback stabilization for the Navier–Stokes equations: theory and calculations A. V. Fursikov and A. A. Kornev; 8. Interacting vortex pairs in inviscid and viscous planar flows T. Gallay; 9. Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier–Stokes equations J. D. Gibbon and D. D. Holm; 10. Exploring symmetry plane conditions in numerical Euler solutions R. M. Kerr and M. D. Bustamante; 11. On the decay of solutions of the Navier–Stokes system with potential forces I. Kukavica; 12. Leray–Hopf solutions to Navier–Stokes equations with weakly converging initial data G. Seregin.

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Book SynopsisFreshwater fish are one of the most diverse groups of vertebrates, but are also amongst the most threatened. With contributions from leaders in the field, this is the first assessment of the global state of freshwater fish diversity, synthesising the opportunities, challenges and barriers facing the conservation of freshwater fish biodiversity. The book includes the first global assessment of the number, type and distribution of threatened freshwater fish species, discussing the features of freshwater fish biology and ecology that render so many species vulnerable to extinction. Introductory chapters on why freshwater fish are so sensitive to environmental change and disturbance lead into chapters providing detailed reviews of the key threatening processes and potential solutions. A concluding chapter summarises the key issues and looks to the future for opportunities and challenges for the conservation and management of freshwater fish.Trade Review'It is not often that I moved to write that a book is excellently and authoritatively written and edited throughout, but this is one of those rare occasions … I unhesitatingly recommend this book to anyone involved with freshwater fish conservation in any capacity. … The excellent reviews and thoughts presented here will certainly bring such readers rapidly up to speed on the current state of freshwater fish conservation around the world. Finally, this book also lends itself to adoption as a teaching text for advanced undergraduate and postgraduate classes, with all but the last chapter ending with a series of discussion questions which would serve well as tutorial, essay and even examination subjects!' Ian J. Winfield, Journal of Fish BiologyTable of ContentsList of contributors; Preface; 1. Lost fishes, who is counting? The extent of the threat to freshwater fish biodiversity William R. T. Darwall and Jörg Freyhof; 2. Why are freshwater fish so threatened? Gerard P. Closs, Paul L. Angermeier, William R. T. Darwall and Stephen R. Balcombe; 3. Climate change effects on freshwater fishes, conservation and management Jani Heino, Jaakko Erkinaro, Ari Huusko and Miska Luoto; 4. Challenges and opportunities for fish conservation in dam-impacted waters Julian D. Olden; 5. Chemical pollution Nathaniel L. Scholz and Jenifer K. McIntyre; 6. Multiple stressor effects on freshwater fish: a review and meta-analysis Christoph D. Matthaei and Katharina Lange; 7. Infectious disease and the conservation of freshwater fish Martin Krkosek and Robert Poulin; 8. Non-indigenous fishes and their role in freshwater fish imperilment M. Jake Vander Zanden, Nicolas W. R. Lapointe and Michael P. Marchetti; 9. Riparian management and the conservation of stream ecosystems and fishes Mark S. Wipfli and John S. Richardson; 10. Fragmentation, connectivity and fish species persistence in freshwater ecosystems Keith B. Gido, James E. Whitney, Joshuah S. Perkin and Thomas F. Turner; 11. Conservation of migratory fishes in freshwater ecosystems Peter B. McIntyre, Catherine Reidy Liermann, Evan Childress, Ellen J. Hamann, J. Derek Hogan, Stephanie R. Januchowski-Hartley, Aaron A. Koning, Thomas M. Neeson, Daniel L. Oele and Brenda M. Pracheil; 12. Protecting apex predators Kirk O. Winemiller, Paul Humphries and Bradley J. Pusey; 13. Artificial propagation of freshwater fishes: benefits and risks to recipient ecosystems from stocking, translocation, and re-introduction John Epifanio and Robin Waples; 14. Freshwater conservation planning Virgilio Hermoso, Simon Linke, Stephanie R. Januchowski-Hartley and Mark J. Kennard; 15. Sustainable inland fisheries - perspectives from the recreational, commercial and subsistence sectors from around the globe Steven J. Cooke, Vivian M. Nguyen, John M. Dettmers, Robert Arlinghaus, Michael C. Quist, Denis Tweddle, Olaf L. F. Weyl, Rajeev Raghavan, Marcela Portocarrero-Aya, Edwin Agudelo Córdoba and Ian G. Cowx; 16. Understanding and conserving genetic diversity in a world dominated by alien introductions and native transfers: the case study of primary and peripheral freshwater fishes in Southern-Europe Valerio Ketmaier and Pier Giorgio Bianco; 17. Maintaining taxonomic skills: the decline of taxonomy - a threat to fish conservation Maria J. Collares-Pereiram, Paul H. Skelton and Ian G. Cowx; 18. Synthesis - what is the future of freshwater fishes? Gerard P. Closs, Martin Krkosek and Julian D. Olden; Index.

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Book SynopsisThe availability of large data sets has allowed researchers to uncover complex properties such as large-scale fluctuations and heterogeneities in many networks, leading to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. This book presents a comprehensive account of these effects. A vast number of systems, from the brain to ecosystems, power grids and the internet, can be represented as large complex networks. This book will interest graduate students and researchers in many disciplines, from physics and statistical mechanics to mathematical biology and information science. Its modular approach allows readers to readily access the sections of most interest to them, and complicated maths is avoided so the text can be easily followed by non-expertTrade ReviewReview of the hardback: 'With a focus in dynamical processes, this book is an excellent introduction … on the statistical mechanics approach of networks … Not only [does] it consist of a wide array of commonly used techniques in the discipline but also it provides multitudes of the techniques' applied examples … this book could serve as an introduction book and a reference to new-to-the-topic JASSS readers. To conclude, I believe that this book has contributed another step in integrating the vast multidisciplinary approaches in network science.' Journal of Artificial Societies and Social SimulationReview of the hardback: '… the book does a terrific and admirable job at putting some order into the wealth of research that has emerged during the last decade … a fantastic resource book on dynamical processes on complex networks, and its wide scope promises to keep it relevant for several years to come.' Journal of Statistical PhysicsReview of the hardback: '… a very useful book that fills an important gap in the market of books on networks … I will be opening this book whenever I want to start modelling a dynamical process on a network.' Contemporary Physics'The book does a remarkably good job in getting to the mathematical foundations of dynamical processes and complex networks. Hence, it should belong in the bookshelf of any sociologist who is seriously interested in complex and dynamic networks. It gives a great overview of techniques in the field and provides the mathematical depth one wishes for in a manner sociologists can understand. In sum, the book has potential to become a reference like Wasserman and Faust (1994) and offers significant (technical) value to sociologists who seriously want to get into the mathematics behind dynamical processes and complex networks.' Thomas U. Grund, Journal of Mathematical SociologyTable of ContentsPreface; Acknowledgements; List of abbreviations; 1. Preliminaries: networks and graphs; 2. Networks and complexity; 3. Network models; 4. Introduction to dynamical processes: theory and simulation; 5. Phase transitions on complex networks; 6. Resilience and robustness of networks; 7. Synchronization phenomena in networks; 8. Walking and searching on networks; 9. Epidemic spreading in population networks; 10. Social networks and collective behavior; 11. Traffic on complex networks; 12. Networks in biology: from the cell to ecosystems; 13. Postface: critically examining complex networks science; Appendixes; References; Index.

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Book SynopsisCovering all the main animal groups, from jellyfish to mammals, this book considers key questions about evolution. Its conversational, nontechnical style makes it an ideal text for beginning undergraduates and general readers. The chapters cover both evolutionary pattern (trees, relationships) and evolutionary process (mechanisms, including Darwinian natural selection).Trade Review'Wallace Arthur, a renowned evolutionary biologist, has written another of his excellent and easily approachable books introducing concepts, ideas and evidence of evolution. This new book is written in an informal style that a non-biologist should be able to follow without difficulty. He covers animal evolution from its beginning in deep time, and explains current ideas simply … Highly recommended for schools and biology students of all levels as well as the general reader.' Jennifer A. Clack, University Museum of Zoology, Cambridge'In Evolving Animals, the reader is taken on a tour through the major events in the history of animal life, from the Cambrian explosion to vertebrate origins, from water-to-land transitions to human evolution - with the benefit of enjoying the crystal-clear prose of a consummate writer who knows well how to produce a widely accessible book without any loss of accuracy or sacrifice in coverage. One of the world leaders in evolutionary developmental biology, Wallace Arthur draws extensively from this field to reconstruct animal evolution from a developmental perspective. In the end, more than being a book on zoology this is a book on evolution - adaptation, novelties, convergence, evolutionary trends in complexity of structure and behaviour, but also speciation and extinction - punctuated by frequent insights into the history of biology and informative glimpses of the new frontiers of phylogenetic reconstruction.' Alessandro Minelli, University of Padova, Italy'Wallace Arthur has written a clear, lively and enjoyable guide to the animal kingdom and its evolution. He leads the reader through what we know about animals, their forms, relationships, and origins in the deep past, but more importantly he tells how we know it in a way that's accessible to a wide range of readers.' Rudolf A. Raff, Indiana University'As an old-fashioned zoologist/embryologist, I enjoyed reading [this], and undergraduate biologists will gain a breadth of understanding of animals unattainable from any other book I know. This is a good little book, bringing zoology back into the academic gamut.' Jack Cohen, The BiologistTable of ContentsPreface; Acknowledgements; 1. What is an animal?; 2. Before there were animals; 3. How to make a fossil; 4. The Cambrian explosion; 5. How to make a species; 6. Jellyfish and their kin; 7. How to make a tree; 8. The enigmatic urbilaterian; 9. Animal symmetry and heads; 10. A plethora of worms; 11. Trends in animal complexity; 12. Where the octopus is king; 13. How to make an animal; 14. Exoskeletons galore; 15. Extinction; 16. Mouth first, mouth second; 17. Comparing embryos; 18. Larvae, mouthparts and moulting; 19. The animal toolkit; 20. Vertebrate origins and evolution; 21. From water to land to water; 22. Variation and inheritance; 23. Evolutionary novelties; 24. Human origins and evolution; 25. Animal plasticity; 26. The nature of adaptation; 27. The direction of evolution; 28. Animal extremophiles; 29. Extraterrestrial animals?; 30. The ghost in the machine; Appendix; References; Index.

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Book SynopsisComputing is revolutionizing the practice of biology. This book, which assumes no prior computing experience, provides students with the tools to write their own Python programs and to understand fundamental concepts in computational biology and bioinformatics. Each major part of the book begins with a compelling biological question, followed by the algorithmic ideas and programming tools necessary to explore it: the origins of pathogenicity are examined using gene finding, the evolutionary history of sex determination systems is studied using sequence alignment, and the origin of modern humans is addressed using phylogenetic methods. In addition to providing general programming skills, this book explores the design of efficient algorithms, simulation, NP-hardness, and the maximum likelihood method, among other key concepts and methods. Easy-to-read and designed to equip students with the skills to write programs for solving a range of biological problems, the book is accompanied by nuTrade Review'In my twenty years as a professor, I have never run across a textbook on bioinformatics algorithms that a biologist can read from cover to cover and understand. This is the one.' Pavel Pevzner, Ronald R. Taylor Distinguished Professor of Computer Science, University of California, San Diego'This is an awesome book for anyone to get into computing. It is easy to follow and clearly structured so the reader understands what they are learning and why. The book provides the fundamentals concepts of computational biology and bioinformatics in parallel to gaining actual skills in computing and the ability to write your own Python programs! What I love about the book is how the authors ensure the concepts and skills are applicable to a clear and defined biological problem. The authors help demystify the various topics and bring the reader to understand the algorithms behind the programming tools by applying these to resolve an actual biological problem. This book is also an excellent resource for those involved in training and education, and it provides plenty of exercise to use in the actual classroom.' Maria Victoria Schneider, The Genome Analysis Centre (TGAC), UK'There is a wide agreement that biological science curricula should change and that a better understanding of computational notions and practice is required, starting at undergraduate level. Only a handful of academic programs, and fewer textbooks, are offering such computational experience to life science students, beyond a general introductory programming course. Libeskind-Hadas and Bush take a novel, exciting approach to this challenge. They designed an introductory programming and computer science principles course, using Python, and built around a carefully selected suit of computational problems with a biological motivation. The book covers all basic notions and programming practices that are taught in standard CS introductory course, and even adds some advanced computational ideas. Most importantly, it will be far more friendly and relevant to the vast majority of life science students, who are likely to discover through it both the beauty of computer science and its relevance to their own discipline.' Benny Chor, Tel-Aviv University, IsraelTable of ContentsPreface; Meet python; Part I. Python versus Pathogens: 1. Computing GC content; 2. Pathogenicity islands; 3. Open reading frames and genes; 4. Finding genes (at last!); Part II. Sequence Alignment and Sex Determination: 5. Recursion; 6. The use-it-or-lose-it principle; 7. Dictionaries, memoization, and speed; 8. Sequence alignments and the evolution of sex chromosomes; Part III. Phylogenetic Reconstruction and the Origin of Modern Humans: 9. Representing and working with trees; 10. Drawing trees; 11. The UPGMA algorithm; Part IV. Additional Topics: 12. RNA secondary structure prediction; 13. Gene regulatory networks and the maximum likelihood method; 14. Birds, bees, and genetic algorithms; Where to go from here; Index.

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Book SynopsisThis concise introduction covers all of the measure theory and probability most useful for statisticians. Originating from the authors' own graduate course, it is perfect for a two-term course or for self-study. It is especially useful to graduate students in related fields who want to shore up their mathematical foundation.Table of ContentsPreface; Acknowledgements; 1. Point sets and certain classes of sets; 2. Measures: general properties and extension; 3. Measurable functions and transformations; 4. The integral; 5. Absolute continuity and related topics; 6. Convergence of measurable functions, Lp-spaces; 7. Product spaces; 8. Integrating complex functions, Fourier theory and related topics; 9. Foundations of probability; 10. Independence; 11. Convergence and related topics; 12. Characteristic functions and central limit theorems; 13. Conditioning; 14. Martingales; 15. Basic structure of stochastic processes; References; Index.

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Book SynopsisThis first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and BÃcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padà approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevà equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exerTable of ContentsPreface; 1. Introduction to difference equations; 2. Discrete equations from transformations of continuous equations; 3. Integrability of P∆Es; 4. Interlude: lattice equations and numerical algorithms; 5. Continuum limits of lattice P∆Es; 6. One-dimensional lattices and maps; 7. Identifying integrable difference equations; 8. Hirota's bilinear method; 9. Multi-soliton solutions and the Cauchy matrix scheme; 10. Similarity reductions of integrable P∆Es; 11. Discrete Painlevé equations; 12. Lagrangian multiform theory; Appendix A. Elementary difference calculus and difference equations; Appendix B. Theta functions and elliptic functions; Appendix C. The continuous Painlevé equations and the Garnier system; Appendix D. Some determinantal identities; References; Index.

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Book SynopsisCharles Hermite (1822â1901) was a French mathematician who made significant contributions to pure mathematics, and especially to number theory and algebra. In 1858 he solved the equation of the fifth degree by elliptic functions, and in 1873 he proved that e (the base of natural logarithms) is transcendental. The legacy of his work can be shown in the large number of mathematical terms which bear the adjective 'Hermitian'. As a teacher at the Ãcole Polytechnique, the Facultà des Sciences de Paris and the Ãcole Normale SupÃrieure he was influential and inspiring to a new generation of scientists in many disciplines. The four volumes of his collected papers were published between 1905 and 1908.

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