Mathematics Books

Book SynopsisEnumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years'' experience of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study. The author provides proofs for many of the theorems to show the range of techniques available, and uses examples to link enumerative combinatorics to other areas of study. The main section of the book introduces the key tools of the subject (generating functions and recurrence relations), which are then used to study the most important combinatorial objects, namely subsets, partitions, and permutations of a set. Later chapters deal with more specialised topics, including permanents, SDRs, group actions and the RedfieldPólya theory of cycle indices, Möbius inversion, the Tutte polynomial, and species.Trade Review'It's indeed a very good introduction to enumerative combinatorics and has all the trappings of a pedagogically sound enterprise, in the old-fashioned sense: exercises, good explanations (not too terse, but certainly not too wordy), and mathematically serious (nothing namby-pamby here). It's an excellent book.' Michael Berg, MAA Reviews'Cameron's Notes on Counting is a clever introductory book on enumerative combinatorics … Overall, the text is well-written with a friendly tone and an aesthetic organization, and each chapter contains an ample number of quality exercises. Summing Up: Recommended.' A. Misseldine, CHOICETable of Contents1. Introduction; 2. Formal power series; 3. Subsets, partitions and permutations; 4. Recurrence relations; 5. The permanent; 6. q-analogues; 7. Group actions and cycle index; 8. Mobius inversion; 9. The Tutte polynomial; 10. Species; 11. Analytic methods: a first look; 12. Further topics; 13. Bibliography and further directions; Index.

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Book SynopsisProbability has applications in many areas of modern science, not to mention in our daily life. Its importance as a mathematical discipline cannot be overrated, and it is a fascinating and surprising topic in its own right. This engaging textbook with its easy-to-follow writing style provides a comprehensive yet concise introduction to the subject. It covers all of the standard material for undergraduate and first-year-graduate-level courses as well as many topics that are usually not found in standard texts, such as Bayesian inference, Markov chain Monte Carlo simulation, and Chernoff bounds.Trade Review'This is an attractive textbook for an introductory probability course at the upper undergraduate level. It covers not only the standard material for such a course (discrete probability, the axioms of probability, conditional probability, discrete and continuous random variables, jointly distributed random variables, limit theorems, Markov chains, etc.) but also some topics that might be considered more unusual, such as Kelly betting, renewal-reward stochastic processes, and the law of iterated logarithms. Topics from statistics (confidence intervals, Student-t distribution, Baysian inference, etc.) also appear. The book is quite well-written, nicely motivated, demonstrates considerable enthusiasm for the material, and gives lots of examples of the usefulness of probability. Mark Hunacek, MAA ReviewsAs with its predecessor, Probability: A Lively Introduction has an engaging and sympathetic tone which will be welcomed by those wrestling with this endlessly fascinating but tricky subject. Robert A. J. Matthews, Significance'This text serves as an excellent introduction to probability theory. Tijms has achieved the difficult feat of writing a book that is useful as both a textbook and a reference resource. As he wisely points out in the introduction, a key step in attracting students' attention to this field is providing clear, natural examples. In this book, every chapter is full of such examples. Besides covering the topics expected in an entry-level book, the author also covers multivariate normal distributions and the chi-square test, generating functions, and Markov chains (both the discrete time and the continuous time cases). Many students will appreciate the four appendixes at the end of the book. The first three contain the necessary background in enumerative combinatorics, set theory, and calculus, and make the book even more widely accessible in doing so. The fourth appendix introduces a more advanced concept, Monte Carlo simulations. There are plenty of excellent exercises in each chapter, half of which come with detailed solutions (not just numerical answers).' M. Bona, Choice'In this book, Henk Tijms aims at sharing his passion and enthusiasm for the fascinating world of probability with his readers. I can only say that he convincingly succeeded to do so!' Ivo Adan, European Journal of Operational Research'A most interesting aspect of this text is its exposition. The text relies heavily on a narrative approach: graphics and lengthy displayed calculations are infrequent. Happily, the author writes well, with an obvious enthusiasm (the 'liveliness' of the title is correct) and a gift for choosing appropriate and revealing examples. Often these examples provide jumping-off points for further discussion or exploration. The material is also presented accurately and at an appropriate level of rigor. One oddity is that theorems are not presented in the classic boxed-off fashion followed by a clearly marked proof. Instead, theorems (which the author calls 'rules') are stated and proofs or sketches of proofs are given within the narrative. The text also features an abundance of interesting exercises, ranging from elementary to challenging. Full solutions to the odd-numbered problems appear at the end of the book, and the publisher offers a password-protected site with solutions to all the exercises in the text.' Thomas Polaski, Mathematical Reviews'This is indeed a lively introduction to probability theory. The book is addressed basically to undergraduate students and their teachers. All traditional notions, results, ideas and techniques are included and discussed in detail. This is done smoothly and gradually in a master style.' Jordan M. Stoyanov, ZB Math ReviewsTable of Contents1. Foundations of probability theory; 2. Conditional probability; 3. Discrete random variables; 4. Continuous random variables; 5. Jointly distributed random variables; 6. Multivariate normal distribution; 7. Conditioning by random variables; 8. Generating functions; 9. Additional topics in probability; 10. Discrete-time Markov chains; 11. Continuous-time Markov chains.

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Book SynopsisWick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the HudsonParthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by WallstromRota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a ''field calculus'' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, DysonSchwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathemaTrade Review'This book offers an excellent account of the probabilistic aspects of quantum theory, focused on the interplay between quantum field theory and quantum stochastic calculus. The text is highly accessible thanks to the careful choice of topics and the systematic use of elegant combinatorial and algebraic methods. This makes the book suitable for graduate level teaching and self-study. I highly recommend it as a timely addition to the classical literature on quantum probability.' Madalin Guta, University of NottinghamTable of ContentsPreface; Notation; 1. Introduction to combinatorics; 2. Probabilistic Moments and Cumulants; 3. Quantum probability; 4. Quantum fields; 5. Combinatorial species; 6. Combinatorial aspects of quantum fields: Feynman diagrams; 7. Entropy, large deviations and legendre transforms; 8. Introduction to Fock spaces; 9. Operators and fields on the Boson Fock space; 10. L2-representations of the Boson Fock space; 11. Local fields on the Boson Fock space: free fields; 12. Local fields on the Boson Fock space: interacting fields; 13. Quantum stochastic calculus; 14. Quantum stochastic limits; Bibliography; Index.

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Book SynopsisGain an in-depth understanding of converter-interfaced energy storage systems with this unique text, covering modelling, dynamic behaviour, control, and stability analysis. Providing comprehensive coverage, it demonstrates the technical and economic aspects of energy storage systems, and provides a thorough overview of energy storage technologies. Several different modelling techniques are presented, including power system models, voltage-sourced converter models, and energy storage system models. Using a novel stochastic control approach developed by the authors, you will learn about the impact of energy storage on the dynamic interaction of microgrids with distribution and transmission systems. Compare the numerous real-world simulation data and numerical examples provided with your own models and control strategies. Accompanied online by a wealth of numerical examples and supporting data, this is the ideal text for graduate students, researchers, and industry professionals working iTrade Review'This is a timely and impressive book on an emerging and important topic. The comprehensive and in-depth overview of energy storage technologies, modelling, and dynamic simulation will make the book a valuable reference for practicing engineers and researchers working with the planning and operation of the future electric power system. The extensive list of references will be of great help for deepened studies.' Göran Andersson, Eidgenössische Technische Hochschule Zürich'Energy storage systems (ESS) are considered by many as the Holy Grail of the upcoming decarbonised future. From rooftop PV microsystems to giant pumped storage units, virtually all ESS are expected to be interfaced through power converters, for the sake of added flexibility and efficiency. This volume, co-authored by one of the most recognized experts in modelling, analysis and control of power systems dynamic phenomena, constitutes a self-contained and unique blend of general concepts, motivating factors and technical details, satisfying in this way the interests of a wide audience and filling an important gap in the technical literature.' Antonio Gomez-Exposito, Universidad de Sevilla'Excellent and timely material written by experienced authors! You must read this book.' Jean Mahseredjian, Polytechnique MontréalTable of ContentsPart I. Context: 1. Need for energy storage; 2. Technical and economic aspects; 3. Energy storage technologies; Part II. Modelling: 4. Power system model; 5. Voltage-sourced converter model; 6. Energy storage system models; Part III. Dynamic Analysis: 7. Comparison of dynamic models; 8. Control techniques; 9. Stability analysis; Part IV. Appendices.

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Book SynopsisThis is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.Trade Review'This 2-volume book is a very welcome addition to the existing literature in modular representation theory. It contains a wealth of material much of which is here presented in textbook form for the first time. It gives an excellent overview of the state of the art in this fascinating subject and also of the many challenging and fundamental open problems. It is well written and will certainly become a standard reference.' Burkhard Kűlshammer, MathSciNetTable of ContentsIntroduction; 6. Blocks and source algebras; 7. Modules over finite p-groups; 8. Local structure; 9. Isometries and bimodules; 10. Structural results in block theory; 11. Blocks with cyclic defect groups; 12. Blocks with Klein four defect groups; Appendix; References; Index.

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Book SynopsisThis text organizes a range of results in chromatic homotopy theory, running a single thread through theorems in bordism and a detailed understanding of the moduli of formal groups. It emphasizes the naturally occurring algebro-geometric models that presage the topological results, taking the reader through a pedagogical development of the field. In addition to forming the backbone of the stable homotopy category, these ideas have found application in other fields: the daughter subject ''elliptic cohomology'' abuts mathematical physics, manifold geometry, topological analysis, and the representation theory of loop groups. The common language employed when discussing these subjects showcases their unity and guides the reader breezily from one domain to the next, ultimately culminating in the construction of Witten''s genus for String manifolds. This text is an expansion of a set of lecture notes for a topics course delivered at Harvard University during the spring term of 2016.Trade Review'It has a down-to-earth and inviting style (no small achievement in a book about functorial algebraic geometry). It is elegant, precise, and incisive, and it is strong on both theory and calculation.' Michael Berg, MAA Reviews'This book is likely to be quite useful to graduate students in algebraic topology. For years it has been an informal tradition for students of algebraic topology to teach themselves enough of the foundations of algebraic geometry to be able to translate between theorems about Hopf algebroids and theorems about algebraic stacks, and then to proceed to translate, as much as possible, calculations and theorems in algebraic topology into equivalent formulations in terms of moduli stacks of formal groups and related objects. This book does a great service to such students (and their advisors!), as it gives good answers to many of the questions such students inevitably ask.' Andrew Salch, MatSciNet'The presentation is lucid, pedagogical, and also offers a fresh point of view on classical topics. It draws from several mostly unpublished sources, for instance Strickland's manuscripts or various sets of notes by Goerss, Hopkins, and Lurie, and combines them in a single uniform treatment. Moreover, it contains a wealth of references to the published and unpublished literature that guides the interested reader to further topics that are only discussed in passing.' Tobias Barthel, zbMATH OpenTable of ContentsForeword Matthew Ando; Preface; Introduction; 1. Unoriented bordism; 2. Complex bordism; 3. Finite spectra; 4. Unstable cooperations; 5. The σ-orientation; Appendix A. Power operations; Appendix B. Loose ends; References; Index.

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Book SynopsisBiological systems are extremely complex and have emergent properties that cannot be explained or even predicted by studying their individual parts in isolation. The reductionist approach, although successful in the early days of molecular biology, underestimates this complexity. As the amount of available data grows, so it will become increasingly important to be able to analyse and integrate these large data sets. This book introduces novel approaches and solutions to the Big Data problem in biomedicine, and presents new techniques in the field of graph theory for handling and processing multi-type large data sets. By discussing cutting-edge problems and techniques, researchers from a wide range of fields will be able to gain insights for exploiting big heterogonous data in the life sciences through the concept of ''network of networks''.Trade Review'… Networks of Networks in Biology should be of interest and a good introductory resource for molecular biologists, cell biologists, and biochemists, as well as bioinformaticians not yet acquainted with multilayer networks.' Ingo Brigandt, Quarterly Review of BiologyTable of ContentsPreface; Part I. Networks in Biology: 1. An Introduction to Biological Networks Nuria Planell, Xabier Martinez de Morentin and David Gomez-Cabrero; 2. Graph Theory Akram Dehnokhalaji and Nasim Nasrabadi; Part II. Network Analysis: 3. Structural Analysis of Biological Networks Narsis A. Kiani and Mikko Kivelä; 4. Networks From an Information-Theoretic and Algorithmic Complexity Perspective Hector Zenil and Narsis A. Kiani; 5. Integration and Feature Identification in Multi-layer Network using a Heat Diffusion Approach Gordon Ball and Jesper Tegnér; Part III. Multi-layer Networks: 6. Large Multiplex Networks Ginestra Bianconi; 7. Large Existing Tools for Analysis of Multilayer Networks Manlio De Domenico and Massimo Stella; 8. Large Dynamics on Multilayer Networks Manlio De Domenico and Massimo Stella; Part IV. Applications: 9. The Network of Networks Involved in Human Disease Celine Sin and Jörg Menche; 10. Towards a Multi-Layer Network Analysis of Disease: Challenges and Opportunities Through the Lens of Multiple Sclerosis Jesper Tegnér, Ingrid Kockum, Mika Gustafsson and David Gomez-Cabrero; 11. Microbiome: A Multi-Layer Network View Is Required Rodrigo Bacigalupe, Saeed Shoai and David Gomez-Cabrero; Part V. Conclusion : Concluding Remarks: Open Questions and Challenges Ginestra Bianconi, David Gomez-Cabrero, Jesper Tegnér and Narsis A. Kiani; Index.

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Book SynopsisA large part of mathematical analysis, both pure and applied, takes place on Polish spaces: topological spaces whose topology can be given by a complete metric. This analysis is not only simpler than in the general case, but, more crucially, contains many important special results. This book provides a detailed account of analysis and measure theory on Polish spaces, including results about spaces of probability measures. Containing more than 200 elementary exercises, it will be a useful resource for advanced mathematical students and also for researchers in mathematical analysis. The book also includes a straightforward and gentle introduction to the theory of optimal transportation, illustrating just how many of the results established earlier in the book play an essential role in the theory.Trade Review'This book provides a detailed and concise account of analysis and measure theory on Polish spaces, including results about probability measures. Containing more than 200 elementary exercises, it will be a useful resource for advanced mathematical students and also for researchers in analysis.' Luca Granieri, Mathematical ReviewsTable of ContentsIntroduction; Part I. Topological Properties: 1. General topology; 2. Metric spaces; 3. Polish spaces and compactness; 4. Semi-continuous functions; 5. Uniform spaces and topological groups; 6. Càdlàg functions; 7. Banach spaces; 8. Hilbert space; 9. The Hahn–Banach theorem; 10. Convex functions; 11. Subdifferentials and the legendre transform; 12. Compact convex Polish spaces; 13. Some fixed point theorems; Part II. Measures on Polish Spaces: 14. Abstract measure theory; 15. Further measure theory; 16. Borel measures; 17. Measures on Euclidean space; 18. Convergence of measures; 19. Introduction to Choquet theory; Part III. Introduction to Optimal Transportation: 20. Optimal transportation; 21. Wasserstein metrics; 22. Some examples; Further reading; Index.

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Book SynopsisThis book surveys the mathematical and computational properties of finite sets of points in the plane, covering recent breakthroughs on important problems in discrete geometry, and listing many open problems. It unifies these mathematical and computational views using forbidden configurations, which are patterns that cannot appear in sets with a given property, and explores the implications of this unified view. Written with minimal prerequisites and featuring plenty of figures, this engaging book will be of interest to undergraduate students and researchers in mathematics and computer science. Most topics are introduced with a related puzzle or brain-teaser. The topics range from abstract issues of collinearity, convexity, and general position to more applied areas including robust statistical estimation and network visualization, with connections to related areas of mathematics including number theory, graph theory, and the theory of permutation patterns. Pseudocode is included for mTrade Review'David Eppstein has managed to unify a huge swath of research on planar point sets through monotone properties and forbidden configurations. For example, finding grid points that avoid the obstacle of a 3-point line is a century-old problem still not entirely resolved. The author's unification naturally uncovers research lacuna, several of which he fills, while others are formulated as sharp new open problems. This rare synthesis of previous work will reinvigorate and redirect the field.' Joseph O'Rourke, Smith College, Massachusetts'David Eppstein takes us on an adventure tour to the study of point configurations in Discrete Geometry. It visits many different topics, connected by the original viewpoint of 'forbidden configurations'. This is interesting, instructive - and fun!' Günter M. Ziegler, Freie Universität Berlin'This unique volume collects and unifies almost a century of work on point configurations on the plane, and their properties that depend on whether each subset of three points is oriented clockwise, oriented counterclockwise, or collinear. Beginning with the Happy Ending Theorem, the author takes us through entertaining problems and into computational geometry. A delight to read as well as a persuasive case for the method of forbidden configurations, the book will be a valuable addition to the library of any discrete or computational geometer.' Peter Winkler, Dartmouth College, New Hampshire'This is a fun read on certain topics in discrete and computational geometry. It begins with 'A Happy Ending' and ends with 'Only the Beginning'. Eppstein's journey through various problems of pointset configurations offers a new view of the subject even to experts of the field. Recommended to everyone who likes geometry and computer science.' Jozsef Solymosi, University of British Columbia'David Eppstein has brought the weight of his formidable expertise and expositional talents on the simplest of shapes: points and lines. He gently guides the reader through a vast array of fascinating topics, their greatest hits to the state-of-the-art. This lovely book will be found on the shelves of mathematicians and computer scientists for many years to come.' Satyan Devadoss, University of San Diego'Erdős's many beautiful, notoriously difficult geometric problems on finite point configurations led to the birth of a new discipline: combinatorial geometry. The field gained additional significance in the 1980s, when it was discovered to be relevant to basic questions in computational geometry. Eppstein's elegantly written and illustrated book takes a fresh algorithmic look at the theory of forbidden geometric patterns. It can be read by specialists as a survey, but it can also serve as an excellent textbook for an introductory course on point configurations.' János Pach, École Polytechnique Fédérale de Lausanne and Rényi Institute, Budapest'There is a lot to like about this book, as Eppstein does a good job of introducing the material to his readers … A reader who sticks with Eppstein will learn a lot about this exciting area that lies on the border of mathematics and computer science.' Darren Glass, MAA Reviews'The result is a first-class treatment: Eppstein deftly sells the subject to the uninitiated, yet carries it to depths experts will appreciate. A generous supply of diagrams gracefully projects many ideas, and the professional-quality design makes the reading experience a pleasure. Summing Up: Highly recommended.' D. V. Feldman, Choice'The book is a great read. It is a valuable addition to the library of any discrete or computational geometer. Moreover, it can also serve as an excellent textbook for an introductory course on point configurations.' László Szabó, MathSciNet'This book is distinguished by a number of attractive features. Perhaps most prominent is its strong unity of approach. The first 7 chapters establish a coherent foundation and language for expressing and investigating the subjects studied in the remaining 10 … Another is its clarity of presentation and reader-friendliness. In most chapters the author adopts the strategy of introducing the topic in terms of an easily-understood problem that is accessible to virtually any reader … If you have any interest in learning about this field, I highly recommend this book.' Frederic Green, SIGACT NewsTable of Contents1. A happy ending; 2. Overview; 3. Configurations; 4. Subconfigurations; 5. Properties, parameters, and obstacles; 6. Computing with configurations; 7. Complexity theory; 8. Collinearity; 9. General position; 10. General-position partitions; 11. Convexity; 12. More on convexity; 13. Integer realizations; 14. Stretched permutations; 15. Configurations from graphs; 16. Universality; 17. Stabbing; 18. The big picture.

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Book SynopsisMarkov chains and hidden Markov chains have applications in many areas of engineering and genomics. This book provides a basic introduction to the subject by first developing the theory of Markov processes in an elementary discrete time, finite state framework suitable for senior undergraduates and graduates. The authors then introduce semi-Markov chains and hidden semi-Markov chains, before developing related estimation and filtering results. Genomics applications are modelled by discrete observations of these hidden semi-Markov chains. This book contains new results and previously unpublished material not available elsewhere. The approach is rigorous and focused on applications.Trade Review'… this book is of interest to researchers attracted by hidden Markov and semi-Markov models. It covers probabilistic and statistical treatments of the considered topics, and introduces the reader … to possible applications, mainly in genomics. Hence, Ph.D. students and specialists in the area of hidden Markov processes are invited to consider this book as a reference in their activities.' Antonio Di Crescenzo, MathSciNet'… dedicated mostly to graduate students and providing a rigorous and rather complete mathematical introduction to the theory of hidden Markov models as well as hidden semi-Markov models under main assumption that the hidden process is a finite state Markov chain. The semi-Markov models appear when the assumption that the length of time the chain spends in any state is geometrically distributed is relaxed. The authors carefully construct these processes on the canonical probability space and then derive filters and smoother, as well as the Viterbi estimates. The central role plays the EM Algorithm.' Jerzy Ombach, ZB Math ReviewsTable of ContentsPreface; 1. Observed Markov chains; 2. Estimation of an observed Markov chain; 3. Hidden Markov models; 4. Filters and smoothers; 5. The Viterbi algorithm; 6. The EM algorithm; 7. A new Markov chain model; 8. Semi-Markov models; 9. Hidden semi-Markov models; 10. Filters for hidden semi-Markov models; Appendix A. Higher order chains; Appendix B. An example of a second order chain; Appendix C. A conditional Bayes theorem; Appendix D. On conditional expectations; Appendix E. Some molecular biology; Appendix F. Earlier applications of hidden Markov chain models; References; Index.

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Book SynopsisHumanity is confronted by and attracted to extremes. Extreme events shape our thinking, feeling, and actions; they echo in our politics, media, literature, and science. We often associate extremes with crises, disasters, and risks to be averted, yet extremes also have the potential to lead us towards new horizons. Featuring essays by leading intellectuals and public figures arising from the 2017 Darwin College Lectures, this volume explores ''extreme'' events, from the election of President Trump, the rise of populism, and the Brexit referendum, to the 2008 financial crisis, the Syrian war, and climate change. It also celebrates ''extreme'' achievements in the realms of health, exploration, and scientific discovery. A fascinating, engaging, and timely collection of essays by renowned scholars, journalists, and intellectuals, this volume challenges our understanding of what is normal and what is truly extreme, and sheds light on some of the issues facing humanity in the twenty-first cenTable of ContentsNotes on contributors; Acknowledgements; On the notion of 'extremes' Julius F. W. Weitzdörfer; 1. Dealing with extremism David Runciman; 2. Extreme weather Emily Shuckburgh; 3. Probability, risk, and extremes Nassim Nicholas Taleb; 4. Extreme rowing Roz Savage; 5. Extremes of war: stories of survival from Syria Lyse Doucet; 6. Extreme politics: the four waves of national populism in the West Matthew Goodwin; 7. Extreme longevity Sarah Harper; 8. Extremes of power in the universe Andrew C. Fabian; Index.

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Book SynopsisFamous mathematical constants include the ratio of circular circumference to diameter, p = 3.14 , and the natural logarithm base, e = 2.718 . Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, PoissonVoronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, PrandtlBlasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, GaltonWatson trees, electrical capacitance (from potential theory), Zermelo''s navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly atTrade Review'Like the best sequels, this one covers similar ground to the original but finds ways to stay fresh and interesting … any mathematician or math student who picks it up and spends a few minutes with it is likely to find something that is new and of interest to them. … Finch has once again written a collection of essays about a wide range of topics that I expect I will enjoy flipping through for another decade and a half until I look forward to having Volume III land on my desk.' Darren Glass, MAA reviews'This is a remarkable book … [which] can be thought of as a collection of essays that recount stories that are both successful and tangible.' Paul F. Bracken, MathSciNet'Some of the most intriguing formulas of mathematics (like those of Ramanujan) adorn this treasure trove of mathematical gems … Steven R. Finch's incredible labor of love, an encyclopedia of mathematical constants … contain a total of 269 meticulously documented essays from all fields of mathematics.' Osmo Peokonen, The Mathematical Intelligencer'Taken together, Mathematical Constants and Mathematical Constants II form a comprehensive and unique work that is a welcome addition to the mathematician's reference library.' Steven R. Finch, Notices of the AMS'Great care is taken about numerical results and the precise determination of constants. The choice of the material complements the first volume; overall, the topics seem also to be more advanced, but every now and then there is a little pearl which is indeed accessible at high school level. The text is certainly not intended for linear reading - although this might well be possible - but for eclectic readers who want to enjoy themselves and broaden their horizons, or for researchers who need information on a particular constant and further stepping stones.' Rene L. Schilling, The Mathematical Gazette'Great care is taken about numerical results and the precise determination of constants. The choice of the material complements the first volume; overall, the topics seem also to be more advanced, but every now and then there is a little pearl which is indeed accessible at high school level. The text is certainly not intended for linear reading - although this might well be possible - but for eclectic readers who want to enjoy themselves and broaden their horizons, or for researchers who need information on a particular constant and further stepping stones.' Rene L. Schilling, The Mathematical GazetteTable of Contents1. Number theory and combinatorics; 2. Inequalities and approximation; 3. Real and complex analysis; 4. Probability and stochastic processes; 5. Geometry and topology; Index.

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Book SynopsisComplex environmental and hydrological processes are characterized by more than one correlated random variable. These events are multivariate and their treatment requires multivariate frequency analysis. Traditional analysis methods are, however, too restrictive and do not apply in many cases. Recent years have therefore witnessed numerous applications of copulas to multivariate hydrologic frequency analyses. This book describes the basic concepts of copulas, and outlines current trends and developments in copula methodology and applications. It includes an accessible discussion of the methods alongside simple step-by-step sample calculations. Detailed case studies with real-world data are included, and are organized based on applications, such as flood frequency analysis and water quality analysis. Illustrating how to apply the copula method to multivariate frequency analysis, engineering design, and risk and uncertainty analysis, this book is ideal for researchers, professionals and graduate students in hydrology and water resources engineering.Table of Contents1. Introduction; 2. Preliminaries; 3. Copulas and their properties; 4. Symmetric Archimedean copulas; 5. Asymmetric copulas: high dimension; 6. Plackett copula; 7. Non-Archimedean copulas: meta-elliptical copulas; 8. Entropic copulas; 9. Copulas in time series analysis; 10. Rainfall frequency analysis; 11. Flood frequency analysis; 12. Water quality analysis; 13. Drought analysis; 14. Compound extremes; 15. Network design; 16. Suspended sediment yield analysis; 17. Inter-basin transfer; Index.

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Book SynopsisThis book, meant for graduate students and researchers, explores the connections between numerical approximation and statistical inference from a game and decision theoretic perspective, and illustrates these interplays by addressing problems related to numerical homogenization, operator adapted wavelets, and fast solvers.Trade Review'This is a terrific book. A hot new topic, first rate mathematics, real applications. It's an important contribution by marvelous scholars.' Persi Diaconis, Stanford University'This book does a masterful job of bringing together the two seemingly unrelated fields of numerical approximation and statistical inference to produce a general framework for developing solvers that are both provably accurate and scale to extremely large problem sizes. It seamlessly integrates concepts from numerical approximation, statistical inference, information-based complexity, and game theory to reveal a rich mathematical structure that forms a comprehensive foundation for solver development. Of tremendous value to the practitioner is a thorough analysis of solver accuracy and computational requirements. In addition to providing a comprehensive guide to solver development and analysis this book presents a unique perspective that provides numerous valuable insights into the solution of science and engineering problems.' Don Hush, University of New Mexico'This unique book provides a novel game-theoretic approach to Probabilistic Scientific Computing by exploring the interplay between numerical approximation and statistical inference, and exploits such links to develop new fast methods for solving partial differential equations. Gamblets are magic basis functions resulting from a clever adversarial zero sum game between two players and can be used in modeling multiscale problems with no scale separation in numerical homogenization. The book provides original exposition to many topics of the modern era of scientific computing, including sparse representation of Gaussian fields, probabilistic interpretation of numerical errors, linear complexity algorithms, and rigorous settings in the Sobolev and Banach spaces of these topics. It is appropriate for graduate-level courses and as a valuable reference for any scientist who is interested in rigorous understanding and use of modern numerical algorithms in problems where data and mathematical models co-exist.' George Karniadakis, Brown UniversityTable of Contents1. Introduction; 2. Sobolev space basics; 3. Optimal recovery splines; 4. Numerical homogenization; 5. Operator adapted wavelets; 6. Fast solvers; 7. Gaussian fields; 8. Optimal recovery games on $\mathcal{H}^{s}_{0}(\Omega)$; 9. Gamblets; 10. Hierarchical games; 11. Banach space basics; 12. Optimal recovery splines; 13. Gamblets; 14. Bounded condition numbers; 15. Exponential decay; 16. Fast Gamblet Transform; 17. Gaussian measures, cylinder measures, and fields on $\mathcal{B}$; 18. Recovery games on $\mathcal{B}$; 19. Game theoretic interpretation of Gamblets; 20. Survey of statistical numerical approximation; 21. Positive definite matrices; 22. Non-symmetric operators; 23. Time dependent operators; 24. Dense kernel matrices; 25. Fundamental concepts.

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Book SynopsisFinite-state methods are the most efficient mechanisms for analysing textual and symbolic data, providing elegant solutions for an immense number of practical problems in computational linguistics and computer science. This book for graduate students and researchers gives a complete coverage of the field, starting from a conceptual introduction and building to advanced topics and applications. The central finite-state technologies are introduced with mathematical rigour, ranging from simple finite-state automata to transducers and bimachines as ''input-output'' devices. Special attention is given to the rich possibilities of simplifying, transforming and combining finite-state devices. All algorithms presented are accompanied by full correctness proofs and executable source code in a new programming language, C(M), which focuses on transparency of steps and simplicity of code. Thus, by enabling readers to obtain a deep formal understanding of the subject and to put finite-state methodsTrade Review'… this volume is well written and very detailed. It is thus a nice reference for those results for the interested graduate or researcher …' Andreas Maletti, ZB Math ReviewsTable of ContentsPart I. Formal Background: 1. Formal preliminaries; 2. Monoidal finite-state automata; 3. Classical finite-state automata and regular languages; 4. Monoidal multi-tape automata and finite-state transducers; 5. Deterministic transducers; 6. Bimachines; Part II. From Theory to Practice: 7. The C(M) language; 8. C(M) implementation of finite-state devices; 9. The Aho–Corasick algorithm; 10. The minimal deterministic finite-state automaton for a finite language; 11. Constructing finite-state devices for text rewriting; Bibliography; Index.

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Book SynopsisThis state-of-the-art account unifies material developed in journal articles over the last 35 years, with two central thrusts: It describes a broad class of system models that the authors call ''stochastic processing networks'' (SPNs), which include queueing networks and bandwidth sharing networks as prominent special cases; and in that context it explains and illustrates a method for stability analysis based on fluid models. The central mathematical result is a theorem that can be paraphrased as follows: If the fluid model derived from an SPN is stable, then the SPN itself is stable. Two topics discussed in detail are (a) the derivation of fluid models by means of fluid limit analysis, and (b) stability analysis for fluid models using Lyapunov functions. With regard to applications, there are chapters devoted to max-weight and back-pressure control, proportionally fair resource allocation, data center operations, and flow management in packet networks. Geared toward researchers and grTrade Review'The deep and rich theory of stochastic processing networks has served as the analytical foundation for the study of communication networks, cloud computing systems, and manufacturing networks. This book by two of the pioneers of the theory presents an authoritative and comprehensive treatment of the topic, and will serve as an important reference to researchers in the area.' R. Srikant, University of Illinois at Urbana-Champaign'A system of interconnected resources can become overloaded and unstable even though each of its individual resources has the capacity to meet the demands on it. This striking observation, first made thirty years ago, has stimulated a major field of research. This book, written by two of the pioneers and leading researchers in the field, is a clear and authoritative account of the state-of-the-art.' Frank Kelly, University of Cambridge'This book provides an elegant and unified exposition of the general modeling framework of stochastic processing networks (SPNs) and associated theory of stability using fluid models. Much of this material was only previously available in dispersed journal articles. Adopting a continuous-time Markov chain description for SPNs, valid under fairly general assumptions on arrivals, service times and controls, enables a self-contained, accessible treatment. An array of interesting examples and extensions, especially involving applications for telecommunication and data networks, enliven the volume. This monograph will be an invaluable premier resource for graduate students and researchers in computer science, electrical and industrial engineering, applied mathematics and operations management interested in theory and applications of stochastic processing networks.' Ruth J. Williams, University of California, San DiegoTable of Contents1. Introduction; 2. Stochastic processing networks; 3. Markov representations; 4. Extensions and complements; 5. Is stability achievable?; 6. Fluid limits, fluid equations and positive recurrence; 7. Fluid equations that characterize specific policies; 8. Proving fluid model stability using Lyapunov functions; 9. Max-weight and back-pressure control; 10. Proportionally fair resource allocation; 11. Task allocation in server farms; 12. Multi-hop packet networks; Appendix A. Selected topics in real analysis; Appendix B. Selected topics in probability; Appendix C. Discrete-time Markov chains; Appendix D. Continuous-time Markov chains and phase-type distributions; Appendix E. Markovian arrival processes; Appendix F. Convergent square matrices.

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Book SynopsisAfter the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. This volume covers a broad range of topics in mathematical physics, including noncommutative geometry, supergeometry, derived symplectic geometry, higher geometric quantization, intuitionistic quantum logic, problems with the continuum description of spacetime, twistor theory, loop quantum gravity, and geometry in string theory. It is addressed primarily to mathematical physicists and mathematicians, but also to historians and philosophers of these disciplines.Trade Review'The collection would be of interest to any physicist, mathematician, historian, or philosopher seeking a survey of the approaches to dealing with the modern concept of space in physics … Recommended.' E. Kincanon, Choice MagazineTable of ContentsIntroduction Mathieu Anel and Gabriel Catren; Part I. Noncommutative and supercommutative geometries: 1. Noncommutative geometry, the spectral standpoint Alain Connes; 2. The logic of quantum mechanics (revisited) Klaas Landsman; 3. Supergeometry in mathematics and physics Mikhail Kapranov; Part II. Symplectic geometry: 4. Derived stacks in symplectic geometry Damien Calaque; 5. Higher prequantum geometry Urs Schreiber; Part III. Spacetime: 6. Struggles with the continuum John C. Baez; 7. Twistor theory: a geometric perspective for describing the physical world Roger Penrose; 8. Quantum geometry of space Muxin Han; 9. Stringy geometry and emergent space Marcos Mariño.

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Book SynopsisA unique text integrating numerics, mathematics and applications to provide a hands-on approach to using optimization techniques, this mathematically accessible textbook emphasises conceptual understanding and importance of theorems rather than elaborate proofs. It allows students to develop fundamental optimization methods before delving into MATLAB''s optimization toolbox, and to link MATLAB''s results with the results from their own code. Following a practical approach, the text demonstrates several applications, from error-free analytic examples to truss (size) optimization, and 2D and 3D shape optimization, where numerical errors are inevitable. The principle of minimum potential energy is discussed to highlight the deep relationship between engineering and optimization. MATLAB code in every chapter illustrates key concepts and the text demonstrates the coupling between MATLAB and SOLIDWORKS for design optimization. A wide variety of optimization problems are covered including conTrade Review'Design Optimization using MATLAB and SOLIDWORKS by Dr. Suresh provides an excellent review of various optimization methods, especially for structural problems. Its introduction to MATLAB would help students who have had little experience with this software to become familiar with it quickly and apply it to some of the basic optimization problems.' Hamid Torab, Gannon University'Dr. Suresh's text brings his contributions to shape optimization into the classroom by connecting optimization, MATLAB, SOLIDWORKS, and SOLIDLAB into a single textbook. This text enables the reader to build upon this research accomplishment. I look forward to seeing what my students can achieve with this textbook at their fingertips.' Cameron Turner, Clemson UniversityTable of ContentsPreface; Table of Contents; 1. Introduction; 2. Modeling; 3. Introduction to MATLAB; 4. Unconstrained Optimization: Theory; 5. Unconstrained Optimization: Algorithms; 6. MATLAB Optimization Toolbox; 7. Constrained Optimization; 8. Special Classes of Problems; 9. Truss Analysis; 10. Size Optimization of Trusses; 11. Gradient Computation; 12. Finite Element Analysis in 2D; 13. Shape Optimization in 2D; 14. Finite Element Analysis in 3D; 15. SOLIDLAB: A SOLIDWORKS-MATLAB Interface; 16. Shape Optimization using SOLIDLAB; 17. Appendix; 18. References.

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Book SynopsisExperts in data analytics and power engineering present techniques addressing the needs of modern power systems, covering theory and applications related to power system reliability, efficiency, and security. With topics spanning large-scale and distributed optimization, statistical learning, big data analytics, graph theory, and game theory, this is an essential resource for graduate students and researchers in academia and industry with backgrounds in power systems engineering, applied mathematics, and computer science.Trade Review'There are only a few industries that generate an equally large amount of data with a comparable variety, and societal importance. Data analytics is thus rightfully at the heart of modern power systems operations and planning. Focusing on applications in power systems, this book gives an excellent account of recent developments and of the broad range of algorithms and tools in the area of data analytics, as well as of the applications of these tools for solving challenging problems from a novel angle. Covering a wide range of fundamental problems, from state estimation to load scheduling and anomaly detection, the book is not only an excellent source of inspiration, but can also serve as an extensive reference for the gamut of operational problems faced in the power industry.' György Dán, KTH Royal Institute of Technology'The editors have brought together leading researchers at the intersection of data analytics and power systems to provide us with an authoritative reference that is comprehensive, coherent and timely. It treats classical topics such as state estimation, optimal power flow, and anomaly identification, as well as emerging topics such as phase measurement unit data recovery and privacy, probabilistic price forecasting, and distributed load management. It introduces a wide array of modern techniques to power system analysis from sparse representation, graph signal processing, distributed and feedback optimization, statistics and random matrix theory, deep learning, and mean field games. A useful reference for students, researchers, and practitioners.' Steven Low, CaltechTable of ContentsIntroduction; Preface Ali Tajer, Samir M. Perlaza and H. Vincent Poor; 1. Learning power grid topologies Guido Cavraro, Vassilis Kekatos, Liang Zhang and Georgios B. Giannakis; 2. Probabilistic forecasting of power system and market operations Yuting Ji, Lang Tong and Weisi Deng; 3. Deep learning in power systems Yue Zhao and Baosen Zhang; 4. Estimating the system state and network model errors Ali Abur, Murat Gol and Yuzhang Lin; 5. Quickest detection and isolation of tranmission line outages Venugopal V. Veeravalli and Alejandro Dominguez-Garcia; 6. Active sensing for quickest anomaly detection Ali Tajer and Javad Heydari; 7. Random matrix theory for analyzing spatio-temporal data Robert Qiu, Xing He, Lei Chu and Xin Shi; 8. Graph-theoretic analysis of power grid robustness Dorcas Ofori-Boateng, Asim Kumer Dey, Yulia R. Gel and H. Vincent Poor; 9. Bayesian attacks Inaki Esnaola, Samir M Perlaza and Ke Sun; 10. Smart meter data privacy Giulio Giaconia, Deniz Gunduz and H. Vincent Poor; 11. Data quality and privacy enhancement Meng Wang and Joe H Chow; 12. Frequency estimation using voltage phasor angles revisited Danilo P. Mandic, Sithan Kanna, Yili Xia and Anthony G. Constantinides; 13. Graph signal processing for the power grid Anna Scaglione, Raksha Ramakrishna and Mahdi Jamei; 14. A sparse representation approach for anomaly identification Hao Zhu and Chen Chen; 15. Uncertainty-aware power systems operation Daniel Bienstock; 16. Distributed optimization for power and energy systems Emiliano Dall'Anese and Nikolaos Gatsis; 17. Distributed load management Changhong Zhao, Vijay Gupta and Ufuk Topcu; 18. Analytical models for emerging energy storage applications I. Safak Bayram and Michael Devetsikiotis; 19. Distributed power consumption scheduling Samson Lasaulce, Olivier Beaude and Mauricio Gonz´alez; 20. Electric vehicles and mean-field Dario Bauso and Toru Namerikawa; 21. Prosumer behaviour: decision making with bounded horizon Mohsen Rajabpour, Arnold Glass, Robert Mulligan and Narayan B. Mandayam; 22. Storage allocation for price volatility management in electricity markets Amin Masoumzadeh, Ehsan Nekouei and Tansu Alpcan.

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Book SynopsisSets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, hepresents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.Trade Review'Incurvati provides a veritable handbook for researchers and practitioners in the domain of logic and the foundations of mathematics … Each chapter raises significant foundational questions, fertile ground for further research.' R. L. Pour, ChoiceTable of Contents1. Concepts and conceptions; 2. The iterative conception; 3. Challenges to the iterative conception; 4. The naïve conception; 5. The limitation of size conception; 6. The stratified conception; 7. The graph conception.

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Book SynopsisDo you want to deepen your understanding of complex systems and design integrated circuits more quickly? Learn how with this step-by-step guide that shows, from first principles, how to employ estimation techniques to analyze and solve complex problems in IC design using a simplified modeling approach. Applications are richly illustrated using real-world examples from across IC design, from simple circuit theory, to the electromagnetic effects and high frequency design, and systems such as data converters and phase-locked loops. Basic concepts like inductance and capacitance are related to one other and other RF phenomena inside a modern chip, enhancing understanding without the need for simulators. Use the easy-to-follow models presented to start designing your own products, from inductors and amplifiers to more complex systems. Whether you are an early-career professional or researcher, graduate student, or established IC engineer looking to reduce your reliance on commercial softwarTrade Review'The estimation analysis techniques in this book open up a new and unique approach to gaining a deeper understanding of circuits, thus accelerating the optimization and design of a broad range of circuits, which is a critical skill in the fast paced IC design world where time to market is crucial to success.' Joel King, Skyworks Solutions, Inc.'Developing engineering solutions benefits greatly from the proverbial back of the envelope analysis. This book does an excellent job of not only providing a great reference to a number of estimating techniques (limitations clearly identified) for a number of key topics. It also resurrects the concept of engineering estimation, to quickly evaluate ideas and drive to useful conclusions without losing context. This art form is dwindling as today's engineers continue to depend on (very capable) computer simulators, slowing the development of intuition and hence innovation.' Claudio Anzil, Innophase Inc.Table of Contents1. General guidelines in estimation analysis in integrated circuits; 2. Basic amplifier stages; 3. Higher level amplifier stages; 4. Electromagnetism – fundamentals; 5. Electromagnetism – circuit applications; 6. Electromagnetic field simulators; 7. System aspects; Appendix A: basic transistor and technology model; Appendix B: useful mathematical relationships; Index.

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Book SynopsisThis practical introduction covers mathematical methods for the analysis of stochastic models and their biological applications. Based on courses taught at the University of Oxford, the book can be used for self-study or as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics.Trade Review'The text can be used effectively for solitary study or as a textbook for a course offered at the boundary between undergraduate and beginning graduate study … This is a remarkable, even admirable, work that bears the mark of its Oxford origins. Its potential audience includes chemists and mathematicians as well as adventuresome biologists and physicists and perhaps even bright or intrepid general readers.' A. E. Viste, Choice'This textbook is an example-driven introduction to stochastic modeling in mathematical biology … Beyond serving as a course textbook, the book could serve as a good general introduction to the area of stochastic modeling in biology for researchers, particularly given the copious citations to more specialist texts.' Andrew Krause, MAA Reviews'Erban and Chapman's Stochastic Modelling of Reaction–Diffusion Processes will be valuable both as a reference for practitioners and as a textbook for a graduate course on stochastic modelling. Every chapter includes problems for the reader. The problems are well written and appropriate for most intended readers of the book. I hope that this book is widely adopted and that it becomes a standard textbook in the field.' Michael A. Salins, Mathematical Reviews/MathSciNet Review'This book is also available at a reduced price as an e-book on Kindle. Based on the sample I viewed, all the features of the printed book have been perfectly preserved, with no loss of clarity in the layout or the mathematical symbols or the graphs and diagrams.' David Hopkins, The Mathematical GazetteTable of Contents1. Stochastic simulation of chemical reactions; 2. Deterministic versus stochastic modelling; 3. Stochastic differential equations; 4. Diffusion; 5. Efficient stochastic modelling of chemical reactions; 6. Stochastic reaction-diffusion models; 7. SSAs for reaction-diffusion-advection processes; 8. Microscopic models of Brownian motion; 9. Multiscale and multi-resolution methods; Appendix A. Deterministic modelling of chemical reactions; Appendix B. Discrete probability distributions; Appendix C. Continuous probability distributions; References; Index.

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Book SynopsisThe stability of stochastic differential equations in abstract, mainly Hilbert, spaces receives a unified treatment in this self-contained book. It covers basic theory as well as computational techniques for handling the stochastic stability of systems from mathematical, physical and biological problems. Its core material is divided into three parts devoted respectively to the stochastic stability of linear systems, non-linear systems, and time-delay systems. The focus is on stability of stochastic dynamical processes affected by white noise, which are described by partial differential equations such as the NavierStokes equations. A range of mathematicians and scientists, including those involved in numerical computation, will find this book useful. It is also ideal for engineers working on stochastic systems and their control, and researchers in mathematical physics or biology.Trade Review'The text itself is rather detailed, and therefore can be understood by graduate students and young researchers who have taken a solid course in stochastic analysis. Many examples are provided throughout the text to explain the finer points in the results.' Mar´ıa J. Garrido-Atienza, MathSciNetTable of ContentsPreface; 1. Preliminaries; 2. Stability of linear stochastic differential equations; 3. Stability of non linear stochastic differential equations; 4. Stability of stochastic functional differential equations; 5. Some applications related to stochastic stability; Appendix; References; Index.

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Book SynopsisOn its original publication, this book provided the first elementary treatment of representation theory of finite groups of Lie type in book form. This second edition features new material to reflect the continuous evolution of the subject, including entirely new chapters on Hecke algebras, Green functions and Lusztig families. The authors cover the basic theory of representations of finite groups of Lie type, such as linear, unitary, orthogonal and symplectic groups. They emphasise the CurtisAlvis duality map and Mackey''s theorem and the results that can be deduced from it, before moving on to a discussion of DeligneLusztig induction and Lusztig''s Jordan decomposition theorem for characters. The book contains the background information needed to make it a useful resource for beginning graduate students in algebra as well as seasoned researchers. It includes exercises and explicit examples.Trade Review'… a useful resource for beginning graduate students in algebra as well as seasoned researchers.' Mathematical Reviews Clippings'… clearly written; there are useful examples, motivational comments, and exercises scattered throughout the text.' Mark Hunacek, The Mathematical GazetteTable of Contents1. Basic results on algebraic groups; 2. Structure theorems for reductive groups; 3. (B, N)-pairs; parabolic, Levi, and reductive subgroups; centralisers of semi-simple elements; 4. Rationality, the Frobenius endomorphism, the Lang–Steinberg theorem; 5. Harish–Chandra theory; 6. Iwahori–Hecke algebras; 7. The duality functor and the Steinberg character; 8. l-adic cohomology; 9. Deligne–Lusztig induction; the Mackey formula; 10. The character formula and other results on Deligne–Lusztig induction; 11. Geometric conjugacy and Lusztig series; 12. Regular elements; Gelfand–Graev representations; regular and semi-simple characters; 13. Green functions; 14. The decomposition of Deligne–Lusztig characters; References; Index.

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Book SynopsisThis friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in Deep Learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overvTrade Review'In addition to the usual topics of probability theory, a large portion of the book is devoted to presenting modern applications including Bayesian inference and MCMC. Students will appreciate the detailed derivations of formulas and the full solutions of problems. The text is interspersed with personal viewpoints and advice, which gives the book the flavour of a lively lecture by an enthusiastic teacher.' Robert Piché, Tampereen yliopisto, Finland'Adam Prügel-Bennett has created a great toolbox for all scientists working with models that take into account the uncertainty of the real world.' Wolfram Burgard, Albert-Ludwigs-Universität Freiburg, Germany'This is a wonderful book, one that I wish I'd had when learning about probability. Indeed, there are lots of gems in there that I'm looking forward to reading about myself! The book is beautifully illustrated and refreshingly full of insight, without overly formal mathematical jargon. This book would appeal to students and researchers that are competent in mathematics and delight in gaining a deeper understanding of the subject, both from an intuitive and mathematical standpoint. It excels in demonstrating the wide applicability of probabilistic approaches to problem solving and modelling. This book deserves to be on the shelf of any researcher that uses probability to solve problems.' David Barber, University College London'The book can be very recommended all readers, who are interested in this field.' Ludwig Paditz, Theatre and Performance TheoryTable of Contents1. Introduction; 2. Survey of distributions; 3. Monte Carlo; 4. Discrete random variables; 5. The normal distribution; 6. Handling experimental data; 7. Mathematics of random variables; 8. Bayes; 9. Entropy; 10. Collective behavior; 11. Markov chains; 12. Stochastic processes; Appendix A. Answers to exercises; Appendix B. Probability distributions.

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Book SynopsisEvery four years leading researchers gather to survey the latest developments in all aspects of group theory. Initially held in St Andrews, these meetings have become the premier forum for group theory across the whole of the UK. Since 1981, the proceedings of ''Groups St Andrews'' have provided a regular snapshot of the state-of-the-art in group theory and helped to shape the direction of research in the field. This volume contains papers from the 2017 meeting held in Birmingham. It includes expository articles from the invited speakers, and further surveys contributed by the participants. Topics include: generation of finite simple groups, block theory, fusion systems, algebraic groups, one-relator groups, geometric group theory, and Beauville groups.Trade Review''This volume does what the editors intended: it provides a 'snapshot of the state of the art in group theory'. It can serve as a reference work for group theorists, and since many of the articles include open problems, can serve as a source of research topics as well.' Charles Traina, MAA ReviewsTable of ContentsIntroduction; 1. Finite simple groups and fusion systems Michael Aschbacher; 2. Finite and infinite quotients of discrete and indiscrete groups Pierre-Emmanuel Caprace; 3. Local-global conjectures and blocks of finite simple groups Radha Kessar and Gunter Malle; 4. A survey on some methods of generating finite simple groups Ayoub B. M. Basheer and Jamshid Moori; 5. One-relator groups: an overview Gilbert Baumslag, Benjamin Fine and Gerhard Rosenberger; 6. New progress in products of conjugacy classes in finite groups Antonio Beltrán, María José Felipe and Carmen Melchor; 7. Aspherical relative presentations all over again William A. Bogley, Martin Edjvet and Gerald Williams; 8. Simple groups, generation and probabilistic methods Timothy C. Burness; 9. Irreducible subgroups of simple algebraic groups – a survey Timothy C. Burness and Donna M. Testerman; 10. Practical computation with linear groups over infinite domains A. S. Detinko and D. L. Flannery; 11. Beauville p-groups: a survey Ben Fairbairn; 12. Structural criteria in factorised groups via conjugacy class sizes María José Felipe, Ana Martínez-Pastor and Víctor Manuel Ortiz-Sotomayor; 13. Growth in linear algebraic groups and permutation groups: towards a unified perspective Harald A. Helfgott; 14. L2-Betti numbers and their analogues in positive characteristic Andrei Jaikin-Zapirain; 15. On the pronormality of subgroups of odd index in finite simple groups Anatoly Kondrat'ev, Natalia Maslova and Danila Revin; 16. Vertex stabilizers of graphs with primitive automorphism groups and a strong version of the Sims conjecture Anatoly S. Kondrat'ev and Vladimir I. Trofimov; 17. On the character degrees of a Sylow p-subgroup of a finite Chevalley group G(pf) over a bad prime Tung Le, Kay Magaard and Alessandro Paolini; 18. Patterns on symmetric Riemann surfaces Adnan Melekoğlu and David Singerman; 19. Subgroups of twisted wreath products Péter P. Pálfy; 20. Some remarks on self-dual codes invariant under almost simple permutation groups B. G. Rodrigues and T. M. Mudziiri Shumba; 21. Test elements: from pro-p to discrete groups Ilir Snopce and Slobodan Tanushevski.

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Book SynopsisBased on the author''s university lecture courses, this book presents the many facets of one of the most important open problems in operator algebra theory. Central to this book is the proof of the equivalence of the various forms of the problem, including forms involving C*-algebra tensor products and free groups, ultraproducts of von Neumann algebras, and quantum information theory. The reader is guided through a number of results (some of them previously unpublished) revolving around tensor products of C*-algebras and operator spaces, which are reminiscent of Grothendieck''s famous Banach space theory work. The detailed style of the book and the inclusion of background information make it easily accessible for beginning researchers, Ph.D. students, and non-specialists alike.Trade Review'This is a very rich and detailed monograph on an enormously important subject. It is written in the crystal clear and elegant style that is the hallmark of its author, and it offers a lot of information to specialists and novices alike. The book will certainly become an authoritative guide.' Dirk Werner, London Mathematical Society Student Texts'This book is jam packed with information, and should be an invaluable guide to anyone interested in these ideas … For the complete picture and the recent advances, Pisier's book is the place to go.' Bulletin of the American Mathematical SocietyTable of ContentsIntroduction; 1. Completely bounded and completely positive maps: basics; 2. Completely bounded and completely positive maps: a tool kit; 3. C*-algebras of discrete groups; 4. C*-tensor products; 5. Multiplicative domains of c.p. maps; 6. Decomposable maps; 7. Tensorizing maps and functorial properties; 8. Biduals, injective von Neumann algebras and C*-norms; 9. Nuclear pairs, WEP, LLP and QWEP; 10. Exactness and nuclearity; 11. Traces and ultraproducts; 12. The Connes embedding problem; 13. Kirchberg's conjecture; 14. Equivalence of the two main questions; 15. Equivalence with finite representability conjecture; 16. Equivalence with Tsirelson's problem; 17. Property (T) and residually finite groups. Thom's example; 18. The WEP does not imply the LLP; 19. Other proofs that C(n) < n. Quantum expanders; 20. Local embeddability into ${\mathscr{C}}$ and non-separability of $(OS_n, d_{cb})$; 21. WEP as an extension property; 22. Complex interpolation and maximal tensor product; 23. Haagerup's characterizations of the WEP; 24. Full crossed products and failure of WEP for $\mathscr{B}\otimes_{\min}\mathscr{B}$; 25. Open problems; Appendix. Miscellaneous background; References; Index.

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Book SynopsisFrom Bäcklund to Darboux, this monograph presents a comprehensive journey through the transformation theory of constrained Willmore surfaces, a topic of great importance in modern differential geometry and, in particular, in the field of integrable systems in Riemannian geometry. The first book on this topic, it discusses in detail a spectral deformation, Bäcklund transformations and Darboux transformations, and proves that all these transformations preserve the existence of a conserved quantity, defining, in particular, transformations within the class of constant mean curvature surfaces in 3-dimensional space-forms, with, furthermore, preservation of both the space-form and the mean curvature, and bridging the gap between different approaches to the subject, classical and modern. Clearly written with extensive references, chapter introductions and self-contained accounts of the core topics, it is suitable for newcomers to the theory of constrained Wilmore surfaces. Many detailed compTable of ContentsIntroduction; 1. A bundle approach to conformal surfaces in space-forms; 2. The mean curvature sphere congruence; 3. Surfaces under change of flat metric connection; 4. Willmore surfaces; 5. The Euler–Lagrange constrained Willmore surface equation; 6. Transformations of generalized harmonic bundles and constrained Willmore surfaces; 7. Constrained Willmore surfaces with a conserved quantity; 8. Constrained Willmore surfaces and the isothermic surface condition; 9. The special case of surfaces in 4-space; Appendix A. Hopf differential and umbilics; Appendix B. Twisted vs. untwisted Bäcklund transformation parameters; References; Index.

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Book SynopsisSearching for small gaps between consecutive primes is one way to approach the twin primes conjecture, one of the most celebrated unsolved problems in number theory. This book documents the remarkable developments of recent decades, whereby an upper bound on the known gap length between infinite numbers of consecutive primes has been reduced to a tractable finite size. The text is both introductory and complete: the detailed way in which results are proved is fully set out and plenty of background material is included. The reader journeys from selected historical theorems to the latest best result, exploring the contributions of a vast array of mathematicians, including Bombieri, Goldston, Motohashi, Pintz, Yildirim, Zhang, Maynard, Tao and Polymath8. The book is supported by a linked and freely-available package of computer programs. The material is suitable for graduate students and of interest to any mathematician curious about recent breakthroughs in the field.Trade Review'The author has gathered almost 100 year's worth of progress on this family of problems into one volume, and this alone will be very helpful to anyone pursuing research in the field. Recommended.' M. Bona, Choice'a wonderful tale of how two lesser-known mathematicians worked extremely hard to solve an intriguing, long-standing open problem that so many leading experts could not.' Sam Chow, London Mathematical SocietyTable of Contents1. Introduction; 2. The sieves of Brun and Selberg; 3. Early work; 4. The breakthrough of Goldston, Motohashi, Pintz, and Yildirim; 5. The astounding result of Yitang Zhang; 6. Maynard's radical simplification; 7. Polymath's refinements of Maynard's results; 8. Variations on Bombieri–Vinogradov; 9. Further work and the epilogue; Appendix A. Bessel functions of the first kind; Appendix B. A type of compact symmetric operator; Appendix C. Solving an optimization problem; Appendix D. A Brun–Titchmarsh inequality; Appendix E. The Weil exponential sum bound; Appendix F. Complex function theory; Appendix G. The dispersion method of Linnik; Appendix H. One thousand admissible tuples; Appendix I. PGpack mini-manual; References; Index.

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Book SynopsisNumerical Analysis is a broad field, and coming to grips with all of it may seem like a daunting task. This text provides a thorough and comprehensive exposition of all the topics contained in a classical graduate sequence in numerical analysis. With an emphasis on theory and connections with linear algebra and analysis, the book shows all the rigor of numerical analysis. Its high level and exhaustive coverage will prepare students for research in the field and become a valuable reference as they continue their career. Students will appreciate the simple notation, clear assumptions and arguments, as well as the many examples and classroom-tested exercises ranging from simple verification to qualifying exam-level problems. In addition to the many examples with hand calculations, readers will also be able to translate theory into practical computational codes by running sample MATLAB codes as they try out new concepts.Trade Review'This impressive volume covers an unusually broad range of topics in the field of numerical analysis, including numerical linear algebra, polynomial and trigonometric interpolation, best approximation, numerical quadrature, the approximate solution of nonlinear equations and convex optimization, and the numerical solution of ordinary and partial differential equations by finite difference, spectral and finite element methods. A particularly appealing feature of the text is the way in which it integrates a mathematically rigorous exposition with a wealth of illustrative examples, including numerical simulations, sample codes, and exercises. I warmly recommend the book to students and lecturers as an advanced undergraduate or introductory graduate level text.' Endre Süli, University of Oxford'This long-awaited graduate text covers every topic of a traditional, one-year Numerical Analysis course in an accessible, rigorous, and comprehensive way. It's an indispensable assistant for anyone offering the class and a precious source of knowledge for a junior researcher in the field.' Maxim Olshanskii, University of Houston'This is the book I have been waiting for: a textbook of numerical analysis fit for the Twenty-First Century. It sketches a path from the mathematical foundations of the subject to the wide range of its modern methods and algorithms, compromising on neither rigour nor clarity.' Arieh Iserles, University of Cambridge'The book is the only textbook I know that covers the current topics for beginning graduate students in numerical analysis. The chosen topics in the book match exactly what one wishes to cover in a two-semester course sequence in computational mathematics, as the selection of the numerical methods is in align with the modern treatment of the subjects. Many instructors in the field have struggled to find two or more textbooks for the same coverage, but you can have all of them in this book.' Xiaofan Li, Illinois Institute of TechnologyTable of ContentsPart I. Numerical Linear Algebra: 1. Linear operators and matrices; 2. The singular value decomposition; 3. Systems of linear equations; 4. Norms and matrix conditioning; 5. Linear least squares problem; 6. Linear iterative methods; 7. Variational and Krylov subspace methods; 8. Eigenvalue problems; Part II. Constructive Approximation Theory: 9. Polynomial interpolation; 10. Minimax polynomial approximation; 11. Polynomial least squares approximation; 12. Fourier series; 13. Trigonometric interpolation and the Fast Fourier Transform; 14. Numerical quadrature; Part III. Nonlinear Equations and Optimization: 15. Solution of nonlinear equations; 16. Convex optimization; Part IV. Initial Value Problems for Ordinary Di fferential Equations: 17. Initial value problems for ordinary diff erential equations; 18. Single-step methods; 19. Runge–Kutta methods; 20. Linear multi-step methods; 21. Sti ff systems of ordinary diff erential equations and linear stability; 22. Galerkin methods for initial value problems; Part V. Boundary and Initial Boundary Value Problems: 23. Boundary and initial boundary value problems for partial di fferential equations; 24. Finite diff erence methods for elliptic problems; 25. Finite element methods for elliptic problems; 26. Spectral and pseudo-spectral methods for periodic elliptic equations; 27. Collocation methods for elliptic equations; 28. Finite di fference methods for parabolic problems; 29. Finite diff erence methods for hyperbolic problems; Appendix A. Linear algebra review; Appendix B. Basic analysis review; Appendix C. Banach fixed point theorem; Appendix D. A (petting) zoo of function spaces; References; Index.

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Book SynopsisThis rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin''s Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering.Trade Review'High standards of linear control were established in the 1960s in pioneering works by R. Bellman, R. Kalman, and L. Pontryagin. However, this field of research remains active and is permanently enriched with new results and new applications, as the book by S. P. Bhattacharyya and L. H. Keel vividly demonstrates.' Boris Polyak, IFAC Fellow, Institute for Control Science, Moscow'One of the most valuable features of this book is that it integrates the pillars of control theory with recent advancements, resulting in an up-to-date treatment of the topic.' Antonio Visioli, University of BresciaTable of ContentsPreface; 1. A measurement-based approach to linear systems; 2. Classical control theory: a brief overview; 3. The [A,B,C,D] state variable model; 4. Modal structure of state space systems; 5. Controllability, observability and realization theory; 6. State feedback, observers and regulators; 7. The optimal linear quadratic regulator; 8. H¥ and H2 optimal control; 9. The linear multivariable servomechanism; 10. Robustness and fragility of control systems; 11. Analytical design of PID controllers; 12. Multivariable control using single input single output methods; Appendix; References; Index.

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Book SynopsisAfter the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. These books explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. They are addressed primarily to mathematicians and mathematical physicists, but also to historians and philosophers of these disciplines.

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Book SynopsisThis modern introduction to operator theory on spaces with indefinite inner product discusses the geometry and the spectral theory of linear operators on these spaces, the deep interplay with complex analysis, and applications to interpolation problems. The text covers the key results from the last four decades in a readable way with full proofs provided throughout. Step by step, the reader is guided through the intricate geometry and topology of spaces with indefinite inner product, before progressing to a presentation of the geometry and spectral theory on these spaces. The author carefully highlights where difficulties arise and what tools are available to overcome them. With generous background material included in the appendices, this text is an excellent resource for researchers in operator theory, functional analysis, and related areas as well as for graduate students.Table of Contents1. Inner product spaces; 2. Angular operators; 3. Subspaces of Kreĭn spaces; 4. Linear operators on Kreĭn spaces; 5. Selfadjoint projections and unitary operators; 6. Techniques of induced Kreĭn spaces; 7. Plus/minus-operators; 8. Geometry of contractive operators; 9. Invariant maximal semidefinite subspaces; 10. Hankel operators and interpolation problems; 11. Spectral theory for selfadjoint operators; 12. Quasi-contractions; 13. More on definitisable operators; Appendix; References; Symbol index; Subject index.

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Book SynopsisMany areas of mining engineering gather and use statistical information, provided by observing the actual operation of equipment, their systems, the development of mining works, surface subsidence that accompanies underground mining, displacement of rocks surrounding surface pits and underground drives and longwalls, amongst others. In addition, the actual modern machines used in surface mining are equipped with diagnostic systems that automatically trace all important machine parameters and send this information to the main producerâs computer. Such data not only provide information on the technical properties of the machine but they also have a statistical character. Furthermore, all information gathered during stand and lab investigations where parts, assemblies and whole devices are tested in order to prove their usefulness, have a stochastic character. All of these materials need to be developed statistically and, more importantly, based on these results mining engineers must make decisions whether to undertake actions, connected with the further operation of the machines, the further development of the works, etc. For these reasons, knowledge of modern statistics is necessary for mining engineers; not only as to how statistical analysis of data should be conducted and statistical synthesis should be done, but also as to understanding the results obtained and how to use them to make appropriate decisions in relation to the mining operation.This book on statistical analysis and synthesis starts with a short repetition of probability theory and also includes a special section on statistical prediction. The text is illustrated with many examples taken from mining practice; moreover the tables required to conduct statistical inference are included.Table of Contents1.Fundamentals 2.Some areas of application of mathematical statistics in mining 3.Analysis of data 4.Synthesis of data 5.Relationships between random variables 6.Synthesis of data—regression analysis 7.Special topic: Prediction 8.Explanations of some important terms 9.Statistical tables

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Book SynopsisThis engaging, full-color, activity-packed guide is ideal tool for sharpening math skills!McGraw-Hill's Math Grade 2 helps your elementary school student develop the basic math skills needed to succeed in the classroom and on standardized tests. The eye-catching, 4-color page design creates a student-friendly learning experience, and all pages are filled to the brim with activities for maximum educational value. The book includes easy-to-follow instructions, helpful examples, and tons of practice problems with answers to help students master each concept, sharpen their problem-solving skills, and build confidence.This book features:â New two-page guide offers parents a clear outline of Common Core State Standards for math in this grade, as well as Canadian requirements and standards adopted by non-Common Core statesâ Promotes better scores on achievement testsâ Eye-catching, full-color design appeals to

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