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by Martin Gardner (Author)Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi is the inaugural volume in The New Martin Gardner Mathematical Library series. Based off of Gardener's enormously popular Scientific American columns, his puzzles and challenges can now fascinate a whole new generation Paradoxes and paper-folding, Moebius variations and mnemonics, fallacies, magic square, topological curiosities, parlor tricks, and games ancient and modern, from Polyminoes, Nim, Hex, and t...
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by J. K. Lindsey (Author)This introduction to ways of modelling a wide variety of phenomena that occur over time is accessible to anyone with a basic knowledge of statistical ideas. J.K. Lindsey concentrates on tractable models involving simple processes for which explicit probability models, hence likelihood functions, can be specified. (These models are the most useful in statistical applications modelling empirical data.) Examples are drawn from physical, biological and social sciences, to...
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by Andrea Prosperetti (Author)The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of...
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by C. J. Van Rijsbergen (Author)Keith Van Rijsbergen demonstrates how different models of information retrieval (IR) can be combined in the same framework used to formulate the general principles of quantum mechanics. All the standard results can be applied to address problems in IR, such as pseudo-relevance feedback, relevance feedback and ostensive retrieval. The relation with quantum computing is examined. Appendices with background material on physics and mathematics are also included. Nu...
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by Shimon Even (Author), Guy Even (Editor)Shimon Even's Graph Algorithms, published in 1979, was a seminal introductory book on algorithms read by everyone engaged in the field. This thoroughly revised second edition, with a foreword by Richard M. Karp and notes by Andrew V. Goldberg, continues the exceptional presentation from the first edition and explains algorithms in a formal but simple language with a direct and intuitive presentation. The book begins by covering basic material, includi...
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by Marlos A. G. Viana (Author)Experimental data can often be associated with or indexed by certain symmetrically interesting structures or sets of labels that appear, for example, in the study of short symbolic sequences in molecular biology, in preference or voting data, in (corneal) curvature data, and in studies of the handedness and entropy of symbolic sequences and elementary images. The symmetry studies introduced in this book describe the interplay among symmetry transformations that a...
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by David Applebaum (Author)L vy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of L vy processes, then leading on to develop the stochastic calculus for L vy processes in a direct and accessible way. This fully revised edition now features a n...
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by Ernesto Girondo (Author), Gabino González-Diez (Author)Few books on the subject of Riemann surfaces cover the relatively modern theory of dessins d'enfants (children's drawings), which was launched by Grothendieck in the 1980s and is now an active field of research. In this book, the authors begin with an elementary account of the theory of compact Riemann surfaces viewed as algebraic curves and as quotients of the hyperbolic plane by the action of Fuchsian groups of finite type. They then...
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by Allen Hatcher (Author)In most major universities one of the three or four basic first-year graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emp...
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by George Boros (Author), Victor Moll (Author)The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in nineteenth century analysis and it has now been revived with the appearance of symbolic languages. The authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed are as old as calculus itself. In presenting the combina...
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by David A. Freedman (Author)This lively and engaging textbook explains the things you have to know in order to read empirical papers in the social and health sciences, as well as the techniques you need to build statistical models of your own. The author, David A. Freedman, explains the basic ideas of association and regression, and takes you through the current models that link these ideas to causality. The focus is on applications of linear models, including generalized least squares and t...
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by Béla Bollobás (Author)This is a new edition of the now classic text. The already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents an up-to-date and comprehensive account of random graph theory. The theory estimates the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves...
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by Thomas A. Severini (Author)This detailed introduction to distribution theory is designed as a text for the probability portion of the first year statistical theory sequence for Master's and PhD students in statistics, biostatistics, and econometrics. The text uses no measure theory, requiring only a background in calculus and linear algebra. Topics range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distrib...
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by Martin Gardner (Author)Packing spheres, Reversi, braids, polyominoes, board games, and the puzzles of Lewis Carroll. These and other mathematical diversions return to readers with updates to all the chapters, including new game variations, mathematical proofs, and other developments and discoveries. Read about Knuth's Word Ladders program and the latest developments in the digits of pi. Once again these timeless puzzles will charm readers while demonstrating principles of logic, probabilit...
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by Anton Bovier (Author)This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds ...
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by Martin Gardner (Author)Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi is the inaugural volume in The New Martin Gardner Mathematical Library series. Based off of Gardener's enormously popular Scientific American columns, his puzzles and challenges can now fascinate a whole new generation Paradoxes and paper-folding, Moebius variations and mnemonics, fallacies, magic square, topological curiosities, parlor tricks, and games ancient and modern, from Polyminoes, Nim, Hex, and t...
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by Gerda Claeskens (Author), Nils Lid Hjort (Author)Choosing a model is central to all statistical work with data. We have seen rapid advances in model fitting and in the theoretical understanding of model selection, yet this book is the first to synthesize research and practice from this active field. Model choice criteria are explained, discussed and compared, including the AIC, BIC, DIC and FIC. The uncertainties involved with model selection are tackled with discussions of frequent and Ba...
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by Martin Gardner (Author)The hangman's paradox, cat's cradle, gambling, peg solitaire, pi and e. All these and more are back, in Martin Gardner's inimitable style, with updates on new developments and discoveries. Read about how knots and molecules are related, take a trip into the fourth dimension, try out new dissections of stars, crosses and polygons, and challenge yourself with new twists on classic games. Number of Pages: 288 Dimensions: 0.6 x 8.4 x 5.5 IN Publication Date: September 15...
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by Edward Frenkel (Author)The Langlands Program was conceived initially as a bridge between Number Theory and Automorphic Representations, and has now expanded into such areas as Geometry and Quantum Field Theory, tying together seemingly unrelated disciplines into a web of tantalizing conjectures. A new chapter to this grand project is provided in this book. It develops the geometric Langlands Correspondence for Loop Groups, a new approach, from a unique perspective offered by affine Kac-Moo...
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by K. F. Riley (Author), M. P. Hobson (Author)The mathematical methods that physical scientists need for solving substantial problems in their fields of study are set out clearly and simply in this tutorial-style textbook. Students will develop problem-solving skills through hundreds of worked examples, self-test questions and homework problems. Each chapter concludes with a summary of the main procedures and results and all assumed prior knowledge is summarized in one of the appendices. Over...
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by L. Pachter (Editor), B. Sturmfels (Editor)The quantitative analysis of biological sequence data is based on methods from statistics coupled with efficient algorithms from computer science. Algebra provides a framework for unifying many of the seemingly disparate techniques used by computational biologists. This book offers an introduction to this mathematical framework and describes tools from computational algebra for designing new algorithms for exact, accurate results. These algorithms ...
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by Jon Lee (Author)Jon Lee focuses on key mathematical ideas leading to useful models and algorithms, rather than on data structures and implementation details, in this introductory graduate-level text for students of operations research, mathematics, and computer science. The viewpoint is polyhedral, and Lee also uses matroids as a unifying idea. Topics include linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows. Problems and exerci...
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by Katrin Tent (Author), Martin Ziegler (Author)This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many ...
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by Gilles Pisier (Author)The first part of this book is an introduction with emphasis on examples that illustrate the theory of operator spaces. The second part is devoted to applications to C*-algebras, with a systematic exposition of tensor products of C* algebras. The third part of the book describes applications to non self-adjoint operator algebras and similarity problems. The author's counterexample to the "Halmos problem" is presented, along with work on the new concept of "length" of ...
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by Donald B. Rubin (Author)Matched sampling is often used to help assess the causal effect of some exposure or intervention, typically when randomized experiments are not available or cannot be conducted. This book presents a selection of Donald B. Rubin's research articles on matched sampling, from the early 1970s, when the author was one of the major researchers involved in establishing the field, to recent contributions to this now extremely active area. The articles include fundamental th...
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by John Shawe-Taylor (Author), Nello Cristianini (Author)This book provides professionals with a large selection of algorithms, kernels and solutions ready for implementation and suitable for standard pattern discovery problems in fields such as bioinformatics, text analysis and image analysis. It also serves as an introduction for students and researchers to the growing field of kernel-based pattern analysis, demonstrating with examples how to handcraft an algorithm or a kernel for a new spe...
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by Kurt Jacobs (Author)Stochastic processes are an essential part of numerous branches of physics, as well as in biology, chemistry, and finance. This textbook provides a solid understanding of stochastic processes and stochastic calculus in physics, without the need for measure theory. In avoiding measure theory, this textbook gives readers the tools necessary to use stochastic methods in research with a minimum of mathematical background. Coverage of the more exotic Levy processes is includ...
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by Michael B. Marcus (Author), Jay Rosen (Author)Written by two foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and fo...
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by Antonio Ambrosetti (Author), Andrea Malchiodi (Author)Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way that will be appreciated by mathematicians, physicists and engineers. Starting from elementary tools of...
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by Benedict Leimkuhler (Author), Sebastian Reich (Author)The simulation of matter by direct computation of individual atomic motions has become an important element in the design of new drugs and in the construction of new materials. This book demonstrates how to implement the numerical techniques needed for such simulation, thereby aiding the design of new, faster, and more robust solution schemes. Clear explanations and many examples and exercises will ensure the value of this text for stud...
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by P. A. Martin (Author)The interaction of waves with obstacles is an everyday phenomenon in science and engineering, arising for example in acoustics, electromagnetism, seismology and hydrodynamics. The mathematical theory and technology needed to understand the phenomenon is known as multiple scattering, and this book is the first devoted to the subject. The author covers a variety of techniques, describing first the single-obstacle methods and then extending them to the multiple-obstacle c...
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by Hansjörg Geiges (Author)This text on contact topology is the first comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional...