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Lectures on Inductive Logic
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780199666478.jpg" alt="Lectures on Inductive Logic"/><br/></td><td><dl><dt>Author:</dt><dd>Jon Williamson</dd><dt>ISBN:</dt><dd>9780199666478</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Logic / Computer Science / Mathematical Philosophy</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780199666478.001.0001</dd><dt>Published in print:</dt><dd>2017</dd><dt>Published Online:</dt><dd>2017-03-23</dd></dl></td></tr></table><p>Inductive logic (also known as confirmation theory) seeks to determine the extent to which the premisses of an argument entail its conclusion. This book offers an introduction to the field of inductive logic and develops a new Bayesian inductive logic. Chapter 1 introduces perhaps the simplest and most natural account of inductive logic, classical inductive logic, which is attributable to Ludwig Wittgenstein. Classical inductive logic is seen to fail in a crucial way, so there is a need to develop more sophisticated inductive logics. Chapter 2 presents enough logic and probability theory for the reader to begin to study inductive logic, while Chapter 3 introduces the ways in which logic and probability can be combined in an inductive logic. Chapter 4 analyses the most influential approach to inductive logic, due to W.E. Johnson and Rudolf Carnap. Again, this logic is seen to be inadequate. Chapter 5 shows how an alternative approach to inductive logic follows naturally from the philosophical theory of objective Bayesian epistemology. This approach preserves the inferences that classical inductive logic gets right (Chapter 6). On the other hand, it also offers a way out of the problems that beset classical inductive logic (Chapter 7). Chapter 8 defends the approach by tackling several key criticisms that are often levelled at inductive logic. Chapter 9 presents a formal justification of the version of objective Bayesianism which underpins the approach. Chapter 10 explains what has been achieved and poses some open questions.</p>Jon Williamson2017-03-23Everyday Cryptography
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780199695591.jpg" alt="Everyday CryptographyFundamental Principles and Applications"/><br/></td><td><dl><dt>Author:</dt><dd>Keith M. Martin</dd><dt>ISBN:</dt><dd>9780199695591</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Applied Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780199695591.001.0001</dd><dt>Published in print:</dt><dd>2012</dd><dt>Published Online:</dt><dd>2013-12-17</dd></dl></td></tr></table><p>Cryptography is a vital technology that underpins the security of information in computer networks. This book presents an introduction to the role that cryptography plays in providing information security for technologies such as the Internet, mobile phones, payment cards, and wireless local area networks. Focusing on the fundamental principles that ground modern cryptography as they arise in modern applications, it avoids both an over-reliance on transient current technologies and over-whelming theoretical research. A short appendix is included for those looking for a deeper appreciation of some of the concepts involved. By the end of this book, the reader will not only be able to understand the practical issues concerned with the deployment of cryptographic mechanisms, including the management of cryptographic keys, but will also be able to interpret future developments in this increasingly important area of technology.</p>Keith M. Martin2013-12-17Spectral/hp Element Methods for Computational Fluid Dynamics
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198528692.jpg" alt="Spectral/hp Element Methods for Computational Fluid Dynamics"/><br/></td><td><dl><dt>Author:</dt><dd>George Karniadakis, Spencer Sherwin</dd><dt>ISBN:</dt><dd>9780198528692</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Numerical Analysis</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198528692.001.0001</dd><dt>Published in print:</dt><dd>2005</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more limited. More recently, the need to find accurate solutions to the viscous flow equations around complex configurations has led to the development of high-order discretization procedures on unstructured meshes, which are also recognized as more efficient for solution of time-dependent oscillatory solutions over long time periods. This book, an updated edition on the original text, presents the recent and significant progress in multi-domain spectral methods at both the fundamental and application level. Containing material on discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilization and filtering techniques, this text introduces the use of spectral/hp element methods with particular emphasis on their application to unstructured meshes. It provides a detailed explanation of the key concepts underlying the methods along with practical examples of their derivation and application.</p>George Karniadakis and Spencer Sherwin2007-09-01The Decomposition of Global Conformal Invariants (AM-182)
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780691153476.jpg" alt="The Decomposition of Global Conformal Invariants (AM-182)"/><br/></td><td><dl><dt>Author:</dt><dd>Spyros Alexakis</dd><dt>ISBN:</dt><dd>9780691153476</dd><dt>Publisher:</dt><dd>Princeton University Press</dd><dt>Subjects:</dt><dd>Mathematics, Geometry / Topology</dd><dt>DOI:</dt><dd>10.23943/princeton/9780691153476.001.0001</dd><dt>Published in print:</dt><dd>2012</dd><dt>Published Online:</dt><dd>2017-10-19</dd></dl></td></tr></table><p>This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? This book asserts that the Riemannian scalar must be a linear combination of three obvious candidates, each of which clearly satisfies the required property: a local conformal invariant, a divergence of a Riemannian vector field, and the Chern–Gauss–Bonnet integrand. The book provides a proof of this conjecture. The result itself sheds light on the algebraic structure of conformal anomalies, which appear in many settings in theoretical physics. It also clarifies the geometric significance of the renormalized volume of asymptotically hyperbolic Einstein manifolds. The methods introduced here make an interesting connection between algebraic properties of local invariants—such as the classical Riemannian invariants and the more recently studied conformal invariants—and the study of global invariants, in this case conformally invariant integrals.</p>Spyros Alexakis2017-10-19Numerical Methods for Image Registration
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198528418.jpg" alt="Numerical Methods for Image Registration"/><br/></td><td><dl><dt>Author:</dt><dd>Jan Modersitzki</dd><dt>ISBN:</dt><dd>9780198528418</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Applied Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198528418.001.0001</dd><dt>Published in print:</dt><dd>2003</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This text provides an introduction to the theoretical, practical, and numerical aspects of image registration, with special emphasis on medical imaging. Given a so-called reference and template image, the goal of image registration is to find a reasonable transformation such that the transformed template is similar to the reference image. Image registration is utilized whenever information obtained from different viewpoints times and sensors needs to be combined or compared, and unwanted distortion needs to be eliminated. The book provides a systematic introduction to image registration and discusses the basic mathematical principles, including aspects from approximations theory, image processing, numerics, optimization, partial differential equations, and statistics, with a strong focus on numerical methods. A unified variational approach is introduced and enables a separation into data-related issues like image feature or image intensity-based similarity measures, and problem inherent regularization like elastic or diffusion registration. This general framework is further used for the explanation and classification of established methods as well as the design of new schemes and building blocks including landmark-, thin-plate-spline, mutual information, elastic, fluid, demon, diffusion, and curvature registration.</p>Jan Modersitzki2007-09-01An Introduction to Model-Based Survey Sampling with Applications
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198566625.jpg" alt="An Introduction to Model-Based Survey Sampling with Applications"/><br/></td><td><dl><dt>Author:</dt><dd>Ray Chambers, Robert Clark</dd><dt>ISBN:</dt><dd>9780198566625</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Probability / Statistics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198566625.001.0001</dd><dt>Published in print:</dt><dd>2012</dd><dt>Published Online:</dt><dd>2012-05-24</dd></dl></td></tr></table><p>This book is an introduction to the model-based approach to survey sampling. It consists of three parts, with Part I focusing on estimation of population totals. Chapters 1 and 2 introduce survey sampling, and the model-based approach, respectively. Chapter 3 considers the simplest possible model, the homogenous population model, which is then extended to stratified populations in Chapter 4. Chapter 5 discusses simple linear regression models for populations, and Chapter 6 considers clustered populations. The general linear population model is then used to integrate these results in Chapter 7. Part II of this book considers the properties of estimators based on incorrectly specified models. Chapter 8 develops robust sample designs that lead to unbiased predictors under model misspecification, and shows how flexible modelling methods like non-parametric regression can be used in survey sampling. Chapter 9 extends this development to misspecfication robust prediction variance estimators and Chapter 10 completes Part II of the book with an exploration of outlier robust sample survey estimation. Chapters 11 to 17 constitute Part III of the book and show how model-based methods can be used in a variety of problem areas of modern survey sampling. They cover (in order) prediction of non-linear population quantities, sub-sampling approaches to prediction variance estimation, design and estimation for multipurpose surveys, prediction for domains, small area estimation, efficient prediction of population distribution functions and the use of transformations in survey inference. The book is designed to be accessible to undergraduate and graduate level students with a good grounding in statistics and applied survey statisticians seeking an introduction to model-based survey design and estimation.</p>Ray Chambers and Robert Clark2012-05-24Proving in the Elementary Mathematics Classroom
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198723066.jpg" alt="Proving in the Elementary Mathematics Classroom"/><br/></td><td><dl><dt>Author:</dt><dd>Andreas J. Stylianides</dd><dt>ISBN:</dt><dd>9780198723066</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Educational Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198723066.001.0001</dd><dt>Published in print:</dt><dd>2016</dd><dt>Published Online:</dt><dd>2016-09-22</dd></dl></td></tr></table><p>Proving in the Elementary Mathematics Classroom addresses a fundamental problem in children’s learning that has received relatively little research attention: Although proving and related concepts (e.g., proof, argumentation, conjecturing) are core to mathematics as a sense-making activity, they currently have a marginal place in elementary classrooms internationally. This book takes a step toward addressing this problem by examining how the place of proving in elementary students’ mathematical work can be elevated through the purposeful design and implementation of mathematics tasks, specifically proving tasks. In particular, the book draws on relevant research and theory and classroom episodes with 8–9-year-olds from England and the United States to examine different kinds of proving tasks and the proving activity they can help generate in the elementary classroom. It examines further the role of elementary teachers in mediating the relationship between proving tasks and proving activity, including major mathematical and pedagogical issues that can arise for them as they implement each kind of proving task in the classroom. In addition to its research contribution in the intersection of the scholarly areas of teaching/learning proving and task design/implementation, the book has important implications for teaching, curricular resources, and teacher education. For example, the book identifies different kinds of proving tasks whose balanced representation in the mathematics classroom and in curricular resources can support a rounded set of learning experiences for elementary students related to proving. It identifies further important mathematical ideas and pedagogical practices related to proving that can be studied in teacher education.</p>Andreas J. Stylianides2016-09-22Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780691174822.jpg" alt="Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time"/><br/></td><td><dl><dt>Author:</dt><dd>Philip Isett</dd><dt>ISBN:</dt><dd>9780691174822</dd><dt>Publisher:</dt><dd>Princeton University Press</dd><dt>Subjects:</dt><dd>Mathematics, Computational Mathematics / Optimization</dd><dt>DOI:</dt><dd>10.23943/princeton/9780691174822.001.0001</dd><dt>Published in print:</dt><dd>2017</dd><dt>Published Online:</dt><dd>2017-10-19</dd></dl></td></tr></table><p>Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. This book uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations. The construction itself—an intricate algorithm with hidden symmetries—mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful “Main Lemma”—used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem—has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture.</p>Philip Isett2017-10-19Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780691160757.jpg" alt="Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)"/><br/></td><td><dl><dt>Author:</dt><dd>Christopher D. Sogge</dd><dt>ISBN:</dt><dd>9780691160757</dd><dt>Publisher:</dt><dd>Princeton University Press</dd><dt>Subjects:</dt><dd>Mathematics, Numerical Analysis</dd><dt>DOI:</dt><dd>10.23943/princeton/9780691160757.001.0001</dd><dt>Published in print:</dt><dd>2014</dd><dt>Published Online:</dt><dd>2017-10-19</dd></dl></td></tr></table><p>Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. The book gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace–Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. The book shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic. It begins with a treatment of the Hadamard parametrix before proving the first main result, the sharp Weyl formula. The book avoids the use of Tauberian estimates and instead relies on sup-norm estimates for eigenfunctions. It also gives a rapid introduction to the stationary phase and the basics of the theory of pseudodifferential operators and microlocal analysis. These are used to prove the Duistermaat-Guillemin theorem. Turning to the related topic of quantum ergodicity, the book demonstrates that if the long-term geodesic flow is uniformly distributed, most eigenfunctions exhibit a similar behavior, in the sense that their mass becomes equidistributed as their frequencies go to infinity.</p>Christopher D. Sogge2017-10-19Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780691160504.jpg" alt="Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)"/><br/></td><td><dl><dt>Author:</dt><dd>Claire Voisin</dd><dt>ISBN:</dt><dd>9780691160504</dd><dt>Publisher:</dt><dd>Princeton University Press</dd><dt>Subjects:</dt><dd>Mathematics, Geometry / Topology</dd><dt>DOI:</dt><dd>10.23943/princeton/9780691160504.001.0001</dd><dt>Published in print:</dt><dd>2014</dd><dt>Published Online:</dt><dd>2017-10-19</dd></dl></td></tr></table><p>This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The book is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by the author. It focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by the author looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.</p>Claire Voisin2017-10-19Electromagnetism of Continuous Media
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198527008.jpg" alt="Electromagnetism of Continuous MediaMathematical Modelling and Applications"/><br/></td><td><dl><dt>Author:</dt><dd>Mauro Fabrizio, Angelo Morro</dd><dt>ISBN:</dt><dd>9780198527008</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Applied Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198527008.001.0001</dd><dt>Published in print:</dt><dd>2003</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This book is devoted to the mathematical modelling of electromagnetic materials. Electromagnetism in matter is developed with particular emphasis on material effects, which are ascribed to memory in time and nonlocality. Within the mathematical modelling, thermodynamics of continuous media plays a central role in that it places significant restrictions on the constitutive equations. Further, as shown in connection with uniqueness, existence and stability, variational settings, and wave propagation, a correct formulation of the pertinent problems is based on the knowledge of the thermodynamic restrictions for the material. The book is divided into four parts. Part I (chapters 1 to 4) reviews the basic concepts of electromagnetism, starting from the integral form of Maxwell’s equations and then addressing attention to the physical motivation for materials with memory. Part II (chapers 5 to 9) deals with thermodynamics of systems with memory and applications to evolution and initial/boundary-value problems. It contains developments and results which are unusual in textbooks on electromagnetism and arise from the research literature, mainly post-1960s. Part III (chapters 10 to 12) outlines some topics of materials modelling — nonlinearity, nonlocality, superconductivity, and magnetic hysteresis — which are of great interest both in mathematics and in applications.</p>Mauro Fabrizio and Angelo Morro2007-09-01Arithmetic Compactifications of PEL-Type Shimura Varieties
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780691156545.jpg" alt="Arithmetic Compactifications of PEL-Type Shimura Varieties"/><br/></td><td><dl><dt>Author:</dt><dd>Kai-Wen Lan</dd><dt>ISBN:</dt><dd>9780691156545</dd><dt>Publisher:</dt><dd>Princeton University Press</dd><dt>Subjects:</dt><dd>Mathematics, Geometry / Topology</dd><dt>DOI:</dt><dd>10.23943/princeton/9780691156545.001.0001</dd><dt>Published in print:</dt><dd>2013</dd><dt>Published Online:</dt><dd>2017-10-19</dd></dl></td></tr></table><p>By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments. PEL-type Shimura varieties, which are natural generalizations of modular curves, are useful for studying the arithmetic properties of automorphic forms and automorphic representations, and they have played important roles in the development of the Langlands program. As with modular curves, it is desirable to have integral models of compactifications of PEL-type Shimura varieties that can be described in sufficient detail near the boundary, which this book explains in detail. Through the discussion, the book generalizes the theory of degenerations of polarized abelian varieties and the application of that theory to the construction of toroidal and minimal compactifications of Siegel moduli schemes over the integers (as developed by Mumford, Faltings, and Chai). The book is designed to be accessible to graduate students who have an understanding of schemes and abelian varieties.</p>Kai-Wen Lan2017-10-19Multi-parameter Singular Integrals. (AM-189)
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780691162515.jpg" alt="Multi-parameter Singular Integrals. (AM-189)"/><br/></td><td><dl><dt>Author:</dt><dd>Brian Street</dd><dt>ISBN:</dt><dd>9780691162515</dd><dt>Publisher:</dt><dd>Princeton University Press</dd><dt>Subjects:</dt><dd>Mathematics, Analysis</dd><dt>DOI:</dt><dd>10.23943/princeton/9780691162515.001.0001</dd><dt>Published in print:</dt><dd>2014</dd><dt>Published Online:</dt><dd>2017-10-19</dd></dl></td></tr></table><p>This book develops a new theory of multi-parameter singular integrals associated with Carnot–Carathéodory balls. The book first details the classical theory of Calderón–Zygmund singular integrals and applications to linear partial differential equations. It then outlines the theory of multi-parameter Carnot–Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. The book then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. This book will interest graduate students and researchers working in singular integrals and related fields.</p>Brian Street2017-10-19Sasakian Geometry
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198564959.jpg" alt="Sasakian Geometry"/><br/></td><td><dl><dt>Author:</dt><dd>Charles Boyer, Krzysztof Galicki</dd><dt>ISBN:</dt><dd>9780198564959</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Geometry / Topology</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198564959.001.0001</dd><dt>Published in print:</dt><dd>2007</dd><dt>Published Online:</dt><dd>2008-01-01</dd></dl></td></tr></table><p>Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate relationship between Sasakian and Kähler geometries, especially when the Kähler structure is that of an algebraic variety. The book is divided into three parts. The first five chapters carefully prepare the stage for the proper introduction of the subject. After a brief discussion of G-structures, the reader is introduced to the theory of Riemannian foliations. A concise review of complex and Kähler geometry precedes a fairly detailed treatment of compact complex Kähler orbifolds. A discussion of the existence and obstruction theory of Kähler-Einstein metrics (Monge-Ampère problem) on complex compact orbifolds follows. The second part gives a careful discussion of contact structures in the Riemannian setting. Compact quasi-regular Sasakian manifolds emerge here as algebraic objects: they are orbifold circle bundles over compact projective algebraic orbifolds. After a discussion of symmetries of Sasakian manifolds in Chapter 8, the book looks at Sasakian structures on links of isolated hypersurface singularities in Chapter 9. What follows is a study of compact Sasakian manifolds in dimensions three and five focusing on the important notion of positivity. The latter is crucial in understanding the existence of Sasaki-Einstein and 3-Sasakian metrics, which are studied in Chapters 11 and 13. Chapter 12 gives a fairly brief description of quaternionic geometry which is a prerequisite for Chapter 13. The study of Sasaki-Einstein geometry was the original motivation for the book. The final chapter on Killing spinors discusses the properties of Sasaki-Einstein manifolds, which allow them to play an important role as certain models in the supersymmetric field theories of theoretical physics.</p>Charles Boyer and Krzysztof Galicki2008-01-01Thiele: Pioneer in Statistics
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198509721.jpg" alt="Thiele: Pioneer in Statistics"/><br/></td><td><dl><dt>Author:</dt><dd>Steffen L. Lauritzen</dd><dt>ISBN:</dt><dd>9780198509721</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Probability / Statistics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198509721.001.0001</dd><dt>Published in print:</dt><dd>2002</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>Thorvald Nicolai Thiele was a brilliant Danish researcher of the 19th century. He was a professor of Astronomy at the University of Copenhagen and the founder of Hafnia, the first Danish private insurance company. Thiele worked in astronomy, mathematics, actuarial science, and statistics, his most spectacular contributions were in the latter two areas, where his published work was far ahead of his time. This book is concerned with his statistical work. It evolves around his three main statistical masterpieces, which are now translated into English for the first time: 1) his article from 1880 where he derives the Kalman filter; 2) his book from 1889, where he lays out the subject of statistics in a highly original way, derives the half-invariants (today known as cumulants), the notion of likelihood in the case of binomial experiments, the canonical form of the linear normal model, and develops model criticism via analysis of residuals; and 3) an article from 1899 where he completes the theory of the half-invariants. This book also contains three chapters, written by A. Hald and S. L. Lauritzen, which describe Thiele's statistical work in modern terms and puts it into an historical perspective.</p>Steffen L. Lauritzen2007-09-01The Theory of Infinite Soluble Groups
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198507284.jpg" alt="The Theory of Infinite Soluble Groups"/><br/></td><td><dl><dt>Author:</dt><dd>John C. Lennox, Derek J. S. Robinson</dd><dt>ISBN:</dt><dd>9780198507284</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Pure Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198507284.001.0001</dd><dt>Published in print:</dt><dd>2004</dd><dt>Published Online:</dt><dd>2007-09-01</dd></dl></td></tr></table><p>This book provides a comprehensive account of the theory of infinite soluble groups, from its foundations up to research level. Topics covered include: polycyclic groups, Cernikov groups, Mal’cev completions, soluble linear groups, P. Hall’s theory of finitely generated soluble groups, soluble groups with finite rank, soluble groups whose abelian subgroups satisfy finiteness conditions, simple modules over polycyclic groups, the Jategaonkar-Roseblade theorem, centrality in finitely generated soluble groups and the Lennox-Roseblade theorem, algorithmic problems for polycyclic and metabelian groups, cohomological topics including groups with finite (co)homological dimension and vanishing theorems, finitely presented soluble groups, constructible soluble groups, the Bieri-Strebel invariant, subnormality, and soluble groups.</p>John C. Lennox and Derek J. S. Robinson2007-09-01Riemann Surfaces
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780198526391.jpg" alt="Riemann Surfaces"/><br/></td><td><dl><dt>Author:</dt><dd>Simon Donaldson</dd><dt>ISBN:</dt><dd>9780198526391</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Geometry / Topology, Analysis</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780198526391.001.0001</dd><dt>Published in print:</dt><dd>2011</dd><dt>Published Online:</dt><dd>2013-12-17</dd></dl></td></tr></table><p>The theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination of much of traditional calculus, making surprising connections with geometry and arithmetic. It is an extremely useful part of mathematics, knowledge of which is needed by specialists in many other fields. It provides a model for a large number of more recent developments in areas including manifold topology, global analysis, algebraic geometry, Riemannian geometry, and diverse topics in mathematical physics. This text on Riemann surface theory proves the fundamental analytical results on the existence of meromorphic functions and the Uniformisation Theorem. The approach taken emphasises PDE methods, applicable more generally in global analysis. The connection with geometric topology, and in particular the role of the mapping class group, is also explained. To this end, some more sophisticated topics have been included, compared with traditional texts at this level. While the treatment is novel, the roots of the subject in traditional calculus and complex analysis are kept well in mind. Part I sets up the interplay between complex analysis and topology, with the latter treated informally. Part II works as a rapid first course in Riemann surface theory, including elliptic curves. The core of the book is contained in Part III, where the fundamental analytical results are proved.</p>Simon Donaldson2013-12-17The Factorization Method for Inverse Problems
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780199213535.jpg" alt="The Factorization Method for Inverse Problems"/><br/></td><td><dl><dt>Author:</dt><dd>Andreas Kirsch, Natalia Grinberg</dd><dt>ISBN:</dt><dd>9780199213535</dd><dt>Publisher:</dt><dd>Oxford University Press</dd><dt>Subjects:</dt><dd>Mathematics, Applied Mathematics</dd><dt>DOI:</dt><dd>10.1093/acprof:oso/9780199213535.001.0001</dd><dt>Published in print:</dt><dd>2007</dd><dt>Published Online:</dt><dd>2008-09-01</dd></dl></td></tr></table><p>This book is devoted to problems of shape identification in the context of (inverse) scattering problems and problems of impedance tomography. In contrast to traditional methods which are based on iterative schemes of solving sequences of corresponding direct problems, this book presents a completely different method. The Factorization Method avoids the need to solve the (time consuming) direct problems. Furthermore, no a-priori information about the type of scatterer (penetrable or impenetrable), type of boundary condition, or number of components is needed. The Factorization Method can be considered as an example of a Sampling Method. The book aims to construct a binary criterium on the known data to decide whether or not a given point z is inside or outside the unknown domain D. By choosing a grid of sampling points z in a region known to contain D, the characteristic function of D can be computed (in the case of finite data only approximately). The book also introduces some alternative Sampling Methods.</p>Andreas Kirsch and Natalia Grinberg2008-09-01Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780691153704.jpg" alt="Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)"/><br/></td><td><dl><dt>Author:</dt><dd>Umberto ZannierDavidMasserDavid Masser</dd><dt>ISBN:</dt><dd>9780691153704</dd><dt>Publisher:</dt><dd>Princeton University Press</dd><dt>Subjects:</dt><dd>Mathematics, Geometry / Topology</dd><dt>DOI:</dt><dd>10.23943/princeton/9780691153704.001.0001</dd><dt>Published in print:</dt><dd>2012</dd><dt>Published Online:</dt><dd>2017-10-19</dd></dl></td></tr></table><p>This book considers the so-called unlikely intersections, a topic that embraces well-known issues, such as Lang's and Manin–Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension. The book is an expansion of the Hermann Weyl Lectures delivered by the author at the Institute for Advanced Study in Princeton in May 2010.The book consists of four chapters and seven brief appendixes. The first chapter considers multiplicative algebraic groups, presenting proofs of several developments, ranging from the origins to recent results, and discussing many applications and relations with other contexts. The second chapter considers an analogue in arithmetic and several applications of this. The third chapter introduces a new method for approaching some of these questions, and presents a detailed application of this to a relative case of the Manin–Mumford issue. The fourth chapter focuses on the André–Oort conjecture (outlining work by Pila).</p>Umberto Zannier2017-10-19Circles Disturbed
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<table><tr><td width="200px"><img width="150px" src="/view/covers/9780691149042.jpg" alt="Circles DisturbedThe Interplay of Mathematics and Narrative"/><br/></td><td><dl><dt>Author:</dt><dd>ApostolosDoxiadisApostolos DoxiadisBarryMazurBarry MazurHarvard University</dd><dt>ISBN:</dt><dd>9780691149042</dd><dt>Publisher:</dt><dd>Princeton University Press</dd><dt>Subjects:</dt><dd>Mathematics, History of Mathematics</dd><dt>DOI:</dt><dd>10.23943/princeton/9780691149042.001.0001</dd><dt>Published in print:</dt><dd>2012</dd><dt>Published Online:</dt><dd>2017-10-19</dd></dl></td></tr></table><p>This book brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. “Circles disturbed” reflect the last words of Archimedes before he was slain by a Roman soldier—“Don't disturb my circles”—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities. This book delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of “myths of origins” in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more.</p>Apostolos Doxiadis and Barry Mazur2017-10-19