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Solitons Instantons And Twistors
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Book Synopsis Solitons, Instantons, and Twistors by : Maciej Dunajski
Download or read book Solitons, Instantons, and Twistors written by Maciej Dunajski and published by Oxford University Press. This book was released on 2010 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text aimed at third year undergraduates and graduates in mathematics and physics, presenting elementary twistor theory as a universal technique for solving differential equations in applied mathematics and theoretical physics.
Book Synopsis Solitons and Instantons by : R. Rajaraman
Download or read book Solitons and Instantons written by R. Rajaraman and published by . This book was released on 1987 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry, Lie Theory and Applications by : Sigbjørn Hervik
Download or read book Geometry, Lie Theory and Applications written by Sigbjørn Hervik and published by Springer Nature. This book was released on 2022-02-07 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity. The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.
Book Synopsis From Quantum Cohomology to Integrable Systems by : Martin A. Guest
Download or read book From Quantum Cohomology to Integrable Systems written by Martin A. Guest and published by OUP Oxford. This book was released on 2008-03-13 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum cohomology has its origins in symplectic geometry and algebraic geometry, but is deeply related to differential equations and integrable systems. This text explains what is behind the extraordinary success of quantum cohomology, leading to its connections with many existing areas of mathematics as well as its appearance in new areas such as mirror symmetry. Certain kinds of differential equations (or D-modules) provide the key links between quantum cohomology and traditional mathematics; these links are the main focus of the book, and quantum cohomology and other integrable PDEs such as the KdV equation and the harmonic map equation are discussed within this unified framework. Aimed at graduate students in mathematics who want to learn about quantum cohomology in a broad context, and theoretical physicists who are interested in the mathematical setting, the text assumes basic familiarity with differential equations and cohomology.
Book Synopsis Bayesian Statistical Modelling by : P. Congdon
Download or read book Bayesian Statistical Modelling written by P. Congdon and published by . This book was released on 2001-05-02 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian methods draw upon previous research findings and combine them with sample data to analyse problems and modify existing hypotheses. The calculations are often extremely complex, with many only now possible due to recent advances in computing technology. Bayesian methods have as a result gained wider acceptance, and are applied in many scientific disciplines, including applied statistics, public health research, medical science, the social sciences and economics. Bayesian Statistical Modelling presents an accessible overview of modelling applications from a Bayesian perspective. * Provides an integrated presentation of theory, examples and computer algorithms * Examines model fitting in practice using Bayesian principles * Features a comprehensive range of methodologies and modelling techniques * Covers recent innovations in bayesian modelling, including Markov Chain Monte Carlo methods * Includes extensive applications to health and social sciences * Features a comprehensive collection of nearly 200 worked examples * Data examples and computer code in WinBUGS are available via ftp Whilst providing a general overview of Bayesian modelling, the author places emphasis on the principles of prior selection, model identification and interpretation of findings, in a range of modelling innovations, focussing on their implementation with real data, with advice as to appropriate computing choices and strategies. Researchers in applied statistics, medical science, public health and the social sciences will benefit greatly from the examples and applications featured. The book will also appeal to graduate students of applied statistics, data analysis and Bayesian methods, and will provide a good reference source for both researchers and students.
Book Synopsis Applications of Contact Geometry and Topology in Physics by : Arkady L Kholodenko
Download or read book Applications of Contact Geometry and Topology in Physics written by Arkady L Kholodenko and published by World Scientific. This book was released on 2013-05-03 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although contact geometry and topology is briefly discussed in V I Arnol'd's book “Mathematical Methods of Classical Mechanics ”(Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges “An Introduction to Contact Topology” (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph “Contact Geometry and Nonlinear Differential Equations” (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau–Lifshitz (L–L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L–L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L–L course some problems/exercises are formulated along the way and, again as in the L–L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L–L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text. Contents:Motivation and BackgroundFrom Ideal Magnetohydrodynamics to String and Knot TheoryAll About and Around Woltjer's TheoremTopologically Massive Gauge Theories and Force-Free FieldsContact Geometry and PhysicsSub-Riemannian Geometry, Heisenberg Manifolds and Quantum Mechanics of Landau LevelsAbrikosov Lattices, TGB Phases in Liquid Crystals and Heisenberg GroupSub-Riemannian Geometry, Spin Dynamics and Quantum-Classical Optimal ControlFrom Contact Geometry to Contact TopologyClosing Remarks:The Unreasonable Effectivenessof Contact Geometry and Topology in Physical SciencesAppendices:Heisenberg Group in the Context of Sub-Riemannian Geometry and Optimal ControlSub-Riemannian Dynamics of Josephson JunctionsQuantum Computers and Quantum Random WalksThe Measurement Protocol. Geometry and Topology of Entanglements Readership: Students in applied mathematics and theoretical physics. Keywords:Force-Free Fields;Contact and Sub-Riemannian Geometry;Optimal Control;Theoretical PhysicsKey Features:This book is the world's first book on contact/sub-Riemannian geometry and topology for physicistsUnlike books discussing mathematical methods for physicists, this book discusses physical problems first and only then uses new mathematics to solve these problems. Problems are selected from practically all branches of theoretical physicsThis is done with the purpose of demonstrating that contact geometry should be looked upon as a universal language/technical tool of theoretical physicsReviews: “This book is written in the style of the well-known Landau-Lifshitz multivolume course in theoretical physics and its prime goal, as the author puts it, is to show the diversity of applications of contact geometry and topology. I enjoyed reading this book, in which the author allows readers to see for themselves “the same forest behind different kinds of trees”. I strongly recommend this book to interested readers.” MathSciNet
Book Synopsis Stochastic Integration Theory by : Peter Medvegyev
Download or read book Stochastic Integration Theory written by Peter Medvegyev and published by OUP Oxford. This book was released on 2007-07-26 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate level text covers the theory of stochastic integration, an important area of Mathematics that has a wide range of applications, including financial mathematics and signal processing. Aimed at graduate students in Mathematics, Statistics, Probability, Mathematical Finance, and Economics, the book not only covers the theory of the stochastic integral in great depth but also presents the associated theory (martingales, Levy processes) and important examples (Brownian motion, Poisson process).
Book Synopsis Categories for Quantum Theory by : Chris Heunen
Download or read book Categories for Quantum Theory written by Chris Heunen and published by Oxford University Press. This book was released on 2019-11-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition, and a conceptual way to understand many high-level quantum phenomena. This text lays the foundation for this categorical quantum mechanics, with an emphasis on the graphical calculus which makes computation intuitive. Biproducts and dual objects are introduced and used to model superposition and entanglement, with quantum teleportation studied abstractly using these structures. Monoids, Frobenius structures and Hopf algebras are described, and it is shown how they can be used to model classical information and complementary observables. The CP construction, a categorical tool to describe probabilistic quantum systems, is also investigated. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Prior knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text links with many other areas are highlighted, such as representation theory, topology, quantum algebra, knot theory, and probability theory, and nonstandard models are presented, such as sets and relations. All results are stated rigorously, and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.
Download or read book Operator Theory by Example written by and published by Oxford University Press. This book was released on 2023-01-30 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at graduate students, this textbook provides an accessible and comprehensive introduction to operator theory. Rather than discuss the subject in the abstract, this textbook covers the subject through twenty examples of a wide variety of operators, discussing the norm, spectrum, commutant, invariant subspaces, and interesting properties of each operator. The text is supplemented by over 600 end-of-chapter exercises, designed to help the reader master the topics covered in the chapter, as well as providing an opportunity to further explore the vast operator theory literature. Each chapter also contains well-researched historical facts which place each chapter within the broader context of the development of the field as a whole.
Book Synopsis Stochastic Analysis and Diffusion Processes by : Gopinath Kallianpur
Download or read book Stochastic Analysis and Diffusion Processes written by Gopinath Kallianpur and published by . This book was released on 2014 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with the concept of random processes and Brownian motion and building on the theory and research directions in a self-contained manner, this book provides an introduction to stochastic analysis for graduate students, researchers and applied scientists interested in stochastic processes and their applications.
Book Synopsis Riemann Surfaces by : Simon Donaldson
Download or read book Riemann Surfaces written by Simon Donaldson and published by Oxford University Press. This book was released on 2011-03-24 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.
Book Synopsis An Introduction to Algebraic Geometry and Algebraic Groups by : Meinolf Geck
Download or read book An Introduction to Algebraic Geometry and Algebraic Groups written by Meinolf Geck and published by Oxford University Press. This book was released on 2013-03-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.
Download or read book Real Analysis written by Fon-Che Liu and published by Oxford University Press. This book was released on 2016 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real Analysis is indispensable for in-depth understanding and effective application of methods of modern analysis. This concise and friendly book is written for early graduate students of mathematics or of related disciplines hoping to learn the basics of Real Analysis with reasonable ease. The essential role of Real Analysis in the construction of basic function spaces necessary for the application of Functional Analysis in many fields of scientific disciplines is demonstrated with due explanations and illuminating examples. After the introductory chapter, a compact but precise treatment of general measure and integration is taken up so that readers have an overall view of the simple structure of the general theory before delving into special measures. The universality of the method of outer measure in the construction of measures is emphasized because it provides a unified way of looking for useful regularity properties of measures. The chapter on functions of real variables sits at the core of the book; it treats in detail properties of functions that are not only basic for understanding the general feature of functions but also relevant for the study of those function spaces which are important when application of functional analytical methods is in question. This is then followed naturally by an introductory chapter on basic principles of Functional Analysis which reveals, together with the last two chapters on the space of p-integrable functions and Fourier integral, the intimate interplay between Functional Analysis and Real Analysis. Applications of many of the topics discussed are included to motivate the readers for further related studies; these contain explorations towards probability theory and partial differential equations.
Book Synopsis Introduction to Symplectic Topology by : Dusa McDuff
Download or read book Introduction to Symplectic Topology written by Dusa McDuff and published by Oxford University Press. This book was released on 2017-03-16 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last number of years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. The first edition of Introduction to Symplectic Topology was published in 1995. The book was the first comprehensive introduction to the subject and became a key text in the area. A significantly revised second edition was published in 1998 introducing new sections and updates on the fast-developing area. This new third edition includes updates and new material to bring the book right up-to-date.
Book Synopsis Differential Geometry by : Clifford Henry Taubes
Download or read book Differential Geometry written by Clifford Henry Taubes and published by OUP Oxford. This book was released on 2011-10-13 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Many of the tools used in differential topology are introduced and the basic results about differentiable manifolds, smooth maps, differential forms, vector fields, Lie groups, and Grassmanians are all presented here. Other material covered includes the basic theorems about geodesics and Jacobi fields, the classification theorem for flat connections, the definition of characteristic classes, and also an introduction to complex and Kähler geometry. Differential Geometry uses many of the classical examples from, and applications of, the subjects it covers, in particular those where closed form expressions are available, to bring abstract ideas to life. Helpfully, proofs are offered for almost all assertions throughout. All of the introductory material is presented in full and this is the only such source with the classical examples presented in detail.
Book Synopsis Introduction to Modern Analysis by : Shmuel Kantorovitz
Download or read book Introduction to Modern Analysis written by Shmuel Kantorovitz and published by Oxford University Press. This book was released on 2022-08-15 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an introduction to modern analysis aimed at advanced undergraduate and graduate-level students of mathematics. Professional academics will also find this to be a useful reference work. It covers measure theory, basic functional analysis, single operator theory, spectraltheory of bounded and unbounded operators, semigroups of operators, and Banach algebras. Further, this new edition of the textbook also delves deeper into C*-algebras and their standard constructions, von Neumann algebras, probability and mathematical statistics, and partial differential equations.Most chapters contain relatively advanced topics alongside simpler ones, starting from the very basics of modern analysis and slowly advancing to more involved topics. The text is supplemented by many exercises, to allow readers to test their understanding and practical analysis skills.
Download or read book 4-manifolds written by Selman Akbulut and published by Oxford University Press. This book was released on 2016 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut. The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to constructions and theorems which are supplemented by exercises to help the reader work through the details not covered in the proofs. The book contains a hundred colour illustrations to demonstrate the ideas rather than providing long-winded and potentially unclear explanations. Key results have been selected that relate to the material discussed and the author has provided examples of how to analyse them with the techniques developed in earlier chapters.
