solitons instantons and twistors oxford graduate texts in mathematics

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Solitons Instantons And Twistors

Author : Maciej Dunajski
ISBN : 9780198570622
Genre : Mathematics
File Size : 59. 35 MB
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The book provides a self-contained and accessible introduction to elementary twistor theory; a technique for solving differential equations in applied mathematics and theoretical physics. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basicdifferential geometry, complex manifold theory and the exterior differential system.

Inverse Problems And Applications

Author : Gunther Uhlmann
ISBN : 9781107032019
Genre : Mathematics
File Size : 20. 81 MB
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Inverse problems lie at the heart of contemporary scientific inquiry and technological development. Applications include a variety of medical and other imaging techniques, which are used for early detection of cancer and pulmonary edema, location of oil and mineral deposits in the Earth's interior, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes, and modeling in the life sciences among others. The expository survey essays in this book describe recent developments in inverse problems and imaging, including hybrid or couple-physics methods arising in medical imaging, Calderon's problem and electrical impedance tomography, inverse problems arising in global seismology and oil exploration, inverse spectral problems, and the study of asymptotically hyperbolic spaces. It is suitable for graduate students and researchers interested in inverse problems and their applications.

An Introduction To Quantum Theory

Author : Keith Hannabuss
ISBN : 0191588733
Genre : Science
File Size : 89. 94 MB
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This book provides an introduction to quantum theory primarily for students of mathematics. Although the approach is mainly traditional the discussion exploits ideas of linear algebra, and points out some of the mathematical subtleties of the theory. Amongst the less traditional topics are Bell's inequalities, coherent and squeezed states, and introductions to group representation theory. Later chapters discuss relativistic wave equations and elementary particle symmetries from a group theoretical standpoint rather than the customary Lie algebraic approach. This book is intended for the later years of an undergraduate course or for graduates. It assumes a knowledge of basic linear algebra and elementary group theory, though for convenience these are also summarized in an appendix.

Solitons And Instantons

Author : R. Rajaraman
ISBN : OCLC:311890547
Genre :
File Size : 28. 24 MB
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Real Analysis

Author : Fon-Che Liu
ISBN : 9780198790426
Genre :
File Size : 84. 29 MB
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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.

Introduction To Symplectic Topology

Author : Dusa McDuff
ISBN : 9780192514011
Genre : Mathematics
File Size : 87. 3 MB
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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.

Integrable Systems

Author : N.J. Hitchin
ISBN : 9780199676774
Genre : Mathematics
File Size : 44. 15 MB
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Designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors, this book has its origins in a lecture series given by the internationally renowned authors. Written in an accessible, informal style, it fills a gap in the existing literature.

4 Manifolds

Author : Selman Akbulut
ISBN : 9780198784869
Genre :
File Size : 67. 79 MB
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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.

An Introduction To Algebraic Geometry And Algebraic Groups

Author : Meinolf Geck
ISBN : 9780199676163
Genre : Mathematics
File Size : 60. 77 MB
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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.

Stochastic Analysis And Diffusion Processes

Author : Gopinath Kallianpur
ISBN : 9780199657070
Genre : Mathematics
File Size : 62. 62 MB
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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.

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