An Introduction to Twistor Theory

Author: S. A. Huggett,K. P. Tod

Publisher: Cambridge University Press

ISBN: 9780521456890

Category: Mathematics

Page: 178

View: 2090

This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. It will be valuable also to the physicist as an introduction to some of the mathematics that has proved useful in these areas, and to the mathematician as an example of where sheaf cohomology and complex manifold theory can be used in physics.
Posted in Mathematics

An Introduction to K-Theory for C*-Algebras

Author: M. Rørdam,Flemming Larsen,N. Laustsen

Publisher: Cambridge University Press

ISBN: 9780521789448

Category: Mathematics

Page: 242

View: 4739

This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
Posted in Mathematics

An Introduction to Noncommutative Noetherian Rings

Author: K. R. Goodearl,R. B. Warfield, Jr

Publisher: Cambridge University Press

ISBN: 9780521369251

Category: Mathematics

Page: 303

View: 4098

Introduces and applies the standard techniques in the area (ring of fractions, bimodules, Krull dimension, linked prime ideals).
Posted in Mathematics

An Introduction to Hankel Operators

Author: Jonathan R. Partington

Publisher: Cambridge University Press

ISBN: 9780521367912

Category: Mathematics

Page: 103

View: 4918

Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
Posted in Mathematics

Presentations of Groups

Author: D. L. Johnson

Publisher: Cambridge University Press

ISBN: 9780521585422

Category: Mathematics

Page: 216

View: 396

The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied.This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.
Posted in Mathematics

LMSST: 24 Lectures on Elliptic Curves

Author: John William Scott Cassels

Publisher: Cambridge University Press

ISBN: 9780521425308

Category: Mathematics

Page: 137

View: 7808

The study of special cases of elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centers of research in number theory. This book, addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Wei finite basis theorem, points of finite order (Nagell-Lutz), etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the "Riemann hypothesis for function fields") and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch. Many examples and exercises are included for the reader, and those new to elliptic curves, whether they are graduate students or specialists from other fields, will find this a valuable introduction.
Posted in Mathematics

Hyperbolic Geometry

Author: Birger Iversen

Publisher: Cambridge University Press

ISBN: 0521435080

Category: Mathematics

Page: 298

View: 5897

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon theorem and the relationship between hyperbolic geometries and discrete groups of isometries. Hyperbolic 3-space is also discussed, and the directions that current research in this field is taking are sketched. This will be an excellent introduction to hyperbolic geometry for students new to the subject, and for experts in other fields.
Posted in Mathematics

Integrable Systems

Twistors, Loop Groups, and Riemann Surfaces

Author: N.J. Hitchin,G. B. Segal,R.S. Ward

Publisher: Oxford Graduate Texts in Mathe

ISBN: 0199676771

Category: Mathematics

Page: 136

View: 9189

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.
Posted in Mathematics

Compact Riemann Surfaces

An Introduction to Contemporary Mathematics

Author: Jürgen Jost

Publisher: Springer Science & Business Media

ISBN: 3662034468

Category: Mathematics

Page: 295

View: 7701

This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.
Posted in Mathematics

Dynamical Systems and Ergodic Theory

Author: Mark Pollicott,Michiko Yuri

Publisher: Cambridge University Press

ISBN: 9780521575997

Category: Mathematics

Page: 179

View: 2139

This book is essentially a self-contained introduction to topological dynamics and ergodic theory. It is divided into a number of relatively short chapters with the intention that each may be used as a component of a lecture course tailored to the particular audience. Parts of the book are suitable for a final year undergraduate course or for a master's level course. A number of applications are given, principally to number theory and arithmetic progressions (through van der Waerden's theorem and Szemerdi's theorem).
Posted in Mathematics

Dirac Operators in Riemannian Geometry

Author: Thomas Friedrich

Publisher: American Mathematical Soc.

ISBN: 0821820559

Category: Mathematics

Page: 195

View: 6371

Examines the Dirac operator on Riemannian manifolds, especially its connection with the underlying geometry and topology of the manifold. The presentation includes a review of Clifford algebras, spin groups and the spin representation, as well as a review of spin structures and spin [superscript C] structures. With this foundation established, the Dirac operator is defined and studied, with special attention to the cases of Hermitian manifolds and symmetric spaces. Then, certain analytic properties are established, including self-adjointness and the Fredholm property. An important link between the geometry and the analysis is provided by estimates for the eigenvalues of the Dirac operator in terms of the scalar curvature and the sectional curvature. Considerations of Killing spinors and solutions of the twistor equation on M lead to results about whether M is an Einstein manifold or conformally equivalent to one. Finally, in an appendix, Friedrich gives a concise introduction to the Seiberg-Witten invariants, which are a powerful tool for the study of four-manifolds. There is also an appendix reviewing principal bundles and connections.
Posted in Mathematics

An Introduction to Local Spectral Theory

Author: K. B. Laursen,Michael Neumann

Publisher: Oxford University Press

ISBN: 9780198523819

Category: Mathematics

Page: 591

View: 5050

'This beautifully written book represents a major contribution to the literature in the field of modern local spectral theory.' -Journal of Operator TheoryThis book is a modern treatment of a classical area of operator theory. Written in a meticulous and detailed style, with the modern graduate student of analysis in mind, it contains many simplifications of existing literature. It is full of new results, as well as many illuminating examples. Carefully cross referenced throughout, it also includes an extensive list of the relevant literature.
Posted in Mathematics

Lectures on Kähler Geometry

Author: Andrei Moroianu

Publisher: Cambridge University Press

ISBN: 1139463004

Category: Mathematics

Page: N.A

View: 2257

Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.
Posted in Mathematics

Integrability, Self-duality, and Twistor Theory

Author: Lionel J. Mason,Nicholas Michael John Woodhouse

Publisher: Oxford University Press

ISBN: 9780198534983

Category: Mathematics

Page: 364

View: 8016

It has been known for some time that many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection (for example, the Korteweg-de Vries and nonlinear Schrodinger equations are reductions of the self-dual Yang-Mills equation). This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It has two central themes: first, that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and second that twistor theory provides a uniform geometric framework for the study of B"acklund tranformations, the inverse scattering method, and other such general constructions of integrability theory, and that it elucidates the connections between them."
Posted in Mathematics

An Introduction to Clifford Algebras and Spinors

Author: Roldao Da Rocha, Jr.

Publisher: Oxford University Press

ISBN: 0198782926

Category:

Page: 256

View: 3788

This text explores how Clifford algebras and spinors have been sparking a collaboration and bridging a gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main point of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. Among the existing approaches to Clifford algebras and spinors this book is unique in that it provides a didactical presentation of the topic and is accessible to both students and researchers. It emphasizes the formal character and the deep algebraic and geometric completeness, and merges them with the physical applications. The style is clear and precise, but not pedantic. The sole pre-requisites is a course in Linear Algebra which most students of Physics, Mathematics or Engineering will have covered as part of their undergraduate studies.
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Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 6336

Posted in Mathematics

A Short Course on Banach Space Theory

Author: N. L. Carothers

Publisher: Cambridge University Press

ISBN: 9780521603720

Category: Mathematics

Page: 184

View: 6000

This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: the elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) spaces. While these topics can be traced back to Banach himself, our primary interest is in the postwar renaissance of Banach space theory brought about by James, Lindenstrauss, Mazur, Namioka, Pelczynski, and others. Their elegant and insightful results are useful in many contemporary research endeavors and deserve greater publicity. By way of prerequisites, the reader will need an elementary understanding of functional analysis and at least a passing familiarity with abstract measure theory. An introductory course in topology would also be helpful; however, the text includes a brief appendix on the topology needed for the course.
Posted in Mathematics

New Technical Books

Author: New York Public Library

Publisher: N.A

ISBN: N.A

Category: Engineering

Page: N.A

View: 9893

Posted in Engineering

British Book News

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Best books

Page: N.A

View: 8995

Includes no. 53a: British wartime books for young people.
Posted in Best books