Series: Mathematical Sciences Research Institute Publications
Hardback (ISBN-13: 9780521875417)
Page extent: 420 pages
Size: 234 x 156 mm
Based on the subjects from the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop on 'Recent Progress in Dynamics' in September and October 2004, this volume contains surveys and research articles by leading experts in several areas of dynamical systems that have recently experienced substantial progress. One of the major surveys is on symplectic geometry, which is closely related to classical mechanics and is an exciting addition to modern geometry as well as a research area that has recently experienced explosive growth. The survey on local rigidity of group actions gives a broad and up-to-date account of another flourishing subject. Other papers cover hyperbolic, parabolic, and symbolic dynamics as well as ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this a fascinating look at the state of the art.
* Up to date text in fast moving fields * Many open problems * Combination
of survey and research reports
Paperback (ISBN-13: 9780521715959)
76 line diagrams 6 half-tones 135 exercises
Page extent: 578 pages
Size: 247 x 174 mm
Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with early chapters providing a self-contained introduction to geometric algebra. Topics covered include new techniques for handling rotations in arbitrary dimensions, and the links between rotations, bivectors and the structure of the Lie groups. Following chapters extend the concept of a complex analytic function theory to arbitrary dimensions, with applications in quantum theory and electromagnetism. Later chapters cover advanced topics such as non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored. It can be used as a graduate text for courses on the physical applications of geometric algebra and is also suitable for researchers working in the fields of relativity and quantum theory.
* The only fully self-contained introduction to geometric algebra including
applications in relativistic physics and gravitation * The first full account
of the geometric algebra approach to multiparticle quantum physics and
supersymmetry * A book written by two authors who have shaped the subject
in the last decade
Contents
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
Series: Encyclopedia of Mathematics and its Applications (No. 116)
Hardback (ISBN-13: 9780521883009)
4 tables 14 worked examples
Page extent: 550 pages
Size: 234 x 156 mm
J-contractive and J-inner matrix valued functions have a wide range of applications in mathematical analysis, mathematical physics, control engineering and theory of systems and networks. This book provides a comprehensive introduction to the theory of these functions with respect to the open upper half-plane, and a number of applications are also discussed. The first chapters develop the requisite background material from the geometry of finite dimensional spaces with an indefinite inner product, and the theory of the Nevanlinna class of matrix valued functions with bounded characteristic in the open upper half-plane (with attention to special subclasses). Subsequent chapters develop this theory to include associated pairs of inner matrix valued functions and reproducing kernel Hilbert spaces. Special attention is paid to the subclasses of regular and strongly regular J-inner matrix valued functions, which play an essential role in the study of the extension and interpolation problems.
* Comprehensive and self contained account of the theory of J-contractive
and J-inner matrix valued functions * Applications to a variety of problems
in mathematical analysis, mathematical physics, control engineering and
the mathematical theory of systems and networks * Brings together years
of research, much by the authors themselves, into book form for the first
time
Contents
Preface; 1. Introduction; 2. Algebraic preliminaries; 3. The Nevanlinna class of meromorphic mvf’s; 4. J-contractive and J-inner matrix valued functions; 5. Reproducing kernel Hilbert spaces; 6. Generalized interpolation problems; 7. Generalized Krein extension problems; 8. Darlington representations and related inverse problems; 9. More criteria for strong regularity; 10. Formulas for entropy functionals; Bibliography.
Hardback (ISBN-13: 9780521884006)
33 line diagrams 2 half-tones 196 exercises
Page extent: 376 pages
Size: 247 x 174 mm
Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.
* Focuses on the applications of Lie group theory to physical sciences
and applied mathematics, rather than on theorems and proofs * Each chapter
ends with problems, so readers can monitor their understanding of the subject
* Many examples of Lie groups and Lie algebras are given throughout the
text
Contents
1. Introduction; 2. Lie groups; 2. Matrix groups; 4. Lie algebras; 5. Matrix algebras; 6. Operator algebras; 7. Exponentiation; 8. Structure theory for Lie algebras; 9. Structure theory for simple Lie algebras; 10. Root spaces and Dykin diagrams; 11. Real forms; 12. Riemannian symmetric spaces; 13. Contraction; 14. Hydrogenic atoms; 15. Maxwell’s equations; 16. Lie groups and differential equations; References; Index.
Hardback (ISBN-13: 9780521771948)
86 line diagrams
Page extent: 552 pages
Size: 247 x 174 mm
The past few years have witnessed significant developments in algebraic coding theory. This book provides an advanced treatment of the subject from an engineering perspective, covering the basic principles and their application in communications and signal processing. Emphasis is on codes defined on the line, on the plane, and on curves, with the core ideas presented using commutative algebra and computational algebraic geometry made accessible using the Fourier transform. Starting with codes defined on a line, a background framework is established upon which the later chapters concerning codes on planes, and on curves, are developed. The decoding algorithms are developed using the standard engineering approach applied to those of Reed-Solomon codes, enabling them to be evaluated against practical applications. Integrating recent developments in the field into the classical treatment of algebraic coding, this is an invaluable resource for graduate students and researchers in telecommunications and applied mathematics.
* Replaces exhaustive mathematics with the Fourier transform, covering
algebraic coding from the perspective of an engineer * Integrates recent
developments in the field into the classical engineering framework of error-control
codes * Describes a number of applications of algebraic coding in communications
and signal processing
Contents
1. Sequences and the one-dimensional Fourier transform; 2. The Fourier transform and cyclic codes; 3. The many decoding algorithms for Reed-Solomon codes; 4. Within or beyond the packing radius; 5. Arrays and the two-dimensional Fourier transform; 6. The Fourier transform and bicyclic codes; 7. Arrays and the algebra of bivariate polynomials; 8. Computation of minimal bases; 9. Curves, surfaces, and vector spaces; 10. Codes on curves and surfaces; 11. Other representations of codes on curves; 12. The many decoding algorithms for codes on curves.