(Paperback)
ISBN-10: 0-19-920251-6
ISBN-13: 978-0-19-920251-5
Publication date: 15 July 2006
280 pages, 234mm x 156mm
Series: Oxford Graduate Texts in Mathematics
Description
Starts from basic undergraduate mathematics
Clear, accessible style
Contains numerous examples and exercises
Useful for students and teachers of mathematics and mathematical
physics
Excellent addition to the existing literature
Lie Groups is intended as an introduction to the theory of Lie
groups and their representations at the advanced undergraduate or
beginning graduate level. It covers the essentials of the subject
starting from basic undergraduate mathematics. The correspondence
between linear Lie groups and Lie algebras is developed in its
local and global aspects. The classical groups are analysed in
detail, first with elementary matrix methods, then with the help
of the structural tools typical of the theory of semisimple
groups, such as Cartan subgroups, roots, weights, and reflections.
The fundamental groups of the classical groups are worked out as
an application of these methods. Manifolds are introduced when
needed, in connection with homogeneous spaces, and the elements
of differential and integral calculus on manifolds are presented,
with special emphasis on integration on groups and homogeneous
spaces. Representation theory starts from first principles, such
as Schur's lemma and its consequences, and proceeds from there to
the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil
theorem, all in the context of linear groups.
Readership: Graduate students in pure mathematics.
Contents
Preface
1 The exponential map
2 Lie theory
3 The classical groups
4 Manifolds, homogeneous spaces, Lie groups
5 Integration
6 Representations
Appendix: Analytic Functions and Inverse Function Theorem
References
Index
(Hardback)
ISBN-10: 0-19-929885-8
(Paperback)
ISBN-10: 0-19-929886-6
Publication date: 31 August 2006
208 pages, numerous b/w line drawings, 234mm x 156mm
Description
An accessible, comprehensive text by a well-respected author
Many worked examples and exercises throughout the text
Includes numerous instructive figures and diagrams
Readership: Undergraduate students in mathematics
Contents
Foreword
1 Assumed knowledge
2 Introduction
3 Introduction to axiomatic geometry
4 Field planes and PG(r,F)
5 Coordinatising a projective plane
6 Non-Desarguesian planes
7 Conics
8 Quadrics in PG(3,F)
Reference textbooks
Index
(Hardback)
ISBN-10: 0-19-853382-9
(Paperback)
ISBN-10: 0-19-929789-4
Publication date: 3 August 2006
400 pages, 246mm x 189mm
Description
Lucid and comprehensive exposition
Ideal for undergraduates in mathematics and physical sciences
Provides and develops technique through carefully crafted
examples and exercises
Readership: Undergraduates in mathematics and physical sciences
with basic calculus seeking a thorough grounding in Differential
and Integral Equations.
Contents
Preface
How to use this book
Prerequisites
1 Integral equations and Picard's method
2 Existence and uniqueness
3 The homogeneous linear equation and Wronskians
4 The non-homogeneous linear equation: Variations of parameters
and Green's functions
5 First-order partial differential equations
6 Second-order partial differential equations
7 The diffusion and wave equations and the equation of Laplace
8 The Fredholm alternative
9 Hilbert-Schmidt theory
10 Iterative methods and Neumann series
11 The calculus of variations
12 The Sturm-Liouville equation
13 Series solutions
14 Transform methods
15 Phase-plane analysis
Appendix: The solution of some elementary ordinary differential
equations
Bibliography
Index
Classics in Applied Mathematics 50
Optimal Design of Experiments offers a rare blend of linear
algebra, convex analysis, and statistics. The optimal design for
statistical experiments is first formulated as a concave matrix
optimization problem. Using tools from convex analysis, the
problem is solved generally for a wide class of optimality
criteria such as D-, A-, or E-optimality. The book then offers a
complementary approach that calls for the study of the symmetry
properties of the design problem, exploiting such notions as
matrix majorization and the Kiefer information matrix ordering.
The results are illustrated with optimal designs for polynomial
fit models, Bayes designs, balanced incomplete block designs,
exchangeable designs on the cube, rotatable designs on the
sphere, and many other examples.
Since the book’s initial publication in 1993, readers have used
its methods to derive optimal designs on the circle, optimal
mixture designs, and optimal designs in other statistical models.
Using local linearization techniques, the methods described in
the book prove useful even for nonlinear cases, in identifying
practical designs of experiments.
Audience
This book is indispensable for anyone involved in planning
statistical experiments, including mathematical statisticians,
applied statisticians, and mathematicians interested in matrix
optimization problems.
Contents
Preface
Chapter 1: Experimental Designs in Linear Models
Chapter 2: Optimal Designs for Scalar Parameter Systems
Chapter 3: Information Matrices
Chapter 4: Loewner Optimality
Chapter 5: Real Optimality Criteria
Chapter 6: Matrix Means; Chapter 7: The General Equivalence
Theorem
Chapter 8: Optimal Moment Matrices and Optimal Designs
Chapter 9: D-, A-, E-, T-Optimality; Chapter 10: Admissibility of
Moment and Information Matrices
Chapter 11: Bayes Designs and Discrimination Designs
Chapter 12: Efficient Designs for Finite Sample Sizes
Chapter 13: Invariant Design Problems
Chapter 14: Kiefer Optimality
Chapter 15: Rotatability and Response Surface Designs
Comments and References
Biographies
Bibliography
Index
About the Author
Friedrich Pukelsheim is Chair for Stochastics and Its
Applications at the Institute for Mathematics, University of
Augsburg, Germany. He is a member of the Institute of
Mathematical Statistics, the International Statistical Institute,
and Deutsche Mathematiker-Vereinigung. He serves as editor of
Metrika?International Journal for Theoretical and Applied
Statistics.
Available 2006 / Approx. xxx + 454 pages / Softcover / ISBN 0-89871-604-7
Advances in Design and Control 10
Control Perspectives on Numerical Algorithms and Matrix Problems
organizes the analysis and design of iterative numerical methods
from a control perspective. The authors discuss a variety of
applications, including iterative methods for linear and
nonlinear systems of equations, neural networks for linear and
quadratic programming problems, support vector machines,
integration and shooting methods for ordinary differential
equations, matrix preconditioning, matrix stability, and
polynomial zero finding.
This book opens up a new field of interdisciplinary research that
should lead to insights in the areas of both control and
numerical analysis and shows that a wide range of applications
can be approached from?and benefit from?a control perspective.
Audience
Control Perspectives on Numerical Algorithms and Matrix Problems
is intended for researchers in applied mathematics and control as
well as senior undergraduate and graduate students in both of
these fields. Engineers and scientists who design algorithms on a
heuristic basis and are looking for a framework may also be
interested in the book.
About the Authors
Amit Bhaya is Professor of Electrical Engineering at the Graduate
School of Engineering, Federal University of Rio de Janeiro (COPPE/UFRJ).
He is coauthor of Matrix Diagonal Stability in Systems and
Computation (Birkhauser, 2000) and works in the areas of systems
and control theory, parallel computation, neural networks, matrix
stability theory, and mathematical ecology.
Eugenius Kaszkurewicz is Professor of Electrical Engineering at
the Graduate School of Engineering, Federal University of Rio de
Janeiro (COPPE/UFRJ). He is coauthor of Matrix Diagonal Stability
in Systems and Computation (Birkhauser, 2000) and works in the
areas of stability theory, large-scale systems stability and
control, parallel computation, neural networks, and matrix
stability theory. He is an elected member of the Brazilian
Academy of Sciences and served for several years as Associate
Editor of Automatica, the journal of the International Federation
of Automatic Control.
Contents
List of Figures
List of Tables
Preface
Chapter 1: Brief Review of Control and Stability Theory
Chapter 2: Algorithms as Dynamical Systems with Feedback
Chapter 3: Optimal Control and Variable Structure Design of
Iterative Methods
Chapter 4: Neural-Gradient Dynamical Systems for Linear and
Quadratic Programming Problems
Chapter 5: Control Tools in the Numerical Solution of Ordinary
Differential Equations and in Matrix Problems
Chapter 6: Epilogue
Bibliography
Index
Available March 2006 / Approx. xxiv + 270 pages / Softcover /
ISBN 0-89871-602-0
Mathematical Modeling and Computation 11
Exact and Approximate Modeling of Linear Systems: A Behavioral
Approach elegantly introduces the behavioral approach to
mathematical modeling, an approach that requires models to be
viewed as sets of possible outcomes rather than to be a priori
bound to particular representations. The authors discuss exact
and approximate fitting of data by linear, bilinear, and
quadratic static models and linear dynamic models, a formulation
that enables readers to select the most suitable representation
for a particular purpose.
This book presents exact subspace-type and approximate
optimization-based identification methods, as well as
representation-free problem formulations, an overview of solution
approaches, and software implementation. Readers will find an
exposition of a wide variety of modeling problems starting from
observed data. The presented theory leads to algorithms that are
implemented in C language and in MATLAB.
Audience
This book is written primarily for electrical, mechanical, and
chemical engineers, applied mathematicians, econometricians, and
statisticians. Chapters 3 and 4 will be of interest to
chemometricians, and Chapters 5 and 6 to researchers in the field
of computer vision.
About the Authors
Ivan Markovsky is a Postdoctoral Researcher of Electrical
Engineering at Katholieke Universiteit Leuven, Belgium. His
current research work is focused on identification methods in the
behavioral setting and errors-in-variables estimation problems.
Jan C. Willems is a full-time Visiting Professor of Electrical
Engineering at Katholieke Universiteit Leuven, Belgium, with the
research group on Signals, Identification, System Theory, and
Automation (SISTA). His interests lie mainly in modeling,
identification, control, and issues related to the foundations of
systems theory.
Sabine Van Huffel is a Professor of Electrical Engineering at
Katholieke Universiteit Leuven, Belgium. Her research interests
are in signal processing, numerical linear algebra, errors-in-variables
regression, system identification, pattern recognition, (non)linear
modeling, software, and statistics applied to biomedicine.
Bart De Moor is a Professor of Electrical Engineering at
Katholieke Universiteit Leuven, Belgium. His research interests
are in numerical linear algebra and optimization, system theory,
control and identification, quantum information theory, data
mining, information retrieval, and bioinformatics.
Contents
Preface
Chapter 1: Introduction
Chapter 2: Approximate Modeling via Misfit Minimization
Part I: Static Problems
Chapter 3: Weighted Total Least Squares
Chapter 4: Structured Total Least Squares
Chapter 5: Bilinear Errors-in-Variables Model
Chapter 6: Ellipsoid Fitting
Part II: Dynamic Problems
Chapter 7: Introduction to Dynamical Models
Chapter 8: Exact Identification
Chapter 9: Balanced Model Identification
Chapter 10: Errors-in-Variables Smoothing and Filtering
Chapter 11: Approximate System Identification
Chapter 12: Conclusions
Appendix A: Proofs
Appendix B: Software
Notation
Bibliography
Index
Available March 2006 / x + 210 pages / Softcover / ISBN 0-89871-603-9