2006, Approx. 490 p., Hardcover
ISBN: 3-540-23189-7
About this book
This book presents pedagogical contributions on selected topics
relating Number Theory, Theoretical Physics and Geometry. The
parts are composed of long self-contained pedagogical lectures
followed by shorter contributions on specific subjects organized
by theme. Most courses and short contributions go up to the
recent developments in the fields; some of them follow their
author's original viewpoints. There are contributions on Random
Matrix Theory, Quantum Chaos, Non-commutative Geometry, Zeta
functions, and Dynamical Systems. The chapters of this book are
extended versions of lectures given at a meeting entitled Number
Theory, Physics and Geometry, held at Les Houches in March 2003,
which gathered mathematicians and physicists.
Table of contents
Quantum and Arithmetical Chaos.- Notes on L-functions and Random
Matrix Theory.- Energy Level Statistics.- Lattice Point Problems.-
and Almost Modular Functions.- Arithmetic Quantum Chaos of Maass
Waveforms.- Large N Expansion for Normal and Complex Matrix
Ensembles.- Symmetries Arising from Free Probability Theory.-
Universality and Randomness for the Graphs and Metric Spaces.-
From Physics to Number Theory Via Noncommutative Geometry.- More
Zeta Functions for the Riemann Zeros.- Hilbert Spaces of Entire
Functions and L-Functions.- Dynamical Zeta functions and Closed
Orbits for Geodesic and Hyperbolic Flows.- Continued Fraction
Algorithms for Interval Exchange Maps: an Introduction.- Brjuno
Numbers and Dynamical Systems.- Some Properties of Real and
Complex Brjuno Functions.
Series: Lecture Notes in Statistics, Vol. 183
2005, XIV, 402 p. 121 illus., Softcover
ISBN: 0-387-20331-1
Due: October 2005
About this book
Space, structure, and randomness: these are the three key
concepts underlying Georges Matheron’s scientific work. He
first encountered them at the beginning of his career when
working as a mining engineer, and then they resurfaced in fields
ranging from meteorology to microscopy. What could these
radically different types of applications possibly have in
common? First, in each one only a single realisation of the
phenomenon is available for study, but its features repeat
themselves in space; second, the sampling pattern is rarely
regular, and finally there are problems of change of scale.
This volume is divided in three sections on random sets,
geostatistics and mathematical morphology. They reflect his
professional interests and his search for underlying unity. Some
readers may be surprised to find theoretical chapters mixed with
applied ones. We have done this deliberately. GM always
considered that the distinction between the theory and practice
was purely academic.
When GM tackled practical problems, he used his skill as a
physicist to extract the salient features and to select variables
which could be measured meaningfully and whose values could be
estimated from the available data. Then he used his outstanding
ability as a mathematician to solve the problems neatly and
efficiently. It was his capacity to combine a physicist’s
intuition with a mathematician’s analytical skills that allowed
him to produce new and innovative solutions to difficult problems.
The book should appeal to graduate students and researchers
working in mathematics, probability, statistics, physics, spatial
data analysis, and image analysis. In addition it will be of
interest to those who enjoy discovering links between scientific
disciplines that seem unrelated at first glance. In writing the
book the contributors have tried to put GM’s ideas into
perspective. During his working life, GM was a genuinely creative
scientist. He developed innovative concepts whose usefulness goes
far beyond the confines of the discipline for which they were
originally designed. This is why his work remains as pertinent
today as it was when it was first written.
Table of contents
Personal reminiscences of Georges Matheron, Dietrich Stoyan.- A
few words about Georges Matheron (1930-2000), Jean Serra.-
Introduction.- The genesis of geostatistics in gold and diamond
industries, Danie Krige, Wynand Kleingeld.- Concepts and methods
of geostatistics, Jacques Rivoirard.- Prediction by conditional
simulation: models and algorithms, Jean-Paul Chiles, Christian
Lantuejoul.- Flow in porous media: an attempt to outline Georges
Matheron's contributions, J.P. Delhomme, G. de Marsily.- Over
thirty years of petroleum geostatistics, Pierre Delfiner, Andre
Haas.- The expansion of environmental geostatistics, Roberto
Bruno, Chantal de Fouquet.- Random closed sets, I. Molchanov.-
The Boolean model: from Matheron till Today, Dietrich Stoyan,
Klaus Mecke.- Random structures in physics, Dominique Jeulin.-
Mophological operatorors for the segmentation of colour images,
Jean Serra.- Automatic design of morphological operators, Junior
Barrera, Gerald J.F. Banon, Edward R. Dougherty.- Morphological
decomposition systems with perfect reconstruction: from pyramids
to wavelets, Henk J.A.M. Heijmans, John Goutsias.- Morphological
segmentation revisited, Fernand Meyer.- Ubiquity of the distance
function in mathematical morphology, Michel Schmitt.- Partial
differential equations for morphological operators, Frederic
Guichard, Petros Maragos, Jean-Michel Morel.
Series: Springer Undergraduate Mathematics Series
2006, Approx. 235 p. 22 illus., Softcover
ISBN: 1-85233-986-1
Due: November 2005
About this textbook
Aimed at 3rd and 4th year undergraduates and beginning graduates,
this book provides a gentle introduction to this popular subject.
Assuming a background of a first course in abstract algebra, the
book begins with a review of rings, ideals, quotients and
homomorphisms. Polynomials, a key topic in field theory, are then
introduced in the second chapter. Field extensions and splitting
fields are the topics of Chapters 3 and 4, and there is an
account of ruler and compass constructions, and a proof that
"squaring the circle" is impossible, in Chapter 5.
Chapter 6 uses the theory developed in Chapters 3 and 4 to give a
description of finite fields, and includes a brief account of the
use of such fields in coding theory. The book then concludes with
the Galois group, normal and separable extensions, an account of
polynomial equations, and the celebrated result that the quintic
equation is not soluble by radicals.
The aim is to provide a readable, "student-friendly"
introduction that takes a more "natural" approach to
its subject (as compared to the more formal introductions by
Stewart and Garling), and that features clear explanations and
plenty of worked examples and exercises - with full solutions ?
to encourage independent study.
Table of contents
Rings and Fields;- Integral Domains; Polynomials;- Field
Extensions;- Applications to Geometry;- Splitting Fields;- Finite
Fields;- The Galois Group;- Equations and Groups;- Some Group
Theory;- Groups and Equations;- Regular Polygons;- Solutions;-
Bibliography;- List of Symbols;- Index
Series: Universitext
2005, Approx. 605 p., Softcover
ISBN: 0-387-26040-4
Due: December 2005
About this textbook
Lie groups has been an increasing area of focus and rich research
since the middle of the 20th century. Procesi's masterful
approach to Lie groups through invariants and representations
gives the reader a comprehensive treatment of the classical
groups along with an extensive introduction to a wide range of
topics associated with Lie groups: symmetric functions, theory of
algebraic forms, Lie algebras, tensor algebra and symmetry,
semisimple Lie algebras, algebraic groups, group representations,
invariants, Hilbert theory, and binary forms with fields ranging
from pure algebra to functional analysis.
Key to this unique exposition is the large amount of background
material presented so the book is accessible to a reader with
relatively modest mathematical background. Historical
information, examples, exercises are all woven into the text.
Lie Groups: An Approach through Invariants and Representations
will engage a broad audience, including advanced undergraduates,
graduates, mathematicians in a variety of areas from pure algebra
to functional analysis and physics.
Table of contents
General Methods and Ideas.- Symmetric Functions.- Theory of
Algebraic Forms.- Lie Algebras and Lie Groups.- Tensor Algebra.-
Semisimple Algebras.- Algebraic Groups.- Group Representations.-
Tensor Symmetry.- Semisimple Lie Groups and Algebras.- Invariants.-
Tableaux.- Standard Monomials.- Hilbert Theory.- Binary Forms.-
Symbols.- References
3rd ed., 2006, Approx. 310 p. 30 illus., Hardcover
ISBN: 0-387-25358-0
Due: November 2005
About this book
A practical reference on theory and methods of estimating
measurement errors and uncertainty for both scientists and
engineers in industry and experimental research. Building on the
fundamentals of measurement theory, this book offers a wealth of
practial recommendations and procedures. It differs from the
majority of books in that it balances coverage of probabilistic
methods with detailed information on the characterization,
calibration, standardization and limitations of measuring
instruments, with specific examples from both electrical and
mechanical systems. In addition to a general updating to reflect
current research, new material in this edition includes increased
coverage of indirect measurements, with a new, simpler, more
efficient method for this class of measurements.
Table of contents
Series: Springer Texts in Statistics
2006, Approx. 280 p. 52 illus., Hardcover
ISBN: 0-387-25145-6
Due: November 11, 2005
About this book
The goal of this text is to provide the reader with a single book
where they can find a brief account of many, modern topics in
nonparametric inference. The book is aimed at Master's level or
Ph.D. level students in statistics, computer science, and
engineering. It is also suitable for researchers who want to get
up to speed quickly on modern nonparametric methods.
This text covers a wide range of topics including: the bootstrap,
the nonparametric delta method, nonparametric regression, density
estimation, orthogonal function methods, minimax estimation,
nonparametric confidence sets, and wavelets. The book has a
mixture of methods and theory.
Table of contents
Introduction.- Estimating the CDF and Statistical Functions.- The
Bootstrap and the Jackknife.- Smoothing: General Concepts.-
Nonparametric Regression.- Density Estimation.- Normal Means and
Minimax Theory.- Nonparametric Inference Using Orthogonal
Functions.- Wavelets and Other Adaptive Means.