Series: Springer Texts in Statistics
2004, XIX, 442 p., Hardcover
ISBN: 0-387-40272-1
About this textbook
This textbook can be used for a course for
advanced
undergraduates or M.A.-level courses in statistics
and computer
science departments. It will also serve as
a reference for
practitioners in machine learning.
Written for:
Graduate students, researchers
Table of contents
Probability.- Random Variables.- Expectation.-
Inequalities.-
Convergence of Random Variables.- Models,
Statistical Inference
and Learning.- Estimating the CDF and Statistical
Functionals.-
The Bootstrap.- Parametric Inference.- Hypothesis
Testing and p-values.-
Bayesian Inference.- Statistical Decision
Theory.- Linear and
Logistic Regression.- Multivariate Models.-
Inference about
Independence.- Causal Inference.- Directed
Graphs and Conditional
Independence.- Undirected Graphs.- Loglinear
Models.-
Nonparametric Curve Estimation.- Smoothing
Using Orthogonal
Functions.- Classification.- Probability
Redux: Stochastic
Processes.- Simulation Methods.
Series: Lecture Notes in Mathematics
2004, VIII,186p., Softcover
ISBN: 3-540-20612-4
About this book
The Morse-Sard theorem is a rather subtle
result and the
interplay between the high-order analytic
structure of the
mappings involved and their geometry rarely
becomes apparent. The
main reason is that the classical Morse-Sard
theorem is basically
qualitative. This volume gives a proof and
also an "explanation"
of the quantitative Morse-Sard theorem and
related results,
beginning with the study of polynomial (or
tame) mappings. The
quantitative questions, answered by a combination
of the methods
of real semialgebraic and tame geometry and
integral geometry,
turn out to be nontrivial and highly productive.
The important
advantage of this approach is that it allows
the separation of
the role of high differentiability and that
of algebraic geometry
in a smooth setting: all the geometrically
relevant phenomena
appear already for polynomial mappings. The
geometric properties
obtained are "stable with respect to
approximation",
and can be imposed on smooth functions via
polynomial
approximation.
Written for:
Researchers and graduate students
Table of contents
Preface.- Introduction and Content.- Entropy.-
Multidimensional
Variations.- Semialgebraic and Tame Sets.-
Some Exterior Algebra.-
Behavior of Variations under Polynomial Mappings.-
Quantitative
Transversality and Cuspidal Values for Polynomial
Mappings.-
Mappings of Finite Smoothness.- Some Applications
and Related
Topics.- Glossary.- References.
Series: David Hilbert's Lectures on the Foundations
of
Mathematics and Physics, 1891 to 1933
2004, Approx. 690pp., Hardcover
ISBN: 3-540-64373-7
About this book
This volume contains six sets of notes for
lectures on the
foundations of geometry held by Hilbert in
the period 1891-1902.
It also reprints the first edition of Hilbert?s
celebrated
Grundlagen der Geometrie of 1899, together
with the important
additions which appeared first in the French
translation of 1900.
The lectures document the emergence of a
new approach to
foundational study (the ?axiomatic method?),
which concentrates
on assessing the logical weight of central
propositions by
exploiting to the full the method of independence
proofs by
modelling. This culminates in the lectures
of 1898/1899 (the
immediate precursor of the 1899 monograph)
and 1902. The lectures
contain many reflections and investigations
which never found
their way into print.
Written for:
Historians of logic, mathematics, geometry,
and physics;
researchers and students in those fields
Table of contents
Preface.- Introduction to the Edition.- Introduction
to the
Contents of the Volume.- Lectures on Projective
Geometry (1891).-
Lectures on the Foundations of Geometry (1894).-
Holiday Courses,
1896 and 1898.- Lectures on Euclidean Geometry
(1898-99).- The
Foundations of Geometry: The Festschrift
of 1899.- Lectures on
the Foundations of Geometry (1902).
Series: Lecture Notes in Computational Science
and Engineering
2004, Approx. 300 p., Softcover
ISBN: 3-540-20406-7
About this book
This is the first book that deals systematically
with the
numerical solution of elliptic partial differential
equations by
their reduction to the interface via the
Schur complement.Inheriting
the beneficial features of finite element,
boundary element and
domain decomposition methods, our approach
permits solving
iteratively the Schur complement equation
with linear-logarithmic
cost in the number of the interface degrees
of freedom. The book
presents the detailed analysis of the efficient
data-sparse
approximation techniques to the nonlocal
Poincare-Steklov
interface operators associated with the Laplace,
biharmonic,
Stokes and Lame equations. Another attractive
topic are the
robust preconditioning methods for elliptic
equations with highly
jumping, anisotropic coefficients. A special
feature of the book
is a unified presentation of the traditional
iterative
substructuring and multilevel methods combined
with modern matrix
compression techniques applied to the Schur
complement on the
interface.
Written for:
Graduate students, researchers
Inverse and Ill-Posed Problems Series
The term ``ill-posed problems'' used to mean
problems with
unstable solutions for which small errors
in initial data lead to
a significant error in the results. At present
the theory itself
has been sufficiently well developed. At
the same time the topic
is by no means exhausted.
This study is an attempt at extending well-known
facts to new
classes of problems and at working out novel
approaches to the
solution of these problems. In particular,
this monograph is
devoted to the questions of (consistency)
of ill-posed boundary-value
problems for systems of various types of
the first-order
differential equations with constant coefficients
and to the
methods of their solution.
The introductory chapter gives some facts
of the theory of
matrices and ordinary differential equations.
The first chapter
studies the well posedness of the problem
for an arbitrary system
of ordinary equations and the occurrence
of ill-posed problems
among them. In the second chapter a similar
approach is applied
to various kinds of parabolic systems and
solution methods for
ill-posed problems are given. The final chapter
deals with he
afore mentioned methods to study problems
for hyperbolic-type
equations.
This monograph will be of value to researchers
in the field of
ill-posed problems for differential equations.
2003; viii+144 pages
ISBN 90-6764-395-5
Contents:
Introduction
Conditionally well-posed problems and related
questions
Problems and methods for their investigation
Denotation and terms
Some facts from the theory of matrices
Canonical (normal) forms of matrices
On solutions of systems of algebraic equations
Relation between an arbitrary equation and
a system of first-order
ordinary differential equations. Green's
matrix
CHAPTER 1. CONSTRUCTION OF ILL-POSED PROBLEMS
FOR A SYSTEM OF THE
FIRST ORDER ODE
Correct problem statement for an arbitrary
system of ODE
Problem on the ray t > 0
Problem on the interval
Problem statement. Analysis of boundary conditions
Linearization algorithm
CHAPTER 2. PARABOLIC PROBLEMS
Parabolic systems
Boundary-value problems
The first boundary-value problem
Mixed problem of heat and mass exchange
CHAPTER 3. HYPERBOLIC EQUATIONS
Hyperbolicity and mixed problems
Two-dimensional acoustic problem
Linearized plane problem of gas dynamics
Biblography
Nankai Tracts in Mathematics - Vol. 7
This subject has been of great interest both
to topologists and
to number theorists. The first part of this
book describes some
of the work of Kuo-Tsai Chen on iterated
integrals and the
fundamental group of a manifold. The author
attempts to make his
exposition accessible to beginning graduate
students. He then
proceeds to apply Chen's constructions to
algebraic geometry,
showing how this leads to some results on
algebraic cycles and
the Abel–Jacobi homomorphism. Finally, he
presents a more
general point of view relating Chen's integrals
to a
generalization of the concept of linking
numbers, and ends up
with a new invariant of homology classes
in a projective
algebraic manifold. The book is based on
a course given by the
author at the Nankai Institute of Mathematics
in the fall of 2001.
Contents:
Iterated Integrals, Chen's Flat Connection
and p1
Iterated Integrals on Compact Riemann Surfaces
The Generalized Linking Pairing and the Heat
Kernel
Readership: Researchers and graduate students
in geometry and
topology.
150pp (approx.) Pub. date: Scheduled Spring
2004
ISBN 981-238-720-X
ISBN 981-238-774-9(pbk)