2003, XXII, 488 p., Softcover
ISBN: 0-387-40607-7
Due: October 1, 2003
About this textbook
Comprising the major theorems of probability
theory and the
measure theoretical foundations of the subject,
the main topics
treated here are independence, interchangeability,
and
martingales. Particular emphasis is placed
upon stopping times,
both as tools in proving theorems and as
objects of interest
themselves. No prior knowledge of measure
theory is assumed and a
unique feature of the book is the combined
presentation of
measure and probability. It is easily adapted
for graduate
students familiar with measure theory using
the guidelines given.
Special features include: - A comprehensive
treatment of the law
of the iterated logarithm - The Marcinklewicz-Zygmund
inequality,
its extension to martingales and applications
thereof -
Development and applications of the second
moment analogue of
Walds equation - Limit theorems for martingale
arrays; the
central limit theorem for the interchangeable
and martingale
cases; moment convergence in the central
limit theorem - Complete
discussion, including central limit theorem,
of the random
casting of r balls into n cells - Recent
martingale inequalities
- Cram r-L vy theorem and factor-closed families
of distributions.
Table of contents
Classes of Sets, Measures,and Probability
Spaces.- Binomial
Random Variables.- Independence.- Integration
in a Probability
Space.- Sums of Independent Random Variables.-
Measure
Extensions, Lebesgue-Stieltjes Measure, Kolmogorov
Consistency
Theorem.- Conditional Expectation, Conditional
Independence,
Introduction to Martingales.- Distribution
Functions and
Characteristic Functions.- Central Limit
Theorems.- Limit
Theorems for Independent Random Variables.-
Martingales.-
Infinitely Divisible Laws.
Written for: Graduate students, researchers
2nd printing, 2003, XII, 162 p., Softcover
ISBN: 0-387-40623-9
Due: October 1, 2003
About this textbook
In Euclidean geometry, constructions are
made with ruler and
compass. Projective geometry is simpler:
its constructions
require only a ruler. In projective geometry
one never measures
anything, instead, one relates one set of
points to another by a
projectivity. The first two chapters of this
book introduce the
important concepts of the subject and provide
the logical
foundations. The third and fourth chapters
introduce the famous
theorems of Desargues and Pappus. Chapters
5 and 6 make use of
projectivities on a line and plane, repectively.
The next three
chapters develop a self-contained account
of von Staudt's
approach to the theory of conics. The modern
approach used in
that development is exploited in Chapter
10, which deals with the
simplest finite geometry that is rich enough
to illustrate all
the theorems nontrivially. The concluding
chapters show the
connections among projective, Euclidean,
and analytic geometry.
Table of contents
1. Introduction.- 2. Triangles and Quadrangles.-
3. The Principle
of Duality.- 4. The Fundamental Theorem and
Pappus's Theorem.- 5.
One-dimensional Projectivities.- 6. Two-dimensional
Projectivities.- 7. Polarities.- 8. The Conic.-
9. The Conic,
Continued.- 10. A Finite Projective Plane.-
11. Parallelism.- 12.
Coordinates.
Written for: Undergraduate mathematics students
2004, Approx. 288 p. 50 illus., Hardcover
ISBN: 0-387-95487-2
Due: October 1, 2003
About this textbook
Created to teach students many of the most
important techniques
used for constructing combinatorial designs,
this is an ideal
textbook for advanced undergraduate and graduate
courses in
combinatiorial design theory. The text features
clear
explanations of basic designs, such as Steiner
and Kirkman triple
systems, mutual orthogonal Latin squares,
finite projective and
affine planes, and Steiner quadruple systems.
In these settings,
the student will master various construction
techniques, both
classic and modern, and will be well-prepared
to construct a vast
array of combinatorial designs. Design theory
offers a
progressive approach to the subject, with
carefully ordered
results. It begins with simple constructions
that gradually
increase in complexity. Each design has a
construction that
contains new ideas or that reinforces and
builds upon similar
ideas previously introduced. A new text/reference
covering all
apsects of modern combinatorial design theory.
Graduates and
professionals in computer science, applied
math, combinatorics,
and applied statistics will find the book
an essential resource.
Table of contents
Written for: Graduate students, postgraduates,
practitioners
Series: Springer Monographs in Mathematics
2004, XI, 337 p., Hardcover
ISBN: 3-540-40651-4
About this book
The purpose of this book is to provide a
careful and accessible
account along modern lines of the subject
which the title deals,
as well as to discuss problems of current
interest in the field.
More precisely this book is devoted to the
functional-analytic
approach to a class of degenerate boundary
value problems for
second-order elliptic integro-differential
operators which
includes as particular cases the Dirichlet
and Robin problems.
This class of boundary value problems provides
a new example of
analytic semigroups. As an application, we
construct a strong
Markov process corresponding to such a diffusion
phenomenon that
a Markovian particle moves both by jumps
and continuously in the
state space until it dies at the time when
it reaches the set
where the particle is definitely absorbed.
Written for: Researchers and graduate students
Table of contents
http://www.springeronline.com/sgw/cda/pageitems/document/cda_downloaddocument/0,10900,0-0-45-98471-0,00.pdf
Keywords: Analytic semigroup, Feller semigroup,
Elliptic boundary
value problem, Markov process
2003, XXVIII, 543 p., Softcover
ISBN: 0-387-40615-8
Due: October 1, 2003
About this textbook
This book combines the enlarged and corrected
editions of both
volumes on classical physics stemming from
Thirrings famous
course. The treatment of classical dynamical
systems uses
analysis on manifolds to provide the mathematical
setting for
discussions of Hamiltonian systems, canonical
transformations,
constants of motion, and perturbation theory.
Problems discussed
include: nonrelativistic motion of particles
and systems,
relativistic motion in electromagnetic and
gravitational fields,
and the structure of black holes. The treatment
of classical
fields uses the language of differential
geometry, treating both
Maxwells and Einsteins equations in a compact
and clear fashion.
The book includes discussions of the electromagnetic
field due to
known charge distributions and in the presence
of conductors, as
well as a new section on gauge theories.
It discusses the
solutions of the Einstein equations for maximally
symmetric
spaces and spaces with maximally symmetric
submanifolds, and
concludes by applying these results to the
life and death of
stars. Numerous examples and accompanying
remarks make this an
ideal textbook.
Written for: Physicists
Table of contents
Dynamical Systems.- Analysis of Manifolds.-
Hamiltonian Systems.-
Nonrelativistic Motion.- Relativistic Motion.-
The Structure of
Space and Time Field Theory.- The Electromagnetic
Field of a
Known Charge Distribution.- The Field in
the Presence of
Conductors.- Gravitation.