XII, 468 pp. 50 figs. Hardcover
1-85233-587-4
The new edition of Volumes 2 and 3 of Professor
Cohn's classic 3-volume
set Algebra will comprise of 2 companion,
but self-contained,
volumes. This, the first volume, is composed
of parts of both
Volumes 2 and 3 but is complemented by the
definitions and basic
facts on groups and rings to make the book
self-contained and
independent of Volume 1. It is addressed
to students who have
some knowledge of linear algebra and who
have met groups and
fields, although all the essential facts
are recalled. The
overall aim is to present as many of the
important results in
algebra as will conveniently fit in one volume.
There are
numerous exercises, with occasional hints
(but no solutions) and
some historical remarks. The remaining parts
of the original
Volumes 2 and 3 will be collected into a
second volume (tentatively
titled Further Algebra and Applications)
which will be oriented
more towards applications
Keywords: Algebra, Basic algebra, Fields,
Groups, Rings, Sets
Contents: Preface, Conventions on Terminology,
Sets, Groups,
Lattices and Categories,
Rings and Modules, Algebras, Multi-linear
Algebra, Field Theory,
Quadratic
Forms and Ordered Fields, Valuation Theory,
Commutative Rings,
Infinite
Field Extensions, Bibliography, List of Notations,
Author Index,
Subject
Index.
2002XV, 219 p. Softcover
3-540-44154-9
Nonholonomic systems are a widespread topic
in several scientific
and commercial domains, including robotics,
locomotion and space
exploration. This work sheds new light on
this interdisciplinary
character through the investigation of a
variety of aspects
coming from several disciplines. The main
aim is to illustrate
the idea that a better understanding of the
geometric structures
of mechanical systems unveils new and unknown
aspects to them,
and helps both analysis and design to solve
standing problems and
identify new challenges. In this way, separate
areas of research
such as Classical Mechanics, Differential
Geometry, Numerical
Analysis or Control Theory are brought together
in this study of
nonholonomic systems.
Keywords: Geometric Integration, Geometric
Mechanics,
Nonholomonic Systems, Nonlinear Control Theory,
Symmetry and
Reduction
Series: Lecture Notes in Mathematics. Volume.
1793
2002XVII, 402 Softcover
3-540-44141-7
A certain category of infinite strings of
letters on a finite
alphabet is presented here, chosen among
the 'simplest' possible
one may build, both because they are very
deterministic and
because they are built by simple rules (a
letter is replaced by a
word, a sequence is produced by iteration).
These substitutive
sequences have a surprisingly rich structure.
The authors describe the concepts of quantity
of natural
interactions, with combinatorics on words,
ergodic theory, linear
algebra, spectral theory, geometry of tilings,
theoretical
computer science, diophantine approximation,
trancendence, graph
theory. This volume fulfils the need for
a reference on the basic
definitions and theorems, as well as for
a state-of-the-art
survey of the more difficult and unsolved
problems.
Keywords: Symbolic dynamics, automata sequences,
combinatorics on
words, ergodic theory, substitutive dynamical
systems
Contents: Preface.- 1. Basic notions on substitutions.-
Part I:
Arithmetics and combinatorics.- 2. Substitutions,
arithmetic and
finite automata: an introduction.- 3. Automatic
sequences and
transcendence.- 4. Substitutions and partitions
of the set of
positive integers.- Part II: Dynamics of
Substitutions.- 5.
Substitutions and symbolic dynamical systems.-
6. Sturmian
sequences.- 7. Spectral theory and geometric
representation of
substitutions.- 8. Diophantine approximations,
substitutions, and
fractals.- Part III: Extensions to free groups
and interval
transformations.- 9. Infinite words generated
by invertible
substitutions.- 10. Polynomial dynamical
systems associated with
substitutions.- 11. Piecewise linear transformations
of the unit
interval and Cantor sets.- 12. Some open
problems.- A.
Undecomposable matrices in dimension 3.-
References.- Index.
Series: Lecture Notes in Mathematics. Volume.
1794
3rd rev. ed.2003XIII, 769 p. Hardcover
3-540-44085-2
Set Theory has experienced a rapid development
in recent years,
with major advances in forcing, inner models,
large cardinals and
descriptive set theory. The present book
covers each of these
areas, giving the reader an understanding
of the ideas involved.
It can be used for introductory students
and is broad and deep
enough to bring the reader near the boundaries
of current
research. Students and researchers in the
field will find the
book invaluable both as a study material
and as a desktop
reference.
Keywords: Mengenlehre, set theory
Series: Springer Monographs in Mathematics.
2003XIX, 632 p. Softcover
0-387-95549-6
The field of financial econometrics has exploded
over the last
decade. This book represents an integration
of theory, methods,
and examples using the S-PLUS statistical
modeling language and
the S+FinMetrics module to facilitate the
practice of financial
econometrics. This is the first book to show
the power of S-PLUS
for the analysis of time series data. It
is written for
researchers and practitioners in the finance
industry, academic
researchers in economics and finance, and
advanced MBA and
graduate students in economics and finance.
Readers are assumed
to have a basic knowledge of S-PLUS and a
solid grounding in
basic statistics and time series concepts.
Eric Zivot is an
associate professor and Gary Waterman Distinguished
Scholar in
the Economics Department at the University
of Washington, and is
co-director of the nascent Professional Master's
Program in
Computational Finance. He regularly teaches
courses on
econometric theory, financial econometrics
and time series
econometrics, and is the recipient of the
Henry T. Buechel Award
for Outstanding Teaching. He is an associate
editor of the
Journal of Business and Economic Statistics
and Studies in
Nonlinear Dynamics and Econometrics. He has
published papers in
the leading econometrics journals, including
Econometrica,
Econometric Theory, the Journal of Business
and Economic
Statistics, Journal of Econometrics, and
the Review of Economics
and Statistics. Jiahui Wang is a Research
Scientist at Insightful
Corporation. He received a Ph.D. in Economics
from the university
of Washington in 1997. He has published in
leading econometrics
journals such as Econometrica and Journal
of Business and
Economic Statistics, and is the Principal
Investigator of
National Science Foundation SBIR grants.
In 2002 Dr. Wang was
selected as one of the "2000 Outstanding
Scholars of the 21st
Century" by International Biographical
Centre.
Contents: Time Series Specification, Manipulation
and
Visualization in S-PLUS.- Time Series Concepts.-
Unit Root Tests.-
Modeling Extreme Values.- Time Series Regression
Modeling.-
Univariate GARCH Models.- Modeling Long Memory
Time Series.-
Rolling Analysis.- Systems of Regression
Equations.- Vector
Autoregressive Models.- Multivariate GARCH
Models.- State Space
Models.- Factor Models for Asset Returns.-
Robust Statistical
Methods in Finance.- Modeling Fixed Income
Time Series.