Series: Graduate Texts in Contemporary Physics
2004, XII, 397 p. 158 illus., Hardcover
ISBN: 0-387-40462-7
About this textbook
This book explores the process of modeling
complex systems in the
widest sense of that term, drawing on examples
from such diverse
fields as ecology, epidemiology, sociology,
seismology, as well
as economics. It also provides the mathematical
tools for
studying the dynamics of these systems. Boccara
takes a carefully
inductive approach in defining what it means
for a system to be
"complex" (and at the same time
addresses the equally
elusive concept of emergent properties).
This is the first text
on the subject to draw comprehensive conclusions
from such a wide
range of analogous phenomena.
Written for:
Graduate students, researchers
Series: Undergraduate Texts in Mathematics
2004, XV, 284 p., Softcover
ISBN: 0-387-20172-6
About this textbook
Mathematics is often regarded as the study
of calculation, but in
fact, mathematics is much more. It combines
creativity and logic
in order to arrive at abstract truths. This
book is intended to
illustrate how calculation, creativity, and
logic can be combined
to solve a range of problems in algebra.
Originally conceived as
a text for a course for future secondary-school
mathematics
teachers, this book has developed into one
that could serve well
in an undergraduate course in abstract algebra
or a course
designed as an introduction to higher mathematics.
Not all topics
in a traditional algebra course are covered.
Rather, the author
focuses on integers, polynomials, their ring
structure, and
fields, with the aim that students master
a small number of
serious mathematical ideas. The topics studied
should be of
interest to all mathematics students and
are especially
appropriate for future teachers. One nonstandard
feature of the
book is the small number of theorems for
which full proofs are
given. Many proofs are left as exercises,
and for almost every
such exercise a detailed hint or outline
of the proof is provided.
These exercises form the heart of the text.
Unwinding the meaning
of the hint or outline can be a significant
challenge, and the
unwinding process serves as the catalyst
for learning. Ron Irving
is the Divisional Dean of Natural Sciences
at the University of
Washington. Prior to assuming this position,
he served as Chair
of the Department of Mathematics. He has
published research
articles in several areas of algebra, including
ring theory and
the representation theory of Lie groups and
Lie algebras. In 2001,
he received the University of Washington's
Distinguished Teaching
Award for the course on which this book is
based.
Written for:
Undergraduate students and teachers in mathematics
Series: Springer Series in Statistics
2004, Approx. 650 p., Hardcover
ISBN: 0-387-40852-5
About this book
This book is concerned with data in which
the observations are
independent and in which the response is
multivariate. Anthony
Atkinson has been Professor of Statistics
at the London School of
Economics since 1989. Before that he was
a Professor at Imperial
College, London. He is the author of Plots,
Transformations, and
Regression, co-author of Optimum Experimental
Designs, and joint
editor of The Fascination of Statistics,
a volume celebrating the
centenary of the International Statistical
Institute. Professor
Atkinson has served as editor of The Journal
of the Royal
Statistical Society, Series B and as associate
editor of
Biometrika and Technometrics. He has published
well over 100
articles in these and other journals including
The Annals of
Statistics, Biometrics, The Journal of the
American Statistical
Association, and Statistics and Computing.
Marco Riani, after
receiving his Ph.D. in Statistics in 1995
from the University of
Florence, joined the Faculty of Economics
at Parma University as
postdoctoral fellow. In 1997 he won the prize
for the best
Italian Ph.D. thesis in Statistics. He is
currently Associate
Professor of Statistics in the University
of Parma. He has
published in Technometrics, The Journal of
Computational and
Graphical Statistics, The Journal of Business
and Economic
Statistics, The Journal of Forecasting, Environmetrics,
Computational Statistics and Data Analysis,
Metron, and other
journals.
Written for:
Researchers, graduate students
Series: Springer Texts in Statistics
2004, Approx. 490 p., Hardcover
ISBN: 0-387-20286-2
About this textbook
This book develops the use of statistical
data analysis in
finance, and it uses the statistical software
environment of S-PLUS
as a vehicle for presenting practical implementations
from
financial engineering. It is divided into
three parts. Part I,
Exploratory Data Analysis, reviews the most
commonly used methods
of statistical data exploration. Its originality
lies in the
introduction of tools for the estimation
and simulation of heavy
tail distributions and copulas, the computation
of measures of
risk, and the principal component analysis
of yield curves. Part
II, Regression, introduces modern regression
concepts with an
emphasis on robustness and non-parametric
techniques. The
applications include the term structure of
interest rates, the
construction of commodity forward curves,
and nonparametric
alternatives to the Black Scholes option
pricing paradigm. Part
III, Time Series and State Space Models,
is concerned with
theories of time series and of state space
models. Linear ARIMA
models are applied to the analysis of weather
derivatives, Kalman
filtering is applied to public company earnings
prediction, and
nonlinear GARCH models and nonlinear filtering
are applied to
stochastic volatility models. The book is
aimed at undergraduate
students in financial engineering, master
students in finance and
MBA's, and to practitioners with financial
data analysis concerns.
Written for:
Undergraduate and graduate students and practitioners
in
mathematical finance
2004, Approx. 270 p. 6 illus., Hardcover
ISBN: 0-387-40655-7
About this book
This volume marks the 20th anniversary of
the New York Number
Theory Seminar (NYNTS). Beginning in 1982,
the NYNTS has tried to
present a broad spectrum of research in number
theory and related
fields of mathematics, from physics to geometry
to combinatorics
and computer science. The list of seminar
speakers includes not
only Fields Medallists and other established
researchers, but
also many other younger and less well known
mathematicians whose
theorems are significant and whose work may
become the next big
thing in number theory.
Table of contents
* The spanning number and the independence
number of a subset of
an abelian group * A formula related to the
Frobenius problem in
two dimensions * One bit world * Use of Pade
approximation in
spline construction * Interactions between
number theory and
operator algebras in the study of Riemann
zeta function (d'apres
Bost-Connes and Connes) * A hyperelliptic
curve with real
multiplication of degree two * Humbert's
conic model and the
Kummer surface * Arithmeticity and theta
correspondence of an
orthogonal group * Morphis heights and periodic
points * The
elementary proof of the prime number theorem:
An historical
perspective * Additive bases representations
and the Erdos-Turan
conjecture * The boundary structure of the
sumset in Z^2 * On
NTU's in function fields * Continued fractions
and quadratic
irrationals * The inverse problem for representation
functions of
additive bases * On the ubiquity of Sidon
sets
2nd ed., 2004, XVII, 300 p. 74 illus., Hardcover
ISBN: 0-387-40307-8
About this book
The Shaggy Steed is an unassuming figure
from Irish folklore who
reveals himself as an inspiring teacher of
the forces hidden in
the universe. This book celebrates an unassuming
bit of physics
that also turns out to be an inspiring teacher.
The two-body
problem - the motion of two bodies bound
by the inverse-square
force of gravity and electricity - is the
Shaggy Steed of
physics, guiding the reader to an understanding
of both the
forces and the mathematical beauty hidden
in the physical world.
The book begins with an exposition of the
action principle and
its revelation of invariants created by the
symmetries of nature.
It then turns to the two-body problem and
the grand unifying
themes of symmetry and topology in physics,
both classical and
quantum. On the scale of the solar system
this motion generates
the Kepler ellipse - the fundamental orbit
of celestial mechanics.
On the microscopic scale of the quantum,
the same motion
generates the hydrogen atom - the primal
element. This remarkable
unity of the heavens and the elements rests
upon hidden symmetry
- the symmetry of rotations in four dimensions.
This richly
endowed symmetry also contains the symmetry
of the relativistic
space-time of Einstein. In addition it is
the paradigm for the
unitary symmetries of the elementary particles
and pointed the
way to them. This is a book for those seeking
to know what
breathes life into the equations of physics.
It is also a fine
tutorial book from which one can learn classical
and quantum
mechanics with pleasure. The Shaggy Steed
of Physics is a
spirited companion to the textbooks, a book
that all students of
physics, chemistry, and mathematics will
want to read.
Written for:
Graduate students, advanced undergraduates,
physicists
Table of contents
The Shaggy Steed of Physics.- The Heavens
and the Elements.- The
Law of Motion.- Classical Mechanics: The
Heavens.- Quantum
Mechanics: The Elements.- The Hidden Unity
of Space and Time.-
The Manifold Universe.
2004, XXVIII, 542 p. 77 illus., 4 tabs.,
Hardcover
ISBN: 3-540-20020-7
About this book
Alan Turing's fundamental contributions to
computing led to the
development of modern computing technology,
and his work
continues to inspire researchers in computing
science and beyond.
This book is the definitive collection of
commemorative essays,
and the distinguished contributors have expertise
in such diverse
fields as artificial intelligence, natural
computing,
mathematics, physics, cryptology, cognitive
studies, philosophy
and anthropology. The volume spans the entire
rich spectrum of
Turing's life, research work and legacy.
New light is shed on the
future of computing science by visionary
Ray Kurzweil. Notable
contributions come from the philosopher Daniel
Dennett, the
Turing biographer Andrew Hodges, and the
distinguished logician
Martin Davis, who provides a first critical
essay on an emerging
and controversial field termed hypercomputation.
A special
feature of the book is the play by Valeria
Patera which tackles
the scandal surrounding the last apple, and
presents as an enigma
the life, death and destiny of the man who
did so much to
decipher the Enigma code during the Second
World War. Other
chapters are modern reappraisals of Turing's
work on
computability, and deal with the major philosophical
questions
raised by the Turing Test, while the book
also contains essays
addressing his less well-known ideas on Fibonacci
phyllotaxis and
connectionism.
Written for:
Researchers, students, and professionals