Series: Springer Texts in Statistics
2004, Approx. 400 p., Hardcover
ISBN: 0-387-20270-6
Due: April 2004
About this textbook
This textbook emphasizes the applications
of statistics and
probability to finance. Students are assumed
to have had a prior
course in statistics, but no background in
finance or economics.
The basics of probability and statistics
are reviewed and more
advanced topics in statistics, such as regression,
ARMA and GARCH
models, the bootstrap, and nonparametric
regression using
splines, are introduced as needed. The book
covers the classical
methods of finance such as portfolio theory,
CAPM, and the Black-Scholes
formula, and it introduces the somewhat newer
area of behavioral
finance. Applications and use of MATLAB and
SAS software are
stressed.The book will serve as a text in
courses aimed at
advanced undergraduates and masters students
in statistics,
engineering, and applied mathematics as well
as quantitatively
oriented MBA students. Those in the finance
industry wishing to
know more statistics could also use it for
self-study.
Written for:
Undergraduates, graduates students, practitioners
Table of contents
Introduction.- Probability and Statistical
Models.- Returns.-
Time Series Models.- Portfolio Theory.- Regression.-
The Capital
Asset Pricing Model.- Options Pricing.- Fixed
Income Securities.-
Resampling.- Value-at-Risk.- GARCH models.-
Nonparametric
Regression and Splines.- Behavioral Finance.
Series: Graduate Texts in Mathematics, Vol.
224
2004, Approx. 230 p. 15 illus., Hardcover
ISBN: 0-387-20430-X
Due: March 2004
About this textbook
This text is an introduction to the theory
of differentiable
manifolds and fiber bundles. The only requisites
are a solid
background in calculus and linear algebra,
together with some
basic point-set topology. The first chapter
provides a
comprehensive overview of differentiable
manifolds. The following
two chapters are devoted to fiber bundles
and homotopy theory of
fibrations. Vector bundles have been emphasized,
although
principal bundles are also discussed in detail.
The last three
chapters study bundles from the point of
view of metric
differential geometry: Euclidean bundles,
Riemannian connections,
curvature, and Chern-Weil theory are discussed,
including the
Pontrjagin, Euler, and Chern characteristic
classes of a vector
bundle. These concepts are illustrated in
detail for bundles over
spheres. Chapter 5, with its focus on the
tangent bundle, also
serves as a basic introduction to Riemannian
geometry in the
large. This book can be used for a one-semester
course on
manifolds or bundles, or a two-semester course
in differential
geometry. Gerard Walschap is Professor of
Mathematics at the
University of Oklahoma where he developed
this book for a series
of graduate courses he has taught over the
past few years.
Series: Springer Undergraduate Mathematics
Series
2004, Approx. 310 p. 10 illus., Softcover
ISBN: 1-85233-781-8
Due: May 2004
About this textbook
Measure, Integral and Probability is a gentle
introduction that
makes measure and integration theory accessible
to the average
third-year undergraduate student. The ideas
are developed at an
easy pace in a form that is suitable for
self-study, with an
emphasis on clear explanations and concrete
examples rather than
abstract theory. For this second edition,
the text has been
thoroughly revised and expanded. New features
include: ・ a
substantial new chapter, featuring a constructive
proof of the
Radon-Nikodym theorem, an analysis of the
structure of Lebesgue-Stieltjes
measures, the Hahn-Jordan decomposition,
and a brief introduction
to martingales ・ key aspects of financial
modelling, including
the Black-Scholes formula, discussed briefly
from a measure-theoretical
perspective to help the reader understand
the underlying
mathematical framework. In addition, further
exercises and
examples are provided to encourage the reader
to become directly
involved with the material.
Written for:
2nd and 3rd year undergraduate students in
mathematics Lecturers
Masters? students in mathematical finance
Table of contents
Motivation and Preliminaries.- Measure.-
Measurable Functions.-
Integral.- Spaces of Integrable Functions.-
Product Measures.-
The Radon-Nikodym Theorem.- Limit Theorems.-
Solutions to
Exercises.- Appendix.- References.- Bibliography.-
Index
Series: Sources and Studies in the History
of Mathematics and
Physical Sciences
2004, Approx. 430 p. 79 illus., Hardcover
ISBN: 0-387-20573-X
Due: April 2004
About this book
The question of when and how the basic concepts
that characterize
modern science arose in Western Europe has
long been central to
the history of science. This book examines
the transition from
Renaissance engineering and philosophy of
nature to classical
mechanics oriented on the central concept
of velocity. Descartes,
Galileo, and other protagonists of what the
authors call "preclassical
mechanics" struggled with fundamental
concepts and
contributed crucial insights to classical
mechanics, but it is
not clear that they actually realized these
insights themselves.
This book argues that the emergence of classical
mechanics was
neither a cumulative change nor an abrupt
revolution, but rather
that the transformation was the result of
exploring the limits
and exhausting the possibilities of the existing,
largely
Aristotelian conceptual system.In the dozen
years that have
passed since the appearance of the first
edition, significant
research has been done on Descartes and Galileo
and the origins
of modern science. There have also been important
advances in the
accessibility of sources and in technology
for analyzing them.
For this new edition, the authors take account
of the most
important new results. They include a new
discussion of the
doctrine of proportions, an analysis of the
role of traditional
statics in the construction of Descartes'
impact rules, and go
deeper into the debate between Descartes
and Hobbes on the
explanation of refraction. They also provide
significant new
material on the early development of Galileo's
work on mechanics
and the law of fall. All translations have
been reviewed and
revised for consistency of terminology and
several new documents
have been added. The bibliography has been
updated to take
account of new literature.
Written for:
Historians of science, graduate students
Series: Universitext
2004, XVI, 236 p., Softcover
ISBN: 3-540-20665-5
Due: March 22, 2004
About this textbook
Constructible and perverse sheaves are the
algebraic counterpart
of the decomposition of a singular space
into smooth manifolds, a
great geometrical idea due to R. Thom and
H. Whitney. These
sheaves, generalizing the local systems that
are so ubiquitous in
mathematics, have powerful applications to
the topology of such
singular spaces (mainly algebraic and analytic
complex varieties).
This introduction to the subject can be regarded
as a textbook on
modern algebraic topology, treating the cohomology
of spaces with
sheaf (as opposed to constant)coefficients.
The first 5 chapters
introduce derived categories, direct and
inverse images of sheaf
complexes, Verdier duality, constructible
and perverse sheaves,
vanishing and characteristic cycles. They
also discuss relations
to D-modules and intersection cohomology.
Later chapters apply
this powerful tool to the study of the topology
of singularities,
polynomial functions and hyperplane arrangements.
Some
fundamental results, for which excellent
sources exist, are not
proved but just stated and illustrated by
examples and
corollaries. In this way, the reader is guided
rather quickly
from the basic theory to current research
questions, supported in
this by examples and exercises.
Written for:
Students and lecturers of algebraic geometry
and algebraic
topology
Table of contents
Derived Categories.- Derived Categories in
Topology.- Poincare-Verdier
Duality.- Constructible Sheaves, Vanishing
Cycles and
Characteristic Varieties.- Perverse Sheaves.-
Applications to the
Geometry of Singular Spaces.- References.-
Index.
Series: Springer Series in Statistics
2004, Approx. 340 p., Hardcover
ISBN: 3-540-20722-8
Due: March 22, 2004
About this book
The concept of nonparametric smoothing is
a central idea in
statistics that aims to simultaneously estimate
and modes the
underlying structure. The book considers
high dimensional
objects, as density functions and regression.
The semiparametric
modeling technique compromises the two aims,
flexibility and
simplicity of statistical procedures, by
introducing partial
parametric components. These components allow
to match structural
conditions like e.g. linearity in some variables
and may be used
to model the influence of discrete variables.
The aim of this
monograph is to present the statistical and
mathematical
principles of smoothing with a focus on applicable
techniques.
The necessary mathematical treatment is easily
understandable and
a wide variety of interactive smoothing examples
are given. The
book does naturally split into two parts:
Nonparametric models (histogram,
kernel density estimation, nonparametric
regression) and
semiparametric models (generalized regression,
single index
models, generalized partial linear models,
additive and
generalized additive models). The first part
is intended for
undergraduate students majoring in mathematics,
statistics,
econometrics or biometrics whereas the second
part is intended to
be used by master and PhD students or researchers.
The material
is easy to accomplish since the e-book character
of the text
gives a maximum of flexibility in learning
(and teaching)
intensity.
Written for:
Econometricians, Statisticians
Table of contents
Introduction.- Histogram.- Nonparametric
Density Estimation.-
Nonparametric Regression.- Semiparametric
and Generalized
Regression Models.- Single Index Models.-
Generalized Partial
Linear Models.- Additive Models and Marginal
Effects.-
Generalized Additive Models.