2007, XXXII, 200 p., Softcover
ISBN-10: 0-387-34657-0
ISBN-13: 978-0-387-34657-1
About this book
This handbook, now available in paperback, brings together a
comprehensive collection of mathematical material in one location.
It also offers a variety of new results interpreted in a form
that is particularly useful to engineers, scientists, and applied
mathematicians. The handbook is not specific to fixed research
areas, but rather it has a generic flavor that can be applied by
anyone working with probabilistic and stochastic analysis and
modeling.
Classic results are presented in their final form without
derivation or discussion, allowing for much material to be
condensed into one volume.
Concise compilation of disparate formulae saves time in searching
different sources
Focused application has broad interest for many disciplines:
engineers, computer scientists, statisticians, physicists; as
well as any researcher working in probabilistic and stochastic
analysis and modeling in the natural or social sciences.
The material is timeless and has intrinsic value to today’s and
tomorrow’s practicing engineers and scientists
Endorsed by top experts in field worldwide, ensuring quality and
value
Table of contents
A Brief Biography of Carl Friedrich Gauss.- Preface.-
Acknowledgment.- Introduction.- Basic Definitions and Notation.-
Fundamental One-Dimensional Variables.- Fundamental
Multidimensional Variables.- Difference of Chi-Square Random
Variables.- Sum of Chi-Square Random Variables.- Products of
Random Variables.- Ratios of Random Variables.- Maximum and
Minimum of Pairs of Random Variables.- Quadratic Forms.- Other
Miscellaneous Forms.- Appendix A: Alternative Forms.- One-Dimensional
Distributions and Functions.- Two-Dimensional Distributions and
Functions.- Appendix B: Integrals Involving Q-Functions.- The
Gaussian Q-Function.- The First-Order Marcum Q-Function.- The
Generalized (MTH-Order) Marcum Q-Function.- Appendix C: Bounds on
the Gaussian Q-Function and the Marcum Q-Function.- The Gaussian
Q-Function.- The Marcum Q-Function.- References.- Illustrations.
Series: Universitext
2007, Approx. 320 p., 30 illus., Softcover
ISBN-10: 0-387-48098-6
ISBN-13: 978-0-387-48098-5
About this textbook
The aim of this textbook is to introduce advanced undergraduate
and graduate level students - in either a mathematics or physics
field of study - to manifolds. In the first section of the book,
the Euclidean space and point-set topology are presented to
create a smooth transition from undergraduate calculus. At a
quick, yet accessible pace, the text then continues to explore
manifolds in terms of their relationship to tangent spaces, such
as Lie groups and their Lie algebras. The focus within each
chapter consists of only the most fundamental topics in manifold
theory. This modesty of scope and logical organization lend
clarity to the book. Examples and exercises are provided
throughout the text and solutions to selected exercises are also
included. A novice to manifolds needs a semester of abstract
algebra and a year of real analysis. The author covers
prerequisites from point-set topology in an elaborate Appendix.
An Introduction to Manifolds should enable students to do
calculus on manifolds and recognize their applications in
analysis and topology.
Written for:
First-year graduates, advanced undergraduates and physicists
Table of contents
A Brief Introduction.- Part I. The Euclidean Space.- Smooth
functions on R(n).- Tangent vectors in R(n) as derivations.-
Alternating k-linear functions.- Differential forms on R(n).-
Part II. Manifolds.- Manifolds.- Smooth maps on a manifold.-
Quotient.- Part III. The tangent space.- The tangent space.-
Submanifolds.- Categories and functors.- The image of a smooth
map.- The tangent bundle.- Bump functions and partitions of unity.-
Vector fields.- Part IV. Lie groups and Lie algebras.- Lie groups.-
Lie algebras.- Part V. Differential forms.- Differential 1-forms.-
Differential k-forms.- The exterior derivative.- Part VI.
Integration.- Orientations.- Manifolds with boundary.-
Integration on a manifold.- Part VII. De Rham theory.- De Rham
cohomology.- The long exact sequence in cohomology.- The Mayer-Vietoris
sequence.- Homotopy invariance.- Computation of de Rham
cohomology.- Proof of homotopy invariance.- Appendix A. Point-set
topology.- Appendix B. Inverse function theorem of R(n) and
related results.- Appendix C. Existence of a partition of unity
in general.- Appendix D. Solutions to selected exercises.-
Bibliography.- Index
Series: Universitext
2007, Approx. 480 p., 30 illus., Softcover
ISBN-10: 0-387-48112-5
ISBN-13: 978-0-387-48112-8
About this book
This self-contained monograph focuses on recent important
developments in the study of random fields, stochastic processes
defined over high dimensional parameter spaces. While it replaces
Adler's 1981 classic The Geometry of Random Fields, this is not
an update, but a completely new work with a completely new way of
handling both the Geometry and the Probability that are its
central themes.
There are three quite distinct parts to the monograph. Part I
provides a comprehensive background to the general theory of
Gaussian random fields, treating classical topics such as
continuity and boundedness, entropy and majorising measures,
Borell and Slepian inequalities. The treatment is didactic and
user-friendly. Part II is about Geometry, both integral and
Riemannian, and the material included here is what is needed for
the over-riding probabilistic theme of the book. It contains a
quick review of both these geometric settings, followed by
carefully presented introductions to topics such as Crofton
formulae, curvature measures for stratified manifolds, critical
point theory and tube formulae. This is the only place in which
all these topics, necessary for the study of random fields can be
found in a concise, self-contained, treatment. The most important
part of the book is in Part III, which is about the geometry of
excursion sets of random fields and the related ‘Euler
characteristic approach’ to extremal probabilities. This part
contains path-breaking material of both theoretical and practical
importance and is unique in the way in which it intertwines
probabilistic and geometric problems.
Applications of this theory, which are significant and cover
areas as widespread as brain imaging, physical oceanography and
astrophysics, will be treated in a separate volume with Keith
Worsley.
This monograph will be of interest to probabilists and
statisticians, both applied and theoretical, along with
mathematicians interested in learning about new relationships
between geometry and probability. It is also a basic reference
text for those who will eventually be interested mainly in the
companion volume of applications. Given the clear and pedagogical
style of the book and the current importance of research in
random fields this comprehensive and definitive work will serve
as an indispensable reference work, while at the same time being
an excellent text for self study and graduate courses in
probability, statistics, analysis and geometry.
Table of contents
Preface.- Part I. Gaussian Processes. Gaussian Fields. Gaussian
Inequalities. Orthogonal Expansions. Excursion Probabilities.
Stationary Fields.- Parat II. Geometry. Integral Geometry.
Differential Geometry. Piecewise Smooth Manifolds. Critical Point
Theory. Volume of Tubes.- Part III. The Geometry of Random Fields.
Random Fields on Euclidean Spaces. Random Fields on Manifolds.
Mean Intrinsic Volumes. Excursion Probabilities for Smooth Fields.
Non-Gaussian Geometry.- References.- Index.
Series: Springer Monographs in Mathematics
2007, XII, 400 p., Hardcover
ISBN-10: 0-387-38031-0
ISBN-13: 978-0-387-38031-5
About this book
The purpose of the text is to provide a complete, self-contained
development of the trace formula and theta inversion formula for
SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the
approach taken here is to begin with the heat kernel on SL(2,C)
associated to the invariant Laplacian, which is derived using
spherical inversion. The heat kernel on the quotient space SL(2,Z[i])\SL(2,C)
is gotten through periodization, and further expanded in an
eigenfunction expansion. A theta inversion formula is obtained by
studying the trace of the heat kernel. Following the author's
previous work, the inversion formula then leads to zeta functions
through the Gauss transform.
Table of contents
Introduction.- Spherical Inversion on SL2(C).- The Heat Gaussian
and Kernel.- QED, LEG, Transpose, and Casimir.- Convergence and
Divergence of the Selberg Trace.- The Cuspidal and Non-Cuspidal
Traces.- The Heat Kernel.- The Fundamental Domain.- Gamma
Periodization of the Heat Kernel.- Heat Kernel Convolution.- The
Tube Domain.- The Fourier Expansion of Eisenstein Series.-
Adjointness Formula and the Eigenfunction Expansion.- The
Eisenstein Y-Asymptotics.- The Cuspidal Trace Y-Asymptotics.-
Analytic Evaluations.- Index.- References.
Version: print (book)
2008, Approx. 1000 p., 200 illus., Hardcover
ISBN-10: 0-387-30770-2
ISBN-13: 978-0-387-30770-1
About this book
The Encyclopedia of Algorithms will provide a comprehensive set
of solutions to important algorithmic problems for students and
researchers interested in quickly locating useful information.
The first edition of the reference will focus on high-impact
solutions from the most recent decade; later editions will widen
the scope of the work.
Nearly 500 entries will be organized alphabetically by problem,
with subentries allowing for distinct solutions and special cases
to be listed by the year. An entry will include:
a description of the basic algorithmic problem
the input and output specifications
the key results
examples of applications
citations to the key literature
Open problems, links to downloadable code, experimental results,
data sets, and illustrations may be provided. All entries will be
written by experts with links to Internet sites that outline
their research work will be provided. The entries will be peer-reviewed.
This defining reference will be published in print and on line.
The print publication will include an index of subjects and
authors as well as a chronology for locating recent solutions.
The online edition will supplement this index with hyperlinks as
well as include hyperlinks in the text of the entries to related
entries, xRefer citations, and other useful URLs mentioned above.
Written for:
Entries in this reference will appeal significantly to computer
scientists working in a wide range of areas such as
Bioinformatics, Cryptography, Data Compression, Medical
Informatics, Network and Communication Protocols, Artificial
Intelligence, and Pattern Recognition.
The title will also be useful for scholars, students, and
professionals who work in fields such as mathematics, statistics,
computational biology, economics, finance and stochastics,
medical informatics, data mining, industrial engineering, and
decision science.
Table of contents
VLSI.- distributed computing.- parallel processing,.- automated
design,.- robotics.- graphics.- data base design.- software tools.-
sorting.- searching,.- data structures.- computational geometry.-
linear programming
This textbook is an introduction to probability theory using
measure theory. It is designed for graduate students in a variety
of fields (mathematics, statistics, economics, management,
finance, computer science, and engineering) who require a working
knowledge of probability theory that is mathematically precise,
but without excessive technicalities. The text provides complete
proofs of all the essential introductory results. Nevertheless,
the treatment is focused and accessible, with the measure theory
and mathematical details presented in terms of intuitive
probabilistic concepts, rather than as separate, imposing
subjects. In this new edition, many exercises and small
additional topics have been added and existing ones expanded. The
text strikes an appropriate balance, rigorously developing
probability theory while avoiding unnecessary detail.
Contents:
The Need for Measure Theory
Probability Triples
Further Probabilistic Foundations
Expected Values
Inequalities and Convergence
Distributions of Random Variables
Stochastic Processes and Gambling Games
Discrete Markov Chains
More Probability Theorems
Weak Convergence
Characteristic Functions
Decomposition of Probability Laws
Conditional Probability and Expectation
Martingales
General Stochastic Processes
Readership: Graduate students in mathematics, statistics,
economics, management, finance, computer science and engineering.
Review of the First Edition
“This book is certainly well placed to establish itself as a
core reading in measure-theoretic probability … [it is]
delightful reading and a worthwhile addition to the existing
literature.”
Mathematical Reviews
240pp (approx.) Pub. date: Scheduled Winter 2006
ISBN 981-270-370-5
ISBN 981-270-371-3(pbk)