Included in series
Studies in Computational Mathematics, 11
Hardbound, ISBN: 0-444-51474-0, 300 pages,
publication date: 2004
Description
The first four chapters of this book give
a comprehensive and
unified theory of the Krylov methods. Many
of these are shown to
be particular examples of the block conjugate-gradient
algorithm
and it is this observation that permits the
unification of the
theory. The two major sub-classes of those
methods, the Lanczos
and the Hestenes-Stiefel, are developed in
parallel as natural
generalisations of the Orthodir (GCR) and
Orthomin algorithms.
These are themselves based on Arnoldi's algorithm
and a
generalised Gram-Schmidt algorithm and their
properties, in
particular their stability properties, are
determined by the two
matrices that define the block conjugate-gradient
algorithm.
These are the matrix of coefficients and
the preconditioning
matrix.
In Chapter 5 the"transpose-free"
algorithms based on
the conjugate-gradient squared algorithm
are presented while
Chapter 6 examines the various ways in which
the QMR technique
has been exploited. Look-ahead methods and
general block methods
are dealt with in Chapters 7 and 8 while
Chapter 9 is devoted to
error analysis of two basic algorithms.
In Chapter 10 the results of numerical testing
of the more
important algorithms in their basic forms
(i.e. without look-ahead
or preconditioning) are presented and these
are related to the
structure of the algorithms and the general
theory. Graphs
illustrating the performances of various
algorithm/problem
combinations are given via a CD-ROM.
Chapter 11, by far the longest, gives a survey
of preconditioning
techniques. These range from the old idea
of polynomial
preconditioning via SOR and ILU preconditioning
to methods like
SpAI, AInv and the multigrid methods that
were developed
specifically for use with parallel computers.
Chapter 12 is
devoted to dual algorithms like Orthores
and the reverse
algorithms of Hegedus. Finally certain ancillary
matters like
reduction to Hessenberg form, Chebychev polynomials
and the
companion matrix are described in a series
of appendices.
Key features:
comprehensive and unified approach
up-to-date chapter on preconditioners
complete theory of stability
includes dual and reverse methods
comparison of algorithms on CD-ROM
objective assessment of algorithms
Included in series North-Holland Mathematical
Library, 66
Hardbound, ISBN: 0-444-51631-X, 492 pages,
publication date: 2004
Description
This is the unique book on cross-fertilisations
between stream
ciphers and number theory. It systematically
and comprehensively
covers known connections between the two
areas that are available
only in research papers. Some parts of this
book consist of new
research results that are not available elsewhere.
In addition to
exercises, over thirty research problems
are presented in this
book. In this revised edition almost every
chapter was updated,
and some chapters were completely rewritten.
It is useful as a
textbook for a graduate course on the subject,
as well as a
reference book for researchers in related
fields.
Thomas W. Cusick is Professor of Mathematics
at the State
University of New York Buffalo. Cunsheng
Ding is Associate
Professor of Computer Science at the Hong
Kong University of
Science and Technology. Ari Renvall is Senior
Assistant of
Mathematics at the University of Turku.
Key features:
Unique book on interactions of stream ciphers
and number theory.
Research monograph with many results not
available elsewhere.
A revised edition with the most recent advances
in this subject.
Over thirty research problems for stimulating
interactions
between the two areas.
Written by leading researchers in stream
ciphers and number
theory.
Audience
Cryptographers, mathematicians.
(Hardback) 0-19-852913-9
Publication date: May 2004
Clarendon Press 288 pages, 10 line drawings,
234mm x 156mm
Series: International Series of Monographs
on Physics
Succinct introduction to path integrals and
Schwinger's action
principle
Clear conceptual basis of the path integral
method in the
analyses of anomalies
Explicit and elementary calculations of all
the examples
Path integral formulation of Weyl anomalies
(which is not
commonly available)
Analyses of two-dimensional theory such as
bosonization and
conformal field theory
Covers most recent developments in lattice
gauge theory
Description
'Definitely a book that will fill a need
at the graduate and
research level. ' -Ian Aitchison, University
of Oxford
'An excellent addition to the literature
by one of the pioneers
in understanding anomalies. ' -Roman Jackiw,
Massachusetts
Institute of Technology
Self-contained introduction to the path integral
method in field
theory and its applications to quantum anomalies.
The subjects
covered in the book are relevant to particle
and high-energy
nuclear theory, conformal field theory, applications
to condensed
matter theory, and string theory. No previous
knowledge beyond
the advanced undergraduate quantum mechanics
is assumed.
Readership: Beginning graduate students and
researchers in
theoretical physics, mathematics, and chemistry,
in particular
particle physics theory, high energy nuclear
theory, condensed
matter theory, and string theory.
Contents/contributors
1 Genesis of quantum anomalies
2 Feynman path integrals and Schwinger's
action principle
3 Quantum theory of photons and phase operators
4 Regularization of field theory and chiral
anomalies
5 Jacobians in path integrals and quantum
anomalies
6 Quantum breaking of gauge symmetry
7 Weyl anomaly and renormalization group
8 Two-dimensional field theory and bosonization
9 Index theorem on the lattice and chiral
anomalies
10 Gravitational anomalies
11 Concluding remarks
A Basics of quantum electrodynamics
B Field theory in curved space-time
C References with brief comments
Cloth | 2003 | ISBN: 0-691-11573-7
432 pp. | 6 x 9
This is a major, wide-ranging history of
analytic philosophy
since 1900, told by one of the tradition's
leading contemporary
figures. The first volume takes the story
from 1900 to mid-century.
The second brings the history up to date.
As Scott Soames tells it, the story of analytic
philosophy is one
of great but uneven progress, with leading
thinkers making
important advances toward solving the tradition's
core problems.
Though no broad philosophical position ever
achieved lasting
dominance, Soames argues that two methodological
developments
have, over time, remade the philosophical
landscape. These are (1)
analytic philosophers' hard-won success in
understanding, and
distinguishing the notions of logical truth,
a priori truth, and
necessary truth, and (2) gradual acceptance
of the idea that
philosophical speculation must be grounded
in sound
prephilosophical thought. Though Soames views
this history in a
positive light, he also illustrates the difficulties,
false
starts, and disappointments endured along
the way. As he engages
with the work of his predecessors and contemporaries--from
Bertrand Russell and Ludwig Wittgenstein
to Donald Davidson and
Saul Kripke--he seeks to highlight their
accomplishments while
also pinpointing their shortcomings, especially
where their
perspectives were limited by an incomplete
grasp of matters that
have now become clear.
Soames himself has been at the center of
some of the tradition's
most important debates, and throughout writes
with exceptional
ease about its often complex ideas. His gift
for clear exposition
makes the history as accessible to advanced
undergraduates as it
will be important to scholars. Despite its
centrality to
philosophy in the English-speaking world,
the analytic tradition
in philosophy has had very few synthetic
histories. This will be
the benchmark against which all future accounts
will be measured.
Scott Soames is Professor of Philosophy at
Princeton University.
The author of Beyond Rigidity and Understanding
Truth, he is
coeditor of Propositions and Attitudes and
coauthor of Syntactic
Argumentation and the Structure of English.
Endorsements:
"A history of analytic philosophy and
an excellent piece of
analytic philosophy in its own right. We
can all benefit from
Soames's discussion of the central issues
that have shaped the
subject and his assessment of what we have
achieved and where we
might have gone wrong."--Kit Fine, New
York University
"This monumental study is a careful
assessment of the
successes and the failures of twentieth-century
analytic
philosophy. Soames displays unfailingly sound
judgment throughout.
The work is invaluable to those of us who
have contributed to
this period of very recent history of thought,
and more
importantly, to our students who will build
upon the triumphs and
will profit from the defeats of ourselves
and our predecessors,
carrying philosophy forward into the new
millennium. The work is
also a comprehensive reality check in the
face of persistent
accusations (coming not only from those who
do not understand
analytic philosophy, but also from those
who remain stuck in its
recent failures) that analytic philosophy
is a disease or a
futile exercise in wheel spinning. Analytic
philosophy is, and
has always been, a rational quest for knowledge
and understanding.
Its tools are clarification, argument, and
tutored intuition.
Soames provides perspective concerning the
best of recent
philosophical thought, articulating its most
important
developments, dead ends, and discoveries."--Nathan
Salmon,
University of California, Santa Barbara
"Philosophical Analysis in the Twentieth
Century is a
critical examination of key texts and trends
in analytic
philosophy by one of its leading contemporary
practitioners.
Soames has applied his formidable forensic
talents to highlight
the insights and expose the errors of the
major figures from
Moore to Kripke. These two volumes are an
essential resource for
any serious student of analytic philosophy."--Alex
Byrne,
Massachusetts Institute of Technology
Cloth | 2003 | ISBN: 0-691-11574-5
488 pp. | 6 x 9
This is a major, wide-ranging history of
analytic philosophy
since 1900, told by one of the tradition's
leading contemporary
figures. The first volume takes the story
from 1900 to mid-century.
The second brings the history up to date.
As Scott Soames tells it, the story of analytic
philosophy is one
of great but uneven progress, with leading
thinkers making
important advances toward solving the tradition's
core problems.
Though no broad philosophical position ever
achieved lasting
dominance, Soames argues that two methodological
developments
have, over time, remade the philosophical
landscape. These are (1)
analytic philosophers' hard-won success in
understanding, and
distinguishing the notions of logical truth,
a priori truth, and
necessary truth, and (2) gradual acceptance
of the idea that
philosophical speculation must be grounded
in sound
prephilosophical thought. Though Soames views
this history in a
positive light, he also illustrates the difficulties,
false
starts, and disappointments endured along
the way. As he engages
with the work of his predecessors and contemporaries--from
Bertrand Russell and Ludwig Wittgenstein
to Donald Davidson and
Saul Kripke--he seeks to highlight their
accomplishments while
also pinpointing their shortcomings, especially
where their
perspectives were limited by an incomplete
grasp of matters that
have now become clear.
Soames himself has been at the center of
some of the tradition's
most important debates, and throughout writes
with exceptional
ease about its often complex ideas. His gift
for clear exposition
makes the history as accessible to advanced
undergraduates as it
will be important to scholars. Despite its
centrality to
philosophy in the English-speaking world,
the analytic tradition
in philosophy has had very few synthetic
histories. This will be
the benchmark against which all future accounts
will be measured.
Scott Soames is Professor of Philosophy at
Princeton University.
The author of Beyond Rigidity and Understanding
Truth, he is
coeditor of Propositions and Attitudes and
coauthor of Syntactic
Argumentation and the Structure of English.
Endorsement:
"A history of analytic philosophy and
an excellent piece of
analytic philosophy in its own right. We
can all benefit from
Soames's discussion of the central issues
that have shaped the
subject and his assessment of what we have
achieved and where we
might have gone wrong."--Kit Fine, New
York University