ROBERTO CIPOLLA / University of
Cambridge
AND PETER GIBLIN / University of Liverpool
Computer vision aims to detect and reconstruct
features of surfaces from images.
This book describes how the 3D shape of surfaces
can be recovered from image
sequences of 'outlines'. lt provides all the
necessary background in differential
geometry (assuming knowledge of elementary algebra
and calculus) and in the
analysis of visual motion, emphasising intuitive
visual understanding of the geometric
techniques with computer-generated illustrations.
[t also gives a thorough introduction
to the mathematical techniques and the details of
the implementations, and applies
the methods to data from real images.
Contents: 1. Introduction; 2. Differential
geometry of curves and surfaces; 3. Views of curves and
surfaces; 4. Dynamic analysis of apparent
contours; 5. Reconstruction of surfaces from a family
of views; 6. Recovery of viewer motion from
apparent contours; Bibliography; hndex.
Selling Points: . First book to introduce all the
necessary differential geometry, slanted towards
the applications to computer vision
･ lt is lavishly illustrated by computer-drawn
figures which aim to make the
mathematics more visually understandable
･ Specifically designed to cover the geometry
of, and reconsruction of, surfaces -
which are not dealt with in competing literature
Comparable Titles: PORTEOUS/Geometric
Differentiation/1 994/0521 39063X
CIPOLLA and PENTLAND/Computer Vision for
Human-Machine
Interaction/1 998/0521 622530
BRUCE and GIBLIN/Curves and Singularities 2nd
ed/1992/0521 429994
Subject areascomputer science (computer vision,
robotics), engineering (robotics, computer
Market: academic researchers, professionals,
graduate students
0521 63251 X Hardback 160pp c December1999
86 figures _
SUBIR SACHDEV
Yale University
Quantum Phase Transitions is the first book to
describe in detail the fundamental
changes that can occur in the macroscopic nature
of matter at zero temperature die
to smaII variations in a given external parameter.
Throughout the book the author
interweaves experimental results with presentation
of theoretical models, and well
over 500 references are included. The book will be
of great interest to graduate
students and researchers in condensed matter
physics.
Contents: Part I. Introduction: 1. Basic concepts;
2. The mapping to classical statistical
mechanics: single site models; 3. Overview; Part
ll. Quantum lsing and Rotor Models: 4. The
lsing chain in a transverse Geld; 5. Quantum rotor
models: farge N limit; 6. The d= 1, 0 (N greater
than or equal to 3) rotor models; 7. The d = 2 (N
greater than or equal to 3) rotor models; 8.
Physics close to and above the upper-chtical
dimension; 9. Transport in d a 2; Part [ll. Other
Models: 10. Boston Hubbard model; 11. Dilute Fermi
and Bose gases; 12. Phase transitions of
Fermi liquids; 13. Heisenberg spins: ferromagnets
and antiferromagnets; 14. Spin chains:
bosonization; 15. Magnetic ordering transitions of
disordered systems; 16. Quantum spin glasses.
Selling Points: . First book to cover this very
hot area of physics
･ Author was one of the founders of the field
' Addresses both theory and exp.eriments
Comparable Titles:TSVELIK/Quantum Field Theory in
Condensed Matter Physics/1 995/0521
454670 I
EFETOV/Supersymmetry in Disorder and Chaos/1
996/0521 470978
Subject areascondensed matter physics, statistical
physics, materials physics, theoretical physics
Market: academic researchers, graduate students
0521 58254 7 Hardback 384pp c December1999
66 line diagrams 5 tables
PIETER VERMAAS
Delft University of Technology
Standard quantum mechanics is not a theory that
describes the outside world. Rather,
it only predicts the probabilities with which
measurements have outcomes. However,
quantum mechanics is a fundamental theory of
nature, and attempts have been made,
therefore, to interpret the theory as a
description of the world. This book is a survey of
the so-called modal interpretations of quantum
mechanics, proposed during the 1970s
and 1980s, and more fully developed in the 1990s.
Contents: 1. Introduction; 2. Quantum mechanics;
3. Modal interpretations; Part l. Formalism: 4.
The different versions; 5. The full property
ascription; 6. Joint property ascriptions; 7.
Discontinuities, instabilities and other bad
behaviour; 8. Transition probabilities; 9. Dynamical
autonomy and locality; Part lI. Physics.- 10. The
measurement problem; 1 1. The Born rule; Part lll.
Philosophy: 12. Properties, states, measurement
outcomes and effective states; 13. Holism
versus reductionism; 14. Possibilities and
impossibilities; 15. Conclusions.
Selling Points: . The most complete survey to date
of the modal interpretation of quantum
mechanics
･ Impartial survey; does not attempt to push a
certain case
･ Organised so that it can be read either from
beginning to end or used as a reference
book
Comparable Titles:BUB/Interpreting the Quantum
World/1 997/0521 560829
DICKSON/Quantum Mechanics and Non-Locality/1
998/0521 581273
BUB/Interpreting the Quantum World/Cambridge/1
997/0521 65386X
Subject areasphysics, philosophy of science
Market: academic researchers, graduate students,
undergraduate students
0521 651085 Hardback 270pp c December1999
A. J. BERRICK / National University
of Singapore
AND M. E. KEATING / Imperial
College
This is a concise introduction to ring theory'
module theory and number theory, ideal
for a Rrst year graduate student, as well as an
excellent reference for working
mathematicians in other areas. About 200 exercises
complement the text and
introduce further topics. This book provides the
background material for the authors'
companion volume Categories and Modules, soon to
appear. Armed with these two
texts, the reader will be ready for more advanced
topics in K-theory, homological
algebra and algebraic number theory.
Contents: 1. Basics; 2. Direct sums and their
short exact sequences; 3. Noethehan rings and
polynomial rings; 4. Artinian rings and modules;
5. Dedekind domains; 6. Modules over Dedekind
domains.
Selling Points: ･No prior knowledge is required
of the reader, other than that which can be
acquired in a standard undergraduate course
･ A full set of exercises indicates some of the
deeper applications and
developments ofthe results i,
･ Almost entirely self-contained, yet concise
Comparable Titles: PESKINE/An Algebraic
Introduction to Complex Projective
Geometry/1 996/052 1 480728
BRODMANN and SHARP/Local Cohomology/1998/0521
372860
Subject areasmathematics (algebra)
Market: graduate students, academic researchers
Series: Cambridge Studies in Advanced Mathematics,
65
D521632749 Hardback 288pp c December1999 c
200 exercises
T. PETERFALVI
Universite de Paris VII
The famous and important theorem of W. Feit and
J. G. Thompson states that every
group of odd order is solvable, and the proof of
this has roughly two parts. The first
Part appeared in Bender and Glauberman's Local
Analysis for the Odd Order
Theorem which was number 188 in this series. This
book provides the
character-theoretic second part and thus completes
the proof. All researchers in group
theory should have a copy of this book in their
library.
Contents: Part l. Character Theory for the Odd
Order Theorem: Part lI. A Thereom of Suzuki: 1.
General properties of G; 2. The first case; 3. The
structure of H; 4. Charactehsation of PSU (3, q);
Appendices.
Selling Points: ･The long awaited second part of
an extremely famous proof
･ Author is top name
･ Original work has been much updated
Comparable Titles:BENDER and GLAUBERMAN/Local
Analysis for the Odd Order
Theorem/1 995/0521 4571 65
Subject areasmathematics (group theory)
Market: academic researchers, graduate studentst
Series: London Mathematical Society Lecture Note
Series, 272
052164660X Paperback 180pp c December1999
G. K. BATCHELOR
University of Cambridge
First published in 1967, Professor Batchelor's
classic text on fluid dynamics is still one
of the foremost texts in the subject. The careful
presentation of the underlying theories
of fluids is still timely and applicable, even in
these days of almost limitless computer
power. This re-issue should ensure that a new
generation of graduate students see
the elegance of Professor Batchelor's
presentation.
Contents: Preface; Conventions and notation; 1.
The physical properties of fluids; 2. Kinematics of
the flow field; 3. Equations governing the motion
of a fluid; 4. Flow of a uniform incompressible
viscous fluid; 5. Flow at Barge Reynolds number:
effects of viscosity; 6. Irrotational flow theory and
its applications; 7. FIow of effectively inviscid
liquid with vorticity; Appendices.
SeIIing Points: . Written by one ofthe founders of
modern fluid dynamics
･ A textbook with a strong track record
･ Re-issued in the Cambridge Mathematical
Library following strong current demand
Comparable Titles:BATCHELOR/An lntroduction to
Fluid Dynamics/1967 &1973/0521 098173
Subject areasfluid dynamics, mechanical
engineering, applied mathematics
Market: graduate students ..
Series: Cambridge Mathematical Library
0521 663962 Paperback 634pp c December1999
172 line diagrams
DANIEL W. STROOCK
Massachusetts Institute of Technology
This revised edition of Daniel W. Stroock's
text is suitable for a first-year graduate
course on probability theory. lt is intended for
students with a good grasp of
undergraduate probability and is a reasonably
sophisticated introduction to modern
analysis for those who want to learn what these
two topics have to say about each
other. Although primarily intended for students
and practitioners of probability theory
and analysis, it will also be a valuable reference
for those in fields as diverse as
physics. engineering, and economics,
Contents: 1. Sums of independent random variables;
2. The central limit theorem; 3.
Convergence of measures, infinite divisibility,
and processes with independent increments; 4. A
celebration of Wiener's measure; 5. Conditioning
and martingales; 6. Some applications of
martingale theory; 7. Continuous martingales and
elementary diffiusion theory; 8. A little classical
potential theory.
Selling Points: . Revised edition of a classic
graduate textbook
･ Covers the intersection between probability
and analysis
･ hncludes sections on 1'ndependent random
variables, Central Limit phenomena and
martingales ..
Comparable Titles:AMBEGAOKAFUReasoning about
Luck/0521 447372/1 996/sales 1 905 in
PB/according to reviews (see quotes) this book
will be of interest to engineers and members of
other disciplines
Subject areasmathematics, analysis and probability
theory
Market: graduate students, professionals
0 521 663490 Paperback 528pp c December1999
ROE GOODMAN / Rutgers
University
AND NOLAN R. WALLACH / University of California,
San Diego
This book presents an updated version of Weyl's
invariant theory of the classical
groups, together with many of the important recent
developments. Requiring only an
abstract algebra course as a prerequisite, it will
introduce students of mathematics to
the structure and finite-dimensional
representation theory of the complex classical
groups and will serve as a reference for
researchers in mathematics, statistics,
physics and chemistry whose work involves symmetry
groups, representation theory,
invariant theory and algebraic group theory.
Contents: 1. Classical groups as linear algebraic
groups; 2. Basic structure of classical groups; 3.
Algebras and representations; 4. Polynomials and
tensor invariants; 5. Highest weight theory; 6.
Spinors; 7. Cohomology and characters; 8.
Branching laws; 9. Tensor representations of GL(V);
10. Tensor represenations of 0(V) and Sp(V); 1 1.
Algebraic groups and homogeneous spaces;
12. Representations on Aft(X); A. AIget)raic
geometry; B. Linear and multilinear algebra; C.
Associative algebras and Lie algebras; D.
Manifolds and Lie groups.
Selling Points: . More difficult chapters arranged
so results can be understood without reading
details of proof
･ Self-contained, with appendices developing the
basics of algebraic geometry,
multilinear algebra, enveloping algebras of Lie
algebras, manifolds and Lie groups
･ Over 300 exercises, most with hints for
solution
Comparable Titles:ALPERIN/Local Representation
Theory/1 986/0521 44926X
Subject areasmathematical analysis, algebra,
physics, chemistry
Market: graduate students, academic researchers
Series: Encyclopedia of Mathematics and its
Applications, 68
0 521 58273 3 Hardback 703pp May 1998
100 line diagrams
0 521 66348 2 Paperback 704pp c December 1999
100 line diagrams
Cloth | 1999 |
290 pp. | 6 x 9 | 7 halftones 86 line illus. 31 tables
Have you ever daydreamed about digging a hole to the other side
of the world? Robert Banks not only entertains such ideas but,
better
yet, he supplies the mathematical know-how to turn fantasies into
problem-solving adventures. In this sequel to the popular Towing
Icebergs, Falling Dominoes (Princeton, 1998), Banks presents
another collection of puzzles for readers interested in
sharpening their
thinking and mathematical skills. The problems range from the
wondrous to the eminently practical. In one chapter, the author
helps us
determine the total number of people who have lived on earth; in
another, he shows how an understanding of mathematical curves can
help a thrifty lover, armed with construction paper and scissors,
keep expenses down on Valentine's Day.
In twenty-six chapters, Banks chooses topics that are fairly easy
to analyze using relatively simple mathematics. The phenomena he
describes are ones that we encounter in our daily lives or can
visualize without much trouble. For example, how do you get the
most
pizza slices with the least number of cuts? To go from point A to
point B in a downpour of rain, should you walk slowly, jog
moderately, or
run as fast as possible to get least wet? What is the length of
the seam on a baseball? If all the ice in the world melted, what
would
happen to Florida, the Mississippi River, and Niagara Falls? Why
do snowflakes have six sides?
Covering a broad range of fields, from geography and
environmental studies to map- and flag-making, Banks uses basic
algebra and
geometry to solve problems. If famous scientists have also
pondered these questions, the author shares the historical
details with the
reader. Designed to entertain and to stimulate thinking, this
book can be read for sheer personal enjoyment.
Table of Contents
Preface ix
Acknowledgments xiii
Chapter 1 Broad Stripes and Bright Stars 3
Chapter 2 More Stars, Honeycombs, and Snowflakes 13
Chapter 3 Slicing Things Like Pizzas and Watermelons 23
Chapter 4 Raindrops Keep Falling on My Head and Other Goodies 34
Chapter 5 Raindrops and Other Goodies Revisited 44
Chapter 6 Which Major Rivers Flow Uphill? 49
Chapter 7 A Brief Look at pi, e, and Some Other Famous Numbers 57
Chapter 8 Another Look at Some Famous Numbers 69
Chapter 9 Great Number Sequences: Prime, Fibonacci, and Hailstone
78
Chapter 10 A Fast Way to Escape 97
Chapter 11 How to Get Anywhere in About Forty-Two Minutes 105
Chapter 12 How Fast Should You Run in the Rain? 114
Chapter 13 Great Turtle Races: Pursuit Curves 123
Chapter 14 More Great Turtle Races: Logarithmic Spirals 131
Chapter 15 How Many People Have Ever Lived? 138
Chapter 16 The Great Explosion of 2023 146
Chapter 17 How to Make Fairly Nice Valentines 153
Chapter 18 Somewhere Over the Rainbow 163
Chapter 19 Making Mathematical Mountains 177
Chapter 20 How to Make Mountains out of Molehills 184
Chapter 21 Moving Continents from Here to There 196
Chapter 22 Cartography: How to Flatten Spheres 204
Chapter 23 Growth and Spreading and Mathematical Analogies 219
Chapter 24 How Long Is the Seam on a Baseball? 232
Chapter 25 Baseball Seams, Pipe Connections, and World Travels
247
Chapter 26 Lengths, Areas, and Volumes of All Kinds of Shapes 256
References 279
Index 285
GENERAL ENDOWMENT
Publication Date:
October 1999
991 pages, 7x10 inches, 10 b&w illustrations, 276 line
figures,
27 tables.
Subjects:
History & Philosophy of Science; Physics; Philosophy;
Mathematics
Clothbound:
0-520-08816-6
Paperback:
0-520-08817-4
"This new, vastly better translation of the Principia is the
perfect work for illustrating how science, at its best, succeeds
in turning
data into decisive evidence."--George E. Smith, Tufts
University
"This translation is deeply impressive and will be the
definitive version for a century to come. Cohen's guide is
up-to-date on
matters of Newton scholarship and free from discarded conjectures
of the past."--Curtis Wilson, St. John's College
In his monumental 1687 work Philosophiae Naturalis Principia
Mathematica, known familiarly as the Principia, Isaac Newton laid
out in
mathematical terms the principles of time, force, and motion that
have guided the development of modern physical science. Even
after more
than three centuries and the revolutions of Einsteinian
relativity and quantum mechanics, Newtonian physics continues to
account for many
of the phenomena of the observed world, and Newtonian celestial
dynamics is used to determine the orbits of our space vehicles.
This completely new translation, the first in 270 years, is based
on the third (1726) edition, the final revised version approved
by Newton; it
includes extracts from the earlier editions, corrects errors
found in earlier versions, and replaces archaic English with
contemporary prose
and up-to-date mathematical forms.
Newton's principles describe acceleration, deceleration, and
inertial movement; fluid dynamics; and the motions of the earth,
moon, planets,
and comets. A great work in itself, the Principia also
revolutionized the methods of scientific investigation. It set
forth the fundamental three
laws of motion and the law of universal gravity, the physical
principles that account for the Copernican system of the world as
emended by
Kepler, thus effectively ending controversy concerning the
Copernican planetary system.
The illuminating Guide to the Principia by I. Bernard Cohen,
along with his and Anne Whitman's translation, will make this
preeminent work truly
accessible for today's scientists, scholars, and students.
I. Bernard Cohen is Victor S. Thomas Professor (Emeritus) of the
History of Science at Harvard University. Among his recent books
are
Benjamin Franklin's Science (1996), Interactions (1994), and
Science and the Founding Fathers (1992). Anne Whitman was
coeditor (with I.
Bernard Cohen and Alexander Koyr?) of the Latin edition, with
variant readings, of the Principia (1972). Julia Budenz, author
of From the
Gardens of Flora Baum (1984), is a multilingual classicist and
poet.
Description
The description of the structure of group C*-algebras is a
difficult problem, but relevant to important new developments in
mathematics, such as non-commutative geometry and quantum groups.
Although a significant number of new methods and results have
been obtained, until now they have not been available in book
form.
This volume provides an introduction to and presents research on
the study of group C*-algebras, suitable for all levels of
readers - from graduate students to professional researchers. The
introduction provides the essential features of the methods used.
In Part I, the author offers an elementary overview - using
concrete examples-of using K-homology, BFD functors, and
KK-functors to describe group C*-algebras. In Part II, he uses
advanced ideas and methods from representation theory,
differential geometry, and KK-theory, to explain two primary
tools used to study group C*-algebras: multidimensional
quantization and construction of the index of group C*-algebras
through orbit methods.
The structure of group C*-algebras is an important issue both
from a theoretical viewpoint and in its applications in physics
and mathematics. Armed with the background, tools, and research
provided in Methods of Noncommutative Geometry for Group
C*-Algebras, readers can continue this work and make significant
contributions to perfecting the theory and solving this problem.
Audience
mathematicians
mathematical physicists
Students and researchers in non-commutative geometry and harmonic
analysis
Contents
Introduction
The Scope and an Example
Multidimensional Orbit Methods
KK-Theory Invariance IndexC*(G)
Deformation Quantization and Cyclic Theories
Bibliographical Remarks
ELEMENTARY THEORY: AN OVERVIEW
Classification of MD-Groups
Definitions
MD Criteria
Classification Theorem
Bibliographical Remarks
The Structure of C*-Algebras of MD-Groups
The C*-Algebra of Aff R
The Structure of C*(Aff C)
Bibliographical Remarks
Classification of MD4-Groups
Real Diamond Group and Semi-Direct Products R x H3
Classification Theorem
Description of the Co-Adjoint Orbits
Measurable MD4-Foliation
Bibliographical Remarks
The Structure of C*-Algebras of MD4-Foliations
C*-Algebras of Measurable Foliations
The C*-Algebras of Measurable MD4-Foliations
Bibliographic Remarks
ADVANCED THEORY: MULTIDIMENSIONAL QUANTIZATION AND INDEX OF GROUP
C*-ALGEBRAS
Multidimensional Quantization
Induced Representation. Mackey Method of Small Subgroups
Symplectic Manifolds with Flat Action of Lie Groups
Prequantization
Polarization
Bibliographical Remarks
Partially Invariant Holomorphly Induced Representations
Holomorphly Induced Representations. Lie Derivative
The Irreducible Representations of Nilpotent Lie Groups
Representations of Connected Reductive Groups
Representations of Almost Algebraic Lie Groups
The Trace Formula and the Plancher'el Formula
Bibliographical Remarks
Reduction, Modification, and Superversion
Reduction to the Semi-Simple or Reductive Cases
Multidimensional Quantization and U(1)-Covering
Globalization over U(1)-Coverings
Quantization of Mechanical Systems with Supersymmetry
Bibliographical Remarks
Index of Type I C*-Algebras
Compact Type Ideals in Type I C*-Algebras
Canonical Composition series
Index of Type I C*-Algebras
Application to Lie Group Representations
Bibliographical Remarks
Invariant Index of Group C*-Algebras
The Structure of Group C*-Algebras
Construction of IndexC*(G)
Reduction of the Indices
General Remarks on Computation of Indices
Bibliographical Remarks
ISBN: 1584880198
Publication Date: 12/15/99