Monte Carlo methods are a class of computational algorithms
for simulating the behavior of a wide range of various physical
and mathematical systems (with many variables). Their utility has
increased with general availability of fast computers, and new
applications are continually forthcoming. The basic concepts of
Monte Carlo are both simple and straightforward and rooted in
statistics and probability theory, their defining characteristic
being that the methodology relies on random or pseudo-random
sequences of numbers. It is a technique of numerical analysis
based on the approximate solution of a problem using repeated
sampling experiments and observing the proportion of times a
given property is satisfied.
The term Monte Carlo was first used to describe calculational
methods based on chance in the 1940s, but the methods themselves
preceded the term by as much as a century. Quantum Monte Carlo (QMC)
first appeared in 1982 and similarly was preceded by development
of the related calculational methodology. The success of QMC
methods over the past few decades has been remarkable, and this
book will clearly demonstrate that success in its discussion of
applications. For isolated molecules, the basic material of
chemistry, QMC methods have produced exact solutions of the
Schroedinger equation for very small systems and the most
accurate solutions available for very large systems. The range of
applications is impressive: folding of protein molecules,
interactions in liquids, structure modeling in crystals and
enzymes, quantum dots, designing heat shields and aerodynamic
forms, architecture, design, business and economics, and even
cinema and video games (3D modeling).
This book takes a similar approach to Henry Schaefers classic
book Quantum Chemistry (OUP, 1984 now a Dover edition),
collecting summaries of some of the most important papers in the
quantum Monte Carlo literature, tying everything together with
analysis and discussion of applications. Quantum Monte Carlo is a
reference book for quantum Monte Carlo applications, belonging
near the desk of every quantum chemist, physicist, and a wide
range of scientists and engineers across many disciplines,
destined to become a classic.
176 pages; 5-1/2 x 8-1/4;
ISBN13: 978-0-19-531010-8
ISBN10: 0-19-531010-1
(Hardback)
ISBN-10: 0-19-921560-X
ISBN-13: 978-0-19-921560-7
Estimated publication date: April 2007
320 pages, 234x156 mm
Series: Oxford Graduate Texts in Mathematics number 12
Description
Accessible to graduate students in both Mathematics and Physics
Surveys current research and states open problems, particularly
in calibrated geometry
Thorough coverage, major proofs such as the Calabi conjecture are
provided in full
Extensive, up-to-date bibliography
This graduate level text covers an exciting and active area of
research at the crossroads of several different fields in
Mathematics and Physics. In Mathematics it involves Differential
Geometry, Complex Algebraic Geometry, Symplectic Geometry, and in
Physics String Theory and Mirror Symmetry. Drawing extensively on
the author's previous work, the text explains the advanced
mathematics involved simply and clearly to both mathematicians
and physicists. Starting with the basic geometry of connections,
curvature, complex and K?hler structures suitable for beginning
graduate students, the text covers seminal results such as Yau's
proof of the Calabi Conjecture, and takes the reader all the way
to the frontiers of current research in calibrated geometry,
giving many open problems.
Readership: Graduates and researchers in Mathematics and Physics
Contents
Preface
1. Background material
2. Introduction to connections, curvature and holonomy groups
3. Riemannian holonomy groups
4. Calibrated geometry
5. K?hler manifolds
6. The Calabi Conjecture
7. Calabi-Yau manifolds
8. Special Lagrangian geometry
9. Mirror Symmetry and the SYZ Conjecture
10. Hyperk?hler and quaternionic K?hler manifolds
11. The exceptional holonomy groups
12. Associative, coassociative and Cayley submanifolds
References
Index
Paper | May 2007 |ISBN13: 978-0-691-12955-6
Cloth | April 2007 | ISBN13: 978-0-691-12860-3
296 pp. | 6 x 9
This collection of new and original papers on mathematical
aspects of nonlinear dispersive equations includes both
expository and technical papers that reflect a number of recent
advances in the field. The expository papers describe the state
of the art and research directions. The technical papers
concentrate on a specific problem and the related analysis and
are addressed to active researchers.
The book deals with many topics that have been the focus of
intensive research and, in several cases, significant progress in
recent years, including hyperbolic conservation laws, Schrodinger
operators, nonlinear Schrodinger and wave equations, and the
Euler and Navier-Stokes equations.
Jean Bourgain is Professor of Mathematics at the Institute for
Advanced Study in Princeton. In 1994, he won the Fields Medal. He
is the author of Green's Function Estimates for Lattice
Schrodinger Operators and Applications (Princeton). Carlos E.
Kenig is Professor of Mathematics at the University of Chicago.
He is a fellow of the American Academy of Arts and Sciences and
the author of Harmonic Analysis Techniques for Second Order
Elliptic Boundary Value Problems. S. Klainerman is Professor of
Mathematics at Princeton University. He is a MacArthur Fellow and
Bocher Prize recipient. He is the coauthor of The Global
Nonlinear Stability of the Minkowski Space (Princeton).
Another Princeton book by Jean Bourgain:
Green's Function Estimates for Lattice Schrodinger Operators and
Applications. (AM-158).
Series:
Cloth | 2007 | ISBN13: 978-0-691-12161-1
768 pp. | 7 x 10 | 23 line illus. 17 tables.
Until now, students and researchers in nonparametric and
semiparametric statistics and econometrics have had to turn to
the latest journal articles to keep pace with these emerging
methods of economic analysis. Nonparametric Econometrics fills a
major gap by gathering together the most up-to-date theory and
techniques and presenting them in a remarkably straightforward
and accessible format. The empirical tests, data, and exercises
included in this textbook help make it the ideal introduction for
graduate students and an indispensable resource for researchers.
Nonparametric and semiparametric methods have attracted a great
deal of attention from statisticians in recent decades. While the
majority of existing books on the subject operate from the
presumption that the underlying data is strictly continuous in
nature, more often than not social scientists deal with
categorical data--nominal and ordinal--in applied settings. The
conventional nonparametric approach to dealing with the presence
of discrete variables is acknowledged to be unsatisfactory.
This book is tailored to the needs of applied econometricians and
social scientists. Qi Li and Jeffrey Racine emphasize
nonparametric techniques suited to the rich array of data types--continuous,
nominal, and ordinal--within one coherent framework. They also
emphasize the properties of nonparametric estimators in the
presence of potentially irrelevant variables.
Nonparametric Econometrics covers all the material necessary to
understand and apply nonparametric methods for real-world
problems.
Qi Li is Professor of Economics and Hugh Roy Cullen Professor in
Liberal Arts at Texas A&M University. Jeffrey Scott Racine is
Professor of Economics, Professor in the Graduate Program in
Statistics, and Senator William McMaster Chair in Econometrics at
McMaster University.
Endorsements:
"Nonparametric Econometrics by Li and Racine is a must for
any serious econometrician or statistician who is working on
cutting-edge problems. The theoretical treatment of nonparametric
methods is remarkably complete in its coverage of mainstream and
relatively arcane topics. I particularly like Li and Racine's
general treatment of continuous and discrete regressors and of
specification testing, topics that I have not seen handled in
such a comprehensive fashion. I will certainly use this in my
graduate econometrics courses and in conducting my own research."--Robin
Sickles, Rice University
"Very few studies have tried to apply the nonparametric
techniques to analyze real data. The lack of applications of
those techniques is perhaps attributable to the lack of a good
textbook that explains intuitively how and why those techniques
work. This book by Li and Racine serves both applied researchers
and graduate students. It is written in plain language so that it
can be understood by anyone with basic econometrics but zero
knowledge of nonparametric methods. And it contains enough
specifics that clearly spell out steps to implement those methods."--Chunrong
Ai, University of Florida
"This book represents a very significant contribution to the
field of econometrics. It provides an extremely thorough coverage
of our knowledge in the area of nonparametric and semiparametric
methods as they apply to economic models and economic data. And
it makes accessible, for the first time, a body of relatively new
material relating to discrete and 'mixed' data. There is a good
balance of theoretical material and applications. Apart from
serving as a superb teaching text in graduate-level courses where
the students have a strong econometrics/statistics preparation, I
believe this book will become a must-have reference resource for
many researchers."--David E. Giles, University of Victoria
contents
Cloth | May 2007 | ISBN13: 978-0-691-12230-4
640 pp. | 7 x 10 | 18 halftones. 44 line illus. 7 tables.
This book is the essential new introduction to modern string
theory, by one of the world's authorities on the subject.
Concise, clearly presented, and up-to-date, String Theory in a
Nutshell brings together the best understood and most important
aspects of a theory that has been evolving since the early 1980s.
A core model of physics that substitutes one-dimensional extended
"strings" for zero-dimensional point-like particles (as
in quantum field theory), string theory has been the leading
candidate for a theory that would successfully unify all
fundamental forces of nature, including gravity.
Starting with the basic definitions of the theory, Elias Kiritsis
guides readers through classic and modern topics. In particular,
he treats perturbative string theory and its Conformal Field
Theory (CFT) tools in detail while also developing
nonperturbative aspects and exploring the unity of string
interactions. He presents recent topics including black holes,
their microscopic entropy, and the AdS/CFT correspondence. He
also describes matrix model tools for string theory. In all, the
book contains nearly five hundred exercises for the graduate-level
student, and works as a self-contained and detailed guide to the
literature.
String Theory in a Nutshell is the staple one-volume reference on
the subject not only for students and researchers of theoretical
high-energy physics, but also for mathematicians and physicists
specializing in theoretical cosmology and QCD.
Elias Kiritsis is Directeur de Recherche at the CNRS, affiliated
with the Ecole Polytechnique in Paris, and Professor of Physics
at the University of Crete.
Endorsements:
"An excellent reference for any graduate student interested
in string theory. Kiritsis succinctly describes many of the
recent developments that are necessary background to current
research. Topics covered include black holes in string theory,
holography, various dualities among string theories, and
dualities connecting string theory to gauge theories. The basic
frameworks for connecting string theory to four-dimensional
physics are also explained."--Juan Maldacena, Institute for
Advanced Study
"This very well-written book, which builds on the
fundamentals and provides an excellent introduction to the state
of the art in string theory, will be quite useful to students and
to researchers acquainting themselves with this exciting field.
It concisely lays out the successes of string theory to date and
the challenges that await. I have no doubt that the topics
described herein will remain at the heart of the theory even when
our understanding of its dynamics and its role in describing
nature improve."--David Kutasov, University of Chicago
"There is a definite need for a short speedy introduction to
modern string theory. Kiritsis beautifully fill this gap--including
all essential areas, but remaining relatively concise, so that a
beginning student can work through the entire text."--Andrew
Strominger, Harvard University
"String theory textbooks are found on the bookshelves of not
only those theoretical physicists who call themselves string
theorists, but also others, and this book will appeal especially
to this broader category of readers. More universal in its
coverage than are comparable texts, it seeks to explain virtually
all the issues whose knowledge becomes more or less necessary for
every researcher in the field. Indeed, it squeezes all its
material into less than 600 pages of well-defined, short
sentences with a clear technical content--a nearly complete
discussion of the subject that will be really useful to many
experts and future experts."--Lubos Motl, Harvard University
Cloth | May 2007 | ISBN13: 978-0-691-11642-6
336 pp. | 7 x 10 | 31 halftones. 52 line illus. 5 tables.
Topics in Mathematical Modeling is an introductory textbook on
mathematical modeling. The book teaches how simple mathematics
can help formulate and solve real problems of current research
interest in a wide range of fields, including biology, ecology,
computer science, geophysics, engineering, and the social
sciences. Yet the prerequisites are minimal: calculus and
elementary differential equations. Among the many topics
addressed are HIV; plant phyllotaxis; global warming; the World
Wide Web; plant and animal vascular networks; social networks;
chaos and fractals; marriage and divorce; and El Nino.
Traditional modeling topics such as predator-prey interaction,
harvesting, and wars of attrition are also included. Most
chapters begin with the history of a problem, follow with a
demonstration of how it can be modeled using various mathematical
tools, and close with a discussion of its remaining unsolved
aspects.
Designed for a one-semester course, the book progresses from
problems that can be solved with relatively simple mathematics to
ones that require more sophisticated methods. The math techniques
are taught as needed to solve the problem being addressed, and
each chapter is designed to be largely independent to give
teachers flexibility.
The book, which can be used as an overview and introduction to
applied mathematics, is particularly suitable for sophomore,
junior, and senior students in math, science, and engineering.
K. K. Tung is Professor and Chairman of the Department of Applied
Mathematics at the University of Washington. He is the author or
coauthor of more than eighty research papers in atmospheric
sciences and applied mathematics, and editor or chief editor of
two journals in these fields.
Endorsements:
"This book has a refreshing style that should appeal to
undergraduates. Indeed, the author has produced a textbook that
might well achieve his goal of teaching applied mathematics
without those being taught noticing!"--Andrew Wathen,
University of Oxford
"With courses in mathematical modeling getting ever more
popular, this book will make a valuable addition to the subject.
It deals with topics that should be appealing even to students
not majoring in math or science, and the level of mathematical
sophistication is carefully increased throughout the book."--Henrik
Kalisch, University of Bergen, Norway