Editorial Board; Hodes, W. A. /Jensen, R / Magidor, M.:
An International series of research monographs and textbooks in
mahematical logic
and related fields. Poceedings of conferences devoted to topics
of current research
interest may also be included.
Wrutteb by experts, the volumes in this series cover the major
areas of contemporary
logic, such as set theory, recursion theory, proof hteory and
model theory
as well as applications to other fields of mathematics.
The publications in this senries should be usefull both as texts
for courses
and as guides for lectures and seminars. At the same time, the
volumes are suffciently
advanced to serve as a solid basis for further research.
Vol. 1 : Hugh,W.
This volume presents a detailed account of a new method for
obtaining models of Set Theory,
using models of Determinancy. The primary applications is the
identification of a canonical
model of Set theory in Which the Contintmm Hypothesis is false.
Such models have been sought for in the 35 years since Cohen's
discovery of the method of
forcing. The new model belongs to a large class of similarly
obtained models is developed
in some detail through the study of the canonical model and
several of the releted models.
A number of applications in combinatorial set theory are
discussed.
This is a research monograph, the results being presented, making
the account accessible to
advanced graduate students in Mathematical Logic Set Theory.
June 1999 915 pp. 3-11-015708-X \28,900.
voL 2: Arslanov, M. / Lempp, S. (eds.):
Proceedings ofthe Kazan '97 Workshop, 1997
This volume contains papers from the recursion theory session of
the Kazan Workshop
on Recursion add Complexity Theory. Recursion theory, the study
of computability,
is an area of mathe-matical logic thea has traditionally been
particularly strong in
the United States and the former Soviet Union and Western Europe.
The volume features 14 research papers by participants on topics
discussed at the workshop
as well as a list of the open problems presented at the workshop.
Many of the papers focus particularly on applications of
recursion theory to other areas of
mathematics, such as algebra, analysis, models theory, and proof
theory.
July 1999 284 pp. 3-11-016587-2 \26,800.
The Student Mathematical Library is a new series of
undergraduate studentes in mathematics.
This developing series is intended to spark undergraduates'
appreciation for research by
introducing them to interesting topics of modern mathematics.
By enphasizing original topics and approaches, the series aims to
broaden students'
mathematical experiences. Books to be published in the series are
suitable for honors
courses, upper-division seminars, reading courses or self-study.
,
VoI.1: Radin, C.
The Common thread throughout this book is aperiodic tilings;
the best-known example is the
"kite and dart" tiling. This tiling has been widely
discussed, particularly since 1984 when
it was adopted to model quasicrystals.
The presentation uses many different areas of mathematics and
physics to analyze the new
features of such tilings. Although many people are aware of the
exstence of aperiodic tilings,
and maybe even their origin in a question in logic, not everyone
is familiar with their subtleties
and the underlying rich mathematical theory.
For the interested reader, this book fills that gap.
Understanding this new type of tiling requires an unusual variety
of specialties, including ergodic
theory, functional analysis, group theory and ring theory from
mathematics, and statistical mechanics
and wave diffraction from physics. This interdisciplinary
approach also leads to new mathematics
seemingly unrelated to the tilings.
1999 128 pp 0-8218-1933-X \2,900.
VoI.2: Lawler,G./Coyle,L.
This volume is based on classes in probability for advanced
undergraduates held at the IAS/Park City
Mathematics lnstitute. It is derived from both lectures (Chapters
1-10) and computer simulations
(chapters 11-13) that were held during the program. The material
is coordinated so that some of
the major computer simulations relate to topics covered in the
first ten chapters.
The goal is to present topics that are accessible to advanced
undergraduates, yet are areas of
current research in probability. The combination of the lucid yet
informal style of the lectures
and the hands-on nature of the simulations allows readers to
become familiar with some interesting
and active areas of probability.
The first four chapters discuss random walks and the continuous
limit of random walks: Brownian motion.
chapters 5 and 6 consider the fascinating mathematics of card
shuffles, including the notions of
random walks on a symmetric group and the general idea of random
permutations.
chapters 7 and 8 discuss Markov chains9,beginning with a standard
introduction to the theory.
chapter 8 addresses the recent important application of Markov
chains to simulations of random systems
on large finite sets: Markov Chain Monte Carlo.
Random walks and electrical networks are covered in Chapter 9.
Uniform spanning trees, as connected
to probability and random walks, are treated in Chapter 10. The
final three chapters of the book present
simulations. Chapter 10 discusses simnlations for random walks.
Chapter 12 covers simulation topics such as sampling from
continuous distributions, random permutations,
andestimating the number of matI.ices with certain conditions
using MarkoY Chain Monte Carlo.
Chapter 13 presents simulations of stochastic differential
equations for applications in finance.
(The simulations do not require one particular piece of software.
They can be done in symbolic
computation packages or via programming languages such as C.)
The volume concludes with a number of problems ranging from
routine to very difficult.
Of particular note are problems that are typical of simulation
problems given to students by
the authors wheA teaching undergraduate probability.
1999 120 pp. 0-8218-2029-X \3,080.
Forthcoming Titles :
Tenenbaum, G. / Poincare, I. / France, F. / Mendes,
M.:
We have been curious about numbers--and prime numbers--since
antiquity.
One notable new direction this century in the study of primes has
been the influx of ideas from probability.
The goal of this book is to provide insights into the prime
numbers and to describe how a sequence so tautly
determined can incorporate such a striking amount of randomness.
There are two ways in which the book is exceptional. First, some
familiar topics are covered with
refreshing insight and or from new points of view.
Second, interesting recent developments and ideas are presented
that shed new light on the prime numbers
& their distribution among the rest of the integers. i
This book is suitable for anyone who has had a little number
theory and some advanced calculus involving
estimates. This book is the English translation from the French
edition.
1999 120 pp. 0-8218-1647-0 \3,080.
Knobel, R :
This book is based on an undergraduate course taught at the
IASJ/ark City Mathematics Institute,
on linear and nonlinear waves. The first part of the teit
Overviews the concept of a wave, describes
one-dimensional waves using functions of two variables, provides
an introduction to partial differential
equations, and discusses computer-aided visualization techniques.
The second part of the book discusses traveling waves, leading to
a description of solitary waves and soliton
solutions of the Klein-Gordon and Korteweg-deVries equations. The
wave equation is derived to model
the small vibrations of a taut string, and solutions are
constructed via d'Alembert's formula and Fourier series.
The last part of the book discusses waves arising from
conservation laws.
After deriving and discussing the scalar conservation law, its
solution is described using the method of
characteristics, leading to the formation of shock and
rarcfaction waves.
1999 200 pp. 0-8218-2039-7 \4,160.
A New Series Published by the Courant Institute, New York University
This series is based on the research interests
of the faculty and visitors of the Courant
Institute of Mathematical Sciences. Some of the volumes are
reprints from the previous
Lecture Notes series.
These lecture notes originated in advanced
graduate courses and minicourses offered at
the institute. Titles in this series include:
Qing Han and Fanghua Lin
1997, 144 pp., \5,490. ISBN 0-9658703-0-8
The material in this volume is based on a PDE course given at
the Courant Institute. We present basic methods
for obtaining various a priori estimates for second-order
equations of elliptic type with particular emphasis on
maximal principles, Harnack inequalities, and their applications.
The equations one deals with are always linear,
although they also obviously apply to nonlinear problems.
Jalal Shatah and Michael Struwe
1998, 153 pp., \5,490. ISBN 0-9658703-1-6
These notes are an expanded version of lectures given at the
Courant Institute and of a DMV-Seminar held in
May 1997 in Oberwolfach. A large part of these notes is devoted
to the study of semilinear equations with critical
Sobolev exponents and wave maps in two space dimensions. To make
these notes self-contained, we added further
background material.
Percy Deift
1999, 273 pp., \5,490. ISBN 0-9658703-2-4
These notes expand on a set of lectures at the Courant
Institute in 1996-1997 on Riemann-Hilbert problems,
orthogonal polynomials, and random matrix theory. The main goal
of the course was to prove universality for
a variety of statistical quantities arising in the theory of
random matrix models. The main ingredient in the proof is
the steepest descent method for oscillatory Riemann-Hilbert
problems introduced earlier by the author and Xin Zhou.
Tobias H. Colding and William P. Minicozzi II
1999, approx. 120 pp., \5,490. ISBN 0-9658703-3-2
The motivation for these lecture notes on minimal surfaces is
to cover the necessary background material
needed for the authors' work on compactness and convergence of
minimal surfaces in three-manifolds. Some
of these results are described in the last chapter of these
notes. These results about convergence and compactness
of embedded minimal surfaces in three-manifolds are in part
motivated by a question of Pitts and Rubinstein. Roughly
speaking, this question asks to give a bound for the Morse index
of all embedded closed minimal surfaces of fixed genus
in a closed three-manifold. The claim of Pitts and Rubinstein is
that if there is such a bound for a sufficiently large class
of metrics on the three-sphere, then the famous spherical
space-form problem can be settled affirmatively. We also
hope that these notes will help to stimulate interaction between
minimal surface theory and the topology of three-manifolds.
Emmanuel Hebey
1999, 320 pp., \5.490. ISBN 0-9658703-4-0
These notes deal with the theory of Sobolev spaces on
Riemannian manifolds. Much of this book is devoted to the
concept of best constants. This concept appeared very early on to
be crucial for solving limiting cases of some PDEs.
A striking example of this was the major role that best constants
played in the Yamabe problem. These lecture notes
are self-contained; no prior knowledge of differentiable
manifolds and Riemannian geometry is assumed. These notes
should be accessible to graduate students.
vol.4: Matsuo Atushi/Nagatomo Kiyokazu:
Table of Contents
Two-dimensional chiral quantum fields: Fields and their residue
products/ Mutually local fields /
Borcherds identity for local fields Axioms for vertex algebra:
Axioms and their cnsequences /
state-field correspondence / Goddard's axioms and the existence
theorem
Topics and examples: Summary of related notions/ Relation to
other algebraic structures/ Examples
Appendix: A Vertex superalgebras / Analytic method / List of
expansions of (x-y)r(y-z)q(x-z)p / Reference
April 1999 112pp. 4-931469-04-3 \2,000.
vol 3: Ohtsuki Tomotada :
Table of Contents
Preliminaries / The modified Kontsevich invariant / The the
modefied Kontsevich invariant and
quantum invariants / The modified Kontsevich invariant and
Vassiliev invariants /Vassiliev invariants and
quantum invariants / The universal perturbative invariant of
3-manifolds /Finite type invariants
and the universal perturbative invariant / Quantum invariants and
the universal perturbative invanant
April 1999 78 pp 4-931469-03-5 \2,000.
vol 2: Tahkashi Masako / Okada Mitsuhiro / Mariangiola D.-Ciancaglini (eds.) :
Table of Contents
A primer on proofs and types / Intersection types,l-models, and
Bohm tree / Synatax and semantics of
type assignment systems /A type inference approach to program
analysis / Constructivization via approximations
and examples / Proof-theoretic methods in nonclassical logic / An
introduction to linear logic
Dec. 1998 295 pp. 4-931469-02-7 \5,800.
vol 1: Cherednik, I. / Forrester, P. /
Uglov, D.:
Jan. 1998 241 pp. 4-931469-01-9 \4,000.