DIMACS: Series in Discrete Mathematics and Theoretical
Computer Science, Volume: 72.
2006; 246 pp; hardcover
ISBN-10: 0-8218-3596-3
ISBN-13: 978-0-8218-3596-8
The book is a collection of some of the research presented at the
workshop of the same name held in May 2003 at Rutgers University.
The workshop brought together researchers from two different
communities: statisticians and specialists in computational
geometry. The main idea unifying these two research areas turned
out to be the notion of data depth, which is an important notion
both in statistics and in the study of efficiency of algorithms
used in computational geometry. Many of the articles in the book
lay down the foundations for further collaboration and
interdisciplinary research.
Readership
Graduate students and research mathematicians interested in
multivariate analysis and computational geometry.
Table of Contents
R. Serfling -- Depth functions in nonparametric multivariate
inference
R. Y. Liu and K. Singh -- Rank tests for multivariate scale
difference based on data depth
J. Wang and R. Serfling -- On scale curves for nonparametric
description of dispersion
K. Mosler and R. Hoberg -- Data analysis and classification with
the zonoid depth
A. Hartikainen and H. Oja -- On some parametric, nonparametric
and semiparametric discrimination rules
A. Christmann -- Regression depth and support vector machine
R. T. Elmore, T. P. Hettmansperger, and F. Xuan -- Spherical data
depth and a multivariate median
S. Lopez-Pintado and J. Romo -- Depth-based classification for
functional data
J. A. Cuesta-Albertos and R. Fraiman -- Impartial trimmed means
for functional data
G. Aloupis -- Geometric measures of data depth
B. Chakraborty and P. Chaudhuri -- Computation of half-space
depth using simulated annealing
D. Bremner, K. Fukuda, and V. Rosta -- Primal-dual algorithms for
data depth
M. A. Burr, E. Rafalin, and D. L. Souvaine -- Simplicial depth:
An improved definition, analysis, and efficiency for the finite
sample case
J. H. Dula -- Fast algorithms for frames and point depth
S. Krishnan, N. H. Mustafa, and S. Venkatasubramanian --
Statistical data depth and the graphics hardware
Contemporary Mathematics, Volume: 423
2007; approx. 453 pp; softcover
ISBN-10: 0-8218-4080-0
ISBN-13: 978-0-8218-4080-1
Expected publication date is March 17, 2007.
This volume contains original research and survey articles
stemming from the Euroconference "Algebraic and Geometric
Combinatorics". The papers discuss a wide range of problems
that illustrate interactions of combinatorics with other branches
of mathematics, such as commutative algebra, algebraic geometry,
convex and discrete geometry, enumerative geometry, and topology
of complexes and partially ordered sets. Among the topics covered
are combinatorics of polytopes, lattice polytopes, triangulations
and subdivisions, Cohen-Macaulay cell complexes, monomial ideals,
geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig
combinatorics, and graph colorings. This book is aimed at
researchers and graduate students interested in various aspects
of modern combinatorial theories.
Readership
Graduate students and research mathematicians interested in
various topics in combinatorics.
Table of Contents
V. V. Batyrev -- Lattice polytopes with a given h*-polynomial
A. Conca, S. Hosten, and R. R. Thomas -- Nice initial complexes
of some classical ideals
V. C. Quinonez -- Ratliff-Rush monomial ideals
P. Csorba and F. H. Lutz -- Graph coloring manifolds
D. I. Dais -- Geometric combinatorics in the study of compact
toric surfaces
D. I. Dais, M. Henk, and G. M. Ziegler -- On the existence of Crepant resolutions
of Gorenstein abelian quotient singularities in dimensions \geq 4
P. Fiebig -- Kazhdan-Lusztig combinatorics via sheaves on Bruhat
graphs
G. Floystad -- Cohen-Macaulay cell complexes
D. N. Kozlov -- Homology tests for graph colorings
P. McMullen -- Polyhedra and polytopes: Algebra and combinatorics
B. Nill -- Classification of pseudo-symmetric simplicial
reflexive polytopes
A. Paffenholz and A. Werner -- Constructions for 4-polytopes and
the cone of flag vectors
R. T. Zivaljevic -- Groupoids in combinatorics-Applications of a
theory of local symmetries
Graduate Studies in Mathematics, Volume: 79
2007; 268 pp; hardcover
ISBN-10: 0-8218-3960-8
ISBN-13: 978-0-8218-3960-7
Expected publication date is March 23, 2007.
This marvellous and highly original book fills a significant gap
in the extensive literature on classical modular forms. This is
not just yet another introductory text to this theory, though it
could certainly be used as such in conjunction with more
traditional treatments. Its novelty lies in its computational
emphasis throughout: Stein not only defines what modular forms
are, but shows in illuminating detail how one can compute
everything about them in practice. This is illustrated throughout
the book with examples from his own (entirely free) software
package SAGE, which really bring the subject to life while not
detracting in any way from its theoretical beauty. The author is
the leading expert in computations with modular forms, and what
he says on this subject is all tried and tested and based on his
extensive experience. As well as being an invaluable companion to
those learning the theory in a more traditional way, this book
will be a great help to those who wish to use modular forms in
applications, such as in the explicit solution of Diophantine
equations. There is also a useful Appendix by Gunnells on
extensions to more general modular forms, which has enough in it
to inspire many PhD theses for years to come. While the book's
main readership will be graduate students in number theory, it
will also be accessible to advanced undergraduates and useful to
both specialists and non-specialists in number theory.
--John E. Cremona, University of Nottingham
William Stein is an associate professor of mathematics at the
University of Washington at Seattle. He earned a PhD in
mathematics from UC Berkeley and has held positions at Harvard
University and UC San Diego. His current research interests lie
in modular forms, elliptic curves, and computational mathematics.
Readership
Graduate students and research mathematicians interested in
modular forms.
Table of Contents
Modular forms
Modular forms of level 1
Modular forms of weight 2
Dirichlet characters
Eisenstein series and Bernoulli numbers
Dimension formulas
Linear algebra
General modular symbols
Computing with newforms
Computing periods
Solutions to selected exercises
Appendix A: Computing in higher rank
Bibliography
Index
Graduate Studies in Mathematics, Volume: 81
2007; approx. 424 pp; hardcover
ISBN-10: 0-8218-3812-1
ISBN-13: 978-0-8218-3812-9
Expected publication date is March 28, 2007.
The book is a continuation of the previous book by the author (Elements
of Combinatorial and Differential Topology, Graduate Studies in
Mathematics, Volume 74, American Mathematical Society, 2006). It
starts with the definition of simplicial homology and cohomology,
with many examples and applications. Then the Kolmogorov-Alexander
multiplication in cohomology is introduced. A significant part of
the book is devoted to applications of simplicial homology and
cohomology to obstruction theory, in particular, to
characteristic classes of vector bundles. The later chapters are
concerned with singular homology and cohomology, and Cech and de
Rham cohomology. The book ends with various applications of
homology to the topology of manifolds, some of which might be of
interest to experts in the area.
The book contains many problems; almost all of them are provided
with hints or complete solutions.
Readership
Graduate students interested in algebraic topology.
Table of Contents
Simplicial homology
Cohomology rings
Applications of simplicial homology
Singular homology
Cech cohomology and de Rham cohomology
Miscellaneous
Hints and solutions
Bibliography
Index
Mathematical Surveys and Monographs, Volume: 134
2007; 528 pp; hardcover
ISBN-10: 0-8218-4242-0
ISBN-13: 978-0-8218-4242-3
Expected publication date is March 17, 2007.
The theory of crossed products is extremely rich and intriguing. There
are applications not only to operator algebras, but to subjects as varied
as noncommutative geometry and mathematical physics. This book provides
a detailed introduction to this vast subject suitable for graduate students
and others whose research has contact with crossed product C^*-algebras.
In addition to providing the basic definitions and results, the main focus
of this book is the fine ideal structure of crossed products as revealed
by the study of induced representations via the Green-Mackey-Rieffel machine.
In particular, there is an in-depth analysis of the imprimitivity theorems
on which Rieffel's theory of induced representations and Morita equivalence
of C^*-algebras are based. There is also a detailed treatment of the generalized
Effros-Hahn conjecture and its proof due to Gootman, Rosenberg, and Sauvageot.
This book is meant to be self-contained and accessible to any
graduate student coming out of a first course on operator
algebras. There are appendices that deal with ancillary subjects,
which while not central to the subject, are nevertheless crucial
for a complete understanding of the material. Some of the
appendices will be of independent interest.
To view another book by this author, please visit Morita Equivalence and Continuous-Trace C*-Algebras.
Readership
Graduate students and research mathematicians interested in C*-algebras.
Table of Contents
Locally compact groups
Dynamical systems and crossed products
Special cases and basic constructions
Imprimitivity theorems
Induced representations and induced ideals
Orbits and quasi-orbits
Properties of crossed products
Ideal structure
The proof of the Gootman-Rosenberg-Sauvageot theorem
Amenable groups
The Banach *-algebra L^1(G,A)
Bundles of C*-algebras
Groups
Representations of C*-algebras
Direct integrals
Effros's ideal center decomposition
The Fell topology
Miscellany
Notation and Symbol Index
Index
Bibliography
Contemporary Mathematics, Volume: 424
2007; approx. 342 pp; softcover
ISBN-10: 0-8218-4060-6
ISBN-13: 978-0-8218-4060-3
Expected publication date is April 12, 2007.
The papers in this volume are based on talks given at the
International Conference on Analysis and Geometry in honor of the
75th birthday of Yurii Reshetnyak (Novosibirsk, 2004). The topics
include geometry of spaces with bounded curvature in the sense of
Alexandrov, quasiconformal mappings and mappings with bounded
distortion (quasiregular mappings), nonlinear potential theory,
Sobolev spaces, spaces with fractional and generalized
smoothness, variational problems, and other modern trends in
these areas. Most articles are related to Reshetnyak's original
works and demonstrate the vitality of his fundamental
contribution in some important fields of mathematics such as the
geometry in the "large", quasiconformal analysis,
Sobolev spaces, potential theory and variational calculus.
Readership
Graduate students and research mathematicians interested in
relations between analysis and differential geometry.
Table of Contents
I. D. Berg and I. G. Nikolaev -- On an extremal property of quadrilaterals
in an Aleksandrov space of curvature \leq K
V. I. Burenkov, H. V. Guliyev, and V. S. Guliyev -- On
boundedness of the fractional maximal operator from complementary
Morrey-type spaces to Morrey-type spaces
V. N. Dubinin and D. B. Karp -- Generalized condensers and
distortion theorems for conformal mappings of planar domains
M. L. Goldman -- Rearrangement invariant envelopes of generalized
Besov, Sobolev, and Calderon spaces
T. Iwaniec -- Null Lagrangians, the art of integration by parts
M. Karmanova -- Geometric measure theory formulas on rectifiable
metric spaces
A. P. Kopylov -- Stability and regularity of solutions to
elliptic systems of partial differential equations
V. M. Miklyukov -- Removable singularities of differential forms and A-solutions
H. Murakami -- Various generalizations of the volume conjecture
P. Pedregal -- Gradient Young measures and applications to
optimal design
H. M. Riemann -- Wavelets for the cochlea
Y. G. Reshetnyak -- Sobolev-type classes of mappings with values
in metric spaces
L. Szekelyhidi, Jr. -- Counterexamples to elliptic regularity and
convex integration
S. K. Vodopyanov -- Geometry of Carnot-Caratheodory spaces and
differentiability of mappings
S. K. Vodopyanov -- Foundations of the theory of mappings with
bounded distortion on Carnot groups