Expected publication date is October 10,
2002
Description
The classification of finite simple groups
is a landmark result
of modern mathematics. The original proof
is spread over scores
of articles by dozens of researchers. In
this multivolume book,
the authors are assembling the proof with
explanations and
references. It is a monumental task. The
book, along with
background from sections of the previous
volumes, presents
critical aspects of the classification.
In four prior volumes (Surveys of Mathematical
Monographs,
Volumes 40.1, 40.2, 40.3, and 40.4), the
authors began the proof
of the classification theorem by establishing
certain uniqueness
and preuniqueness results. In this volume,
they now begin the
proof of a major theorem from the classification
grid, namely
Theorem {mathcal C}_7.
The book is suitable for graduate students
and researchers
interested in group theory.
Contents
Theorem C_7: General introduction
General group-theoretic results
Theorem C^*_7: Stage 1
Theorem C^*_7: Stage 2
Theorem C^*_7: Stage 3a
Properties of K-groups
Background references
Expository references
Glossary of symbols and terms
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Mathematical Surveys and Monographs,Volume:
40
Publication Year: 2002
ISBN: 0-8218-2776-6
Paging: 467 pp.
Binding: Hardcover
Description
The theory of graph coloring has existed
for more than 150 years.
Historically, graph coloring involved finding
the minimum number
of colors to be assigned to the vertices
so that adjacent
vertices would have different colors. From
this modest beginning,
the theory has become central in discrete
mathematics with many
contemporary generalizations and applications.
Generalization of graph coloring-type problems
to mixed
hypergraphs brings many new dimensions to
the theory of colorings.
A main feature of this book is that in the
case of hypergraphs,
there exist problems on both the minimum
and the maximum number
of colors. This feature pervades the theory,
methods, algorithms,
and applications of mixed hypergraph coloring.
The book has broad appeal. It will be of
interest to both pure
and applied mathematicians, particularly
those in the areas of
discrete mathematics, combinatorial optimization,
operations
research, computer science, software engineering,
molecular
biology, and related businesses and industries.
It also makes a
nice supplementary text for courses in graph
theory and discrete
mathematics. This is especially useful for
students in
combinatorics and optimization. Since the
area is new, students
will have the chance at this stage to obtain
results that may
become classic in the future.
Contents
Introduction
The lower chromatic number of a hypergraph
Mixed hypergraphs and the upper chromatic
number
Uncolorable mixed hypergraphs
Uniquely colorable mixed hypergraphs
mathcal{C}-perfect mixed hypergraphs
Gaps in the chromatic spectrum
Interval mixed hypergraphs
Pseudo-chordal mixed hypergraphs
Circular mixed hypergraphs
Planar mixed hypergraphs
Coloring block designs as mixed hypergraphs
Modelling with mixed hypergraphs
Bibliography
List of figures
Index
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Fields Institute Monographs, Volume:
17
Publication Year: 2002
ISBN: 0-8218-2812-6
Paging: 181 pp.
Binding: Hardcover
Expected publication date is September 18,
2002
Description
The variety of combinatorial properties of
nonnegative matrices
is widely discussed in the mathematical literature,
and there are
many papers on this topic. However, there
are few monographs
devoted to these properties of nonnegative
matrices. This book
fills that gap and presents a summary of
the existing material.
It provides a good entry point into the subject
and includes
exercises to aid students.
The authors focus on the relation of matrices
with nonnegative
elements to various mathematical structures
studied in
combinatorics. In addition to applications
in graph theory,
Markov chains, tournaments, and abstract
automata, the authors
consider relations between nonnegative matrices
and structures
such as coverings and minimal coverings of
sets by families of
subsets. They also give considerable attention
to the study of
various properties of matrices and to the
classes formed by
matrices with a given structure.
The authors discuss enumerative problems
using both combinatorial
and probabilistic methods. It also considers
extremal problems
related to matrices and problems where nonnegative
matrices
provide suitable investigative tools.
This book was developed for the most part
as a theoretical
research text, keeping in mind applications
of nonnegative
matrices. Among the applications, the most
significant included
are in the theory of Markov chains, in linear
programming for
constructing and analyzing economic models,
and in information
theory for designing reliable information
devices. The book is
suitable for specialists in these areas of
engineering and the
applied sciences.
The book contains some classical theorems
and a significant
number of results not previously published
in monograph form,
including results obtained by the authors
in the last few years.
It is appropriate for graduate students and
researchers
interested in combinatorics and its applications.
Contents
Matrices and Configurations
Ryser classes
Nonnegative matrices and extremal combinatorial
problems
Asymptotic methods in the study of nonnegative
matrices
Totally indecomposable, chainable, and prime
matrices
Sequences of nonnegative matrices
Bibliography
Index
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Translations of Mathematical Monographs,
Volume: 213
Publication Year: 2002
ISBN: 0-8218-2788-X
Paging: 269 pp.
Binding: Hardcover
Expected publication date is October 17,
2002
Description
An algebra A on a set X is a family of subsets
of this set closed
under the operations of union and difference
of two subsets. The
main topic of the book is the study of various
algebras and
families of algebras on an abstract set X.
The author shows how
this is related to famous problems by Lebesgue,
Banach, and Ulam
on the existence of certain measures on abstract
sets, with
corresponding algebras being algebras of
measurable subsets with
respect to these measures. In particular
it is shown that for a
certain algebra not to coincide with the
algebra of all subsets
of X is equivalent to the existence of a
nonmeasurable set with
respect to a given measure.
Although these questions don't seem to be
related to mathematical
logic, many results in this area were proved
by "metamathematical"
methods, using the method of forcing and
other tools related to
axiomatic set theory. However, in the present
book, the author
uses "elementary" (mainly combinatorial)
methods to
study properties of algebras on a set. Presenting
new and
original material, the book is written in
a clear and readable
style and illustrated by many examples and
figures.
The book will be useful to researchers and
graduate students
working in set theory, mathematical logic,
and combinatorics.
Contents
Introduction
Main results
The main idea
Finite sequences of algebras (1). Proof of
Theorems 2.1 and 2.2
Countable sequences of algebras (1). Proof
of Theorem 2.4
Proof of the Gitik-Shelah theorem, and more
from set theory
Proof of Theorems 1.17, 2.7, 2.8
Theorems on almost sigma-algebras. Proof
of Theorem 2.9
Finite sequences of algebras (2). The function
mathfrak{g}(n)
A description of the class of functions Psi_*^7
The general problem. Proof of Theorems 2.15
and 2.20
Proof of Theorems 2.21(1,3), 2.24
The inverse problem
Finite sequences of algebras (3). Proof of
Theorems 2.27, 2.31, 2.36,
2.38
Preliminary notions and lemmas
Finite sequences of algebras (4). Proof of
Theorems 2.39(1,2), 2.45(1,2)
Countable sequences of algebras (2). Proof
of Theorems 2.29, 2.32,
2.46
A refinement of theorems on sigma-algebras.
Proof of Theorems 2.34,
2.44
Semistructures and structures of sets. Proof
of Theorem 2.48
Final comments. Generalization of Theorem
2.1
Appendix: On a question of Grinblat by S.
Shelah
Bibliography
Index
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Translations of Mathematical Monographs,
Volume: 214
Publication Year: 2002
ISBN: 0-8218-2765-0
Paging: approximately 264 pp.
Binding: Hardcover
Description
This volume grew out of two AMS conferences held at Columbia
University (New York, NY) and the Stevens Institute of Technology
(Hoboken, NJ) and presents articles on a wide variety of topics
in group theory.
Readers will find a variety of contributions, including a
collection of over 170 open problems in combinatorial group
theory, three excellent survey papers (on boundaries of
hyperbolic groups, on fixed points of free group automorphisms,
and on groups of automorphisms of compact Riemann surfaces), and
several original research papers that represent the diversity of
current trends in combinatorial and geometric group theory.
The book is an excellent reference source for graduate students
and research mathematicians interested in various aspects of
group theory.
Contents
G. Baumslag, A. G. Myasnikov, and V. Shpilrain -- Open problems
in combinatorial group theory. Second edition
I. Kapovich and N. Benakli -- Boundaries of hyperbolic groups
P. Dehornoy -- Thin groups of fractions
A. M. Gaglione, D. Spellman, and B. Fine -- Every abelian group
universally equivalent to a discriminating group is elementarily
equivalent to a discriminating group
S. V. Ivanov -- Weakly finitely presented infinite periodic
groups
B. Khan -- Positively generated subgroups of free groups and the
Hanna Neumann conjecture
A. R. Magid -- On the proalgebraic completion of a finitely
generated group
A. D. Myasnikov, A. G. Myasnikov, and V. Shpilrain -- On the
Andrews-Curtis equivalence
C. F. Rocca, Jr. and E. C. Turner -- Test ranks of finitely
generated abelian groups
G. Rosenberger and M. Scheer -- Classification of the finite
generalized tetrahedron groups
E. Ventura -- Fixed subgroups in free groups: A survey
A. Weaver -- Automorphisms of surfaces
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: Contemporary Mathematics, Volume: 296
Publication Year: 2002
ISBN: 0-8218-2822-3
Paging: 275 pp.
Binding: Softcover