Expected publication date is June 16, 2005
Description
Have you ever wondered ... why elections often produce results
that seem to be displeasing to many of the voters involved? Would
you be surprised to learn that a perfectly fair election can
produce an outcome that literally nobody likes? When voting, we
often think about the candidates or proposals in the election,
but we rarely consider the procedures that we use to express our
preferences and arrive at a collective decision.
The Mathematics of Voting and Elections: A Hands-On Approach will
help you discover answers to these and many other questions.
Easily accessible to anyone interested in the subject, the book
requires virtually no prior mathematical experience beyond basic
arithmetic, and includes numerous examples and discussions
regarding actual elections from politics and popular culture. It
is recommended for researchers and advanced undergraduates
interested in all areas of mathematics and is ideal for
independent study.
Contents
What's so good about majority rule?
Perot, Nader, and other inconveniences
Back into the ring
Trouble in democracy
Explaining the impossible
One person, one vote?
Calculating corruption
The ultimate college experience
Trouble in direct democracy
Proportional (mis)representation
Bibliography
Index
Details:
Series: Mathematical World, Volume: 22
Publication Year: 2005
ISBN: 0-8218-3798-2
Paging: approximately 240 pp.
Binding: Softcover
Expected publication date is June 12, 2005
Description
Recent developments in geometric measure theory and harmonic
analysis have led to new and deep results concerning the
regularity of the support of measures which behave "asymptotically"
(for balls of small radius) as the Euclidean volume. A striking
feature of these results is that they actually characterize
flatness of the support in terms of the asymptotic behavior of
the measure. Such characterizations have led to important new
progress in the study of harmonic measure for non-smooth domains.
This volume provides an up-to-date overview and an introduction
to the research literature in this area. The presentation follows
a series of five lectures given by Carlos Kenig at the 2000
Arkansas Spring Lecture Series. The original lectures have been
expanded and updated to reflect the rapid progress in this field.
A chapter on the planar case has been added to provide a
historical perspective.
Additional background has been included to make the material
accessible to advanced graduate students and researchers in
harmonic analysis and geometric measure theory.
Contents
Introduction
Motivation and statement of the main results
The relation between potential theory and geometry for planar
domains
Preliminary results in potential theory
Reifenberg flat and chord arc domains
Further results on Reifenberg flat and chord arc domains
From the geometry of a domain to its potential theory
From potential theory to the geometry of a domain
Higher codimension and further regularity results
Bibliography
Details:
Series: University Lecture Series,Volume: 35
Publication Year: 2005
ISBN: 0-8218-2728-6
Paging: 155 pp.
Binding: Softcover
Expected publication date is June 5, 2005
Description
Graph algebras are a family of operator algebras which are
associated to directed graphs. These algebras have an attractive
structure theory in which algebraic properties of the algebra are
related to the behavior of paths in the underlying graph. In the
past few years there has been a great deal of activity in this
area, and graph algebras have cropped up in a surprising variety
of situations, including non-abelian duality, non-commutative
geometry, and the classification of simple C^*-algebras.
The first part of the book provides an introduction to the
subject suitable for students who have seen a first course on the
basics of C^*-algebras. In the second part, the author surveys
the literature on the structure theory of graph algebras,
highlights some applications of this theory, and discusses
several recent generalizations which seem particularly promising.
The volume is suitable for graduate students and research
mathematicians interested in graph theory and operator algebras.
Contents
Introduction
Directed graphs and Cuntz-Krieger families
Uniqueness theorems for graph algebras
Proofs of the uniqueness theorems
Simplicity and ideal structure
Arbitrary graphs
Applications to non-abelian duality
K-theory of graph algebras
Cuntz-Pimsner algebras
Topological graphs
Higher-rank graphs
Background material
Bibliography
Index
Details:
Series: CBMS Regional Conference Series in Mathematics, Number:
103
Publication Year: 2005
ISBN: 0-8218-3660-9
Paging: 113 pp.
Binding: Softcover
Expected publication date is June 11, 2005
Description
Written by well-known expert Donald Saari, this book is directed
toward readers who want to learn about the Newtonian N-body
problem. It is also intended for students and experts who are
interested in new expositions of past results in this area,
previously unpublished research conclusions, and new research
problems.
Professor Saari has written the book for a broad audience,
including readers with no previous knowledge about this
fascinating area. He begins each chapter with introductory
material motivated by unanswered research questions. He then
includes some history, discussions intended to develop intuition,
descriptions of open problems, and examples taken from real
problems in astronomy.
The first chapter starts with simple explanations of the apparent
"looping" orbit of Mars and the unexpected "Sunrise,
Sunset" behavior as viewed from Mercury and then leads up to
the unexplained and weird dynamics exhibited by Saturn's F-ring.
The second chapter, which introduces a way to decompose the
velocity of the system, is motivated by a seemingly easy but
unanswered conjecture involving the dynamics of the system when
the system's diameter is a constant. The third chapter, which
describes questions about the structure of the rings of Saturn,
introduces new and surprisingly simple ways to find
configurations of the particles that are "central" to
any discussion of the N-body problem. The fourth chapter analyzes
collisions, and the last chapter discusses the likelihood of
collisions and other events.
The book is suitable for graduate students and researchers
interested in celestial mechanics.
Contents
Introduction
Central configurations
Finding central configurations
Collisions-Both real and imaginary
How likely is it?
Bibliography
Index
Details:
Series: CBMS Regional Conference Series in Mathematics, Number:
104
Publication Year: 2005
ISBN: 0-8218-3250-6
Paging: 235 pp.
Binding: Softcover