Expected publication date is December 7,
2003
Description
This fifth volume of Research In Collegiate
Mathematics Education
(RCME) presents state-of-the-art research
on understanding,
teaching, and learning mathematics at the
post-secondary level.
The articles in RCME are peer-reviewed for
two major features: (1)
advancing our understanding of collegiate
mathematics education,
and (2) readability by a wide audience of
practicing
mathematicians interested in issues affecting
their own students.
This is not a collection of scholarly arcana,
but a compilation
of useful and informative research regarding
the ways our
students think about and learn mathematics.
The volume begins with a study from Mexico
of the cross-cutting
concept of variable followed by two studies
dealing with aspects
of calculus reform. The next study frames
its discussion of
students' conceptions of infinite sets using
the psychological
work of Efraim Fischbein on (mathematical)
intuition. This is
followed by two papers concerned with APOS
theory and other
frameworks regarding mathematical understanding.
The final study
provides some preliminary results on student
learning using
technology when lessons are delivered via
the Internet.
Whether specialists in education or mathematicians
interested in
finding out about the field, readers will
obtain new insights
about teaching and learning and will take
away ideas they can use.
Also available from the AMS are RCME IV ,
III , II , and I in the
series, CBMS (Conference Board of the Mathematical
Sciences)
Issues in Mathematics Education.
This series is published in cooperation with
the Mathematical
Association of America.
Contents
M. Trigueros and S. Ursini -- First-year
undergraduates'
difficulties in working with different uses
of variable
A. Herzig and D. T. Kung -- Cooperative learning
in calculus
reform: What have we learned?
C. Roddick -- Calculus reform and traditional
students' use of
calculus in an engineering mechanics course
P. Tsamir -- Primary intuitions and instruction:
The case of
actual infinity
K. Weller, J. M. Clark, E. Dubinsky, S. Loch,
M. A. McDonald, and
R. R. Merkovsky -- Student performance and
attitudes in courses
based on APOS theory and the ACE teaching
cycle
D. E. Meel -- Models and theories of mathematical
understanding:
Comparing Pirie and Kieren's model of the
growth of mathematical
understanding and APOS theory
J. Bookman and D. Malone -- The nature of
learning in interactive
technological environments: A proposal for
a research agenda
based on grounded theory
Details:
Series: CBMS Issues in Mathematics Education,Volume:
12
Publication Year: 2003
ISBN: 0-8218-3302-2
Paging: 206 pp.
Binding: Softcover
Expected publication date is December 4,
2003
Description
Vertex operator algebras are a class of algebras
underlying a
number of recent constructions, results,
and themes in
mathematics. These algebras can be understood
as "string-theoretic
analogues" of Lie algebras and of commutative
associative
algebras. They play fundamental roles in
some of the most active
research areas in mathematics and physics.
Much recent progress
in both physics and mathematics has benefited
from cross-pollination
between the physical and mathematical points
of view.
This book presents the proceedings from the
workshop, "Vertex
Operator Algebras in Mathematics and Physics",
held at The
Fields Institute. It consists of papers based
on many of the
talks given at the conference by leading
experts in the
algebraic, geometric, and physical aspects
of vertex operator
algebra theory.
The book is suitable for graduate students
and research
mathematicians interested in the major themes
and important
developments on the frontier of research
in vertex operator
algebra theory and its applications in mathematics
and physics.
Contents
T. Abe and K. Nagatomo -- Finiteness of conformal
blocks over the
projective line
P. Bantay -- Permutation orbifolds and their
applications
J. Fuchs and C. Schweigert -- Category theory
for conformal
boundary conditions
R. L. Griess, Jr. -- GNAVOA, I. Studies in
groups, nonassociative
algebras and vertex operator algebras
G. Hohn -- Genera of vertex operator algebras
and three-dimensional
topological quantum field theories
Y.-Z. Huang -- Riemann surfaces with boundaries
and the theory of
vertex operator algebras
H. Li -- Vertex (operator) algebras are "algebras"
of
vertex operators
A. Milas -- Correlation functions, differential
operators and
vertex operator algebras
M. Primc -- Relations for annihilating fields
of standard modules
for affine Lie algebras
A. Recknagel -- From branes to boundary conformal
field theory:
Draft of a dictionary
V. Schomerus -- Open strings and non-commutative
geometry
C. Schweigert and J. Fuchs -- The world sheet
revisited
Details:
Series: Fields Institute Communications,
Volume: 39
Publication Year: 2003
ISBN: 0-8218-2856-8
Paging: 249 pp.
Binding: Hardcover
Expected publication date is December 28,
2003
Description
Since 1961, the Georgia Topology Conference
has been held every
eight years to discuss the newest developments
in topology. The
goals of the conference are to disseminate
new and important
results and to encourage interaction among
topologists who are in
different stages of their careers. Invited
speakers are
encouraged to aim their talks to a broad
audience, and several
talks are organized to introduce graduate
students to topics of
current interest. Each conference results
in high-quality
surveys, new research, and lists of unsolved
problems, some of
which are then formally published. Continuing
in this 40-year
tradition, the AMS presents this volume of
articles and problem
lists from the 2001 conference. Topics covered
include symplectic
and contact topology, foliations and laminations,
and invariants
of manifolds and knots.
Articles of particular interest include John
Etnyre's, "Introductory
Lectures on Contact Geometry", which
is a beautiful
expository paper that explains the background
and setting for
many of the other papers. This is an excellent
introduction to
the subject for graduate students in neighboring
fields. Etnyre
and Lenhard Ng's, "Problems in Low-Dimensional
Contact
Topology" and Danny Calegari's extensive
paper,"Problems
in Foliations and Laminations of 3-Manifolds"
are carefully
selected problems in keeping with the tradition
of the conference.
They were compiled by Etnyre and Ng and by
Calegari with the
input of many who were present. This book
provides material of
current interest to graduate students and
research mathematicians
interested in the geometry and topology of
manifolds.
Contents
J. Roberts -- Rozansky-Witten theory
C. Connell and B. Farb -- Some recent applications
of the
barycenter method in geometry
S. Bigelow -- The Lawrence-Krammer representation
W. H. Meeks III -- Topological properties
of properly embedded minimal surfaces in
mathbb{R}^3
J. B. Etnyre -- Introductory lectures on
contact geometry
V. Colin, E. Giroux, and K. Honda -- On the
coarse classification
of tight contact structures
P. Ghiggini and S. Schonenberger -- On the
classification of
tight contact structures
M. Symington -- Four dimensions from two
in symplectic topology
H. U. Boden, C. M. Herald, and P. Kirk --
On the integer valued
SU(3) Casson invariant
P. M. N. Feehan and T. G. Leness -- On Donaldson
and Seiberg-Witten
invariants
J. S. Carter and M. Saito -- Quandle homology
theory and cocycle
knot invariants
T. Li -- Boundary train tracks of laminar
branched surfaces
S. Schleimer -- Strongly irreducible surface
automorphisms
D. Calegari -- Problems in foliations and
laminations of 3-manifolds
J. B. Etnyre and L. L. Ng -- Problems in
low dimensional contact
topology
Details:
Series: Proceedings of Symposia in Pure Mathematics,
Volume: 71
Publication Year: 2003
ISBN: 0-8218-3507-6
Paging: approximately 368 pp.
Binding: Hardcover
Expected publication date is December 24,
2003
Description
The last twenty years have seen an active
interaction between mathematics and physics.
This book is devoted to one of the new areas
which deals with mathematical structures
related to conformal field theory and its
q-deformations. In the book, the author discusses
the interplay between Knizhnik-Zamolodchikov
type equations, the Bethe ansatz method,
representation theory, and geometry of multi-dimensional
hypergeometric functions.
This book aims to provide an introduction
to the area and expose different facets of
the subject. It contains constructions, discussions
of notions, statements of main results, and
illustrative examples. The exposition is
restricted to the simplest case of the theory
associated with the Lie algebra sl_2.
This book is intended for researchers and
graduate students in
mathematics and in mathematical physics,
in particular to those
interested in applications of special functions.
Contents
Hypergeometric solutions of KZ equations
Cycles of integrals and the monodromy of
the KZ equation
Selberg integral, determinant formulas, and
dynamical equations
Critical points of master functions and the
Bethe ansatz
Elliptic hypergeometric functions
q-hypergeometric solutions of qKZ equations
Bibliography
Index
Details:
Series: CBMS Regional Conference Series in
Mathematics, Number:
98
Publication Year: 2003
ISBN: 0-8218-2867-3
Paging: approximately 124 pp.
Binding: Softcover
Expected publication date is December 25,
2003
Description
The theory of symmetric functions is an old
topic in mathematics which is used as an
algebraic tool in many classical fields.
With lambda-rings, one can regard symmetric
functions as operators on polynomials and
reduce the theory to just a handful of fundamental
formulas.
One of the main goals of the book is to describe
the technique of lambda-rings. The main applications
of this technique to the theory of symmetric
functions are related to the Euclid algorithm
and its occurrence in division, continued
fractions, Pade approximants, and orthogonal
polynomials.
Putting the emphasis on the symmetric group
instead of symmetric
functions, one can extend the theory to non-symmetric
polynomials, with Schur functions being replaced
by Schubert
polynomials. In two independent chapters,
the author describes
the main properties of these polynomials,
following either the
approach of Newton and interpolation methods
or the method of
Cauchy.
The last chapter sketches a non-commutative
version of symmetric
functions, using Young tableaux and the plactic
monoid.
The book contains numerous exercises clarifying
and extending
many points of the main text. It will make
an excellent
supplementary text for a graduate course
in combinatorics.
Contents
Symmetric functions
Symmetric functions as operators and lambda-rings
Euclidean division
Reciprocal differences and continued fractions
Division, encore
Pade approximants
Symmetrizing operators
Orthogonal polynomials
Schubert polynomials
The ring of polynomials as a module over
symmetric ones
The plactic algebra
Complements
Solutions of exercises
Bibliography
Index
Details:
Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: CBMS Regional Conference Series in
Mathematics, ISSN:
0160-7642
Number: 99
Publication Year: 2003
ISBN: 0-8218-2871-1
Paging: approximately 272 pp.
Binding: Softcover