Description
This is a true introduction to algebraic
geometry. The author
makes no assumption that readers know more
than can be expected
of a good undergraduate. He introduces fundamental
concepts in a
way that enables students to move on to a
more advanced book or
course that relies more heavily on commutative
algebra.
The language is purposefully kept on an elementary
level,
avoiding sheaf theory and cohomology theory.
The introduction of
new algebraic concepts is always motivated
by a discussion of the
corresponding geometric ideas. The main point
of the book is to
illustrate the interplay between abstract
theory and specific
examples. The book contains numerous problems
that illustrate the
general theory.
The text is suitable for advanced undergraduates
and beginning
graduate students. It contains sufficient
material for a one-semester
course. The reader should be familiar with
the basic concepts of
modern algebra. A course in one complex variable
would be
helpful, but is not necessary. It is also
an excellent text for
those working in neighboring fields (algebraic
topology, algebra,
Lie groups, etc.) who need to know the basics
of algebraic
geometry.
Contents
Introduction
Affine varieties
Projective varieties
Smooth points and dimension
Plane cubic curves
Cubic surfaces
Introduction to the theory of curves
Bibliography
Index
Details:
Series: Student Mathematical Library,Volume:
20
Publication Year: 2003
ISBN: 0-8218-2952-1
Paging: 213 pp.
Binding: Softcover
Expected publication date is March 29, 2003
Description
The collection consists of four papers in
different areas of
mathematical physics united by the intrinsic
coherence of the
asymptotic methods used. The papers describe
both the known
results and most recent achievements, as
well as new concepts and
ideas in mathematical analysis of quantum
and wave problems.
In the introductory paper "Quantization
and Intrinsic
Dynamics" a relationship between quantization
of symplectic
manifolds and nonlinear wave equations is
described and discussed
from the viewpoint of the weak asymptotics
method (asymptotics in
distributions) and the semiclassical approximation
method. It
also explains a hidden dynamic geometry that
arises when using
these methods.
Three other papers discuss applications of
asymptotic methods to
the construction of wave-type solutions of
nonlinear PDE's, to
the theory of semiclassical approximation
(in particular, the
Whitham method) for nonlinear second-order
ordinary differential
equations, and to the study of the Schrodinger
type equations
whose potential wells are sufficiently shallow
that the discrete
spectrum contains precisely one point.
All the papers contain detailed references
and are oriented not
only to specialists in asymptotic methods,
but also to a wider
audience of researchers and graduate students
working in partial
differential equations and mathematical physics.
Contents
M. Karasev -- Quantization and intrinsic
dynamics
V. G. Danilov, G. A. Omel'yanov, and V. M.
Shelkovich -- Weak
asymptotics method and interaction of nonlinear
waves
M. V. Karasev and A. V. Pereskokov -- Global
asymptotics and
quantization rules for nonlinear differential
equations
P. Zhevandrov and A. Merzon -- Asymptotics
of eigenfunctions in
shallow potential wells and related problems
Details:
Series: American Mathematical Society Translations--Series
2,Volume:
208
Publication Year: 2003
ISBN: 0-8218-3336-7
Paging: 284 pp.
Binding: Hardcover
Expected publication date is April 5, 2003
Description
The technique of diagrammatic morphisms is
an important
ingredient in comprehending and visualizing
certain types of
categories with structure. It was widely
used in this capacity in
many areas of algebra, low-dimensional topology
and physics. It
was also applied to problems in classical
and quantum information
processing and logic.
This volume contains articles based on talks
at the Special
Session, "Diagrammatic Morphisms in
Algebra, Category
Theory, and Topology", at the AMS Sectional
Meeting in San
Francisco. The articles describe recent achievements
in several
aspects of diagrammatic morphisms and their
applications. Some of
them contain detailed expositions on various
diagrammatic
techniques. The introductory article by D.
Yetter is a thorough
account of the subject in a historical perspective.
Contents
D. N. Yetter -- Diagrammatic morphisms
J. C. Baez -- Spin foam perturbation theory
J. W. Barrett -- Unlinked embedded graphs
Y. Bespalov and B. Drabant -- Report on cross
product bialgebras
in braided categories
J. S. Carter, S. Kamada, and M. Saito --
Diagrammatic
computations for quandles and cocycle knot
invariants
B. Day and R. Street -- Lax monoids, pseudo-operads,
and
convolution
M. D urd evich -- Diagrammatic formulation
of multi-braided
quantum groups
C. Frohman and J. Kania-Bartoszynska -- A
matrix model for
quantum SL_2
L. H. Kauffman and D. Radford -- Bi-oriented
quantum algebras,
and a generalized Alexander polynomial for
virtual links
T. Kerler -- Towards an algebraic characterization
of 3-dimensional
cobordisms
Z. Oziewicz -- Operad of graphs, convolution
and quasi Hopf
algebra
J. H. Przytycki and A. S. Sikora -- SU_n-quantum
invariants for
periodic links
R. Street -- Weak omega-categories
Details:
Series: Contemporary Mathematics, Volume:
318
Publication Year: 2003
ISBN: 0-8218-2794-4
Paging: 218 pp.
Binding: Softcover
Expected publication date is April 27, 2003
Description
This volume contains the proceedings of the
conference on
harmonic analysis and related areas. The
conference provided an
opportunity for researchers and students
to exchange ideas and
report on progress in this large and central
field of modern
mathematics.
The volume is suitable for graduate students
and research
mathematicians interested in harmonic analysis
and related areas.
Contents
A. Alfonseca, F. Soria, and A. Vargas --
An almost-orthogonality
principle in L^2 for directional maximal
functions
J.-G. Bak and D. M. Oberlin -- A note on
Fourier restriction for
curves in {mathbb R}^3
Z. M. Balogh and J. T. Tyson -- Potential
theory in Carnot groups
M. Bownik -- Quasi-affine systems and the
Calderon condition
L. Capogna and Q. Han -- Pointwise Schauder
estimates for second
order linear equations in Carnot groups
A. Carbery -- A remark on an inequality of
Katz and Tao
M. Christ -- Slow off-diagonal decay for
Szego kernels associated
to smooth Hermitian line bundles
A. Comech -- Type conditions and Lsp p-Lsp
p, Lsp p-Lsp{p'}
regularity of Fourier integral operators
M. Cowling and H. M. Reimann -- Quasiconformal
mappings on Carnot
groups: Three examples
G. David -- Limits of Almgren quasiminimal
sets
G. Furioli, F. Planchon, and E. Terraneo
-- Unconditional well-posedness
for semilinear Schrodinger and wave equations
in {mathbf{H^s}}
G. Gigante and F. Soria -- A note on oscillatory
integrals and
Bessel functions
L. Grafakos and X. Li -- The bilinear multiplier
problem for the
disc
P. A. Hagelstein -- Long thoughts on a conjecture
of Fava, Gatto,
and Gutierrez
A. Iosevich and E. Sawyer -- Three problems
motivated by the
average decay of the Fourier transform
N. H. Katz -- A partial result on Lipschitz
differentiation
A. Koldobsky -- Sections of star bodies and
the Fourier transform
O. Kovrizhkin -- The uncertainty principle
for relatively dense
sets and lacunary spectra
J. Mateu, X. Tolsa, and J. Verdera -- On
the semiadditivity of
analytic capacity and planar Cantor sets
A. L. Mazzucato -- Decomposition of Besov-Morrey
spaces
A. R. Nahmod -- On Schrodinger and wave maps
C. Perez and R. H. Torres -- Sharp maximal
function estimates for
multilinear singular integrals
M. A. Pinsky -- Fejer asymptotics and the
Hilbert transform
A. Seeger, T. Tao, and J. Wright -- Pointwise
convergence of
lacunary spherical means
C. D. Sogge -- Global existence for nonlinear
wave equations with
multiple speeds
G. Staffilani -- KdV and almost conservation
laws
D. Tataru -- Null form estimates for second
order hyperbolic
operators with rough coefficients
M. E. Taylor -- Multi-dimensional Fejer kernel
asymptotics
J. A. Toth and S. Zelditch -- Norms of modes
and quasi-modes
revisited
W. Trebels and U. Westphal -- K-functionals
on L^1({mathbb R}^n)
related to the Laplacian
Details:
Series: Contemporary Mathematics,Volume:
320
Publication Year: 2003
ISBN: 0-8218-2903-3
Paging: approximately 488 pp.
Binding: Softcover
Also Available in Softcover GSM/56.S
Expected publication date is May 29, 2003
"Great book! The author's teaching experience
shows in every
chapter."
-- E. Zelmanov, University of California,
San Diego
"Vinberg has written an algebra book
that is excellent, both
as a classroom text or for self-study. It
starts with the most
basic concepts and builds in orderly fashion
to moderately
advanced topics ... Well motivated examples
help the student ...
to master the material thoroughly, and exercises
test one's
growing skill in addition to covering useful
auxiliary facts ...
years of teaching abstract algebra have enabled
Vinberg to say
the right thing at the right time."
-- Irving Kaplansky, MSRI
Description
This is a comprehensive textbook on modern
algebra written by an
internationally renowned specialist. It covers
material
traditionally found in advanced undergraduate
and basic graduate
courses and presents it in a lucid style.
The author includes
almost no technically difficult proofs, and
reflecting his point
of view on mathematics, he tries wherever
possible to replace
calculations and difficult deductions with
conceptual proofs and
to associate geometric images to algebraic
objects. The effort
spent on the part of students in absorbing
these ideas will pay
off when they turn to solving problems outside
of this textbook.
Another important feature is the presentation
of most topics on
several levels, allowing students to move
smoothly from initial
acquaintance with the subject to thorough
study and a deeper
understanding. Basic topics are included,
such as algebraic
structures, linear algebra, polynomials,
and groups, as well as
more advanced topics, such as affine and
projective spaces,
tensor algebra, Galois theory, Lie groups,
and associative
algebras and their representations. Some
applications of linear
algebra and group theory to physics are discussed.
The book is written with extreme care and
contains over 200
exercises and 70 figures. It is an ideal
textbook or suitable for
independent study for advanced undergraduates
and graduate
students.
Contents
Algebraic structures
Elements of linear algebra
Elements of polynomial algebra
Elements of group theory
Vector spaces
Linear operators
Affine and projective spaces
Tensor algebra
Commutative algebra
Groups
Linear representations and associative algebras
Lie groups
Answers to selected exercises
Bibliography
Index
Details:
Series: Graduate Studies in Mathematics,Volume:
56
Publication Year: 2003
ISBN: 0-8218-3318-9
Paging: approximately 528 pp.
Binding: Hardcover
ISBN: 0-8218-3413-4
Binding: Softcover