2005, Approx. 1080 p., Hardcover
ISBN: 3-540-23019-X
Due: February 2005
About this book
This handbook presents the first compilation of techniques and
results across much of the present state of the art in K-theory.
Consisting of individual chapters, each an exposition of a
particular subfield or line of development related to K-theory,
written by an expert, it outlines fundamental ideas and
techniques of the past, fundamental open problems, and exciting
directions for future research. Much of the material presented
here appears for the first time in book form. The intent of each
chapter is present to the interested reader, be she an
established K-theorist or someone interested in obtaining an
overview of results, an exposition of both results and techniques
in the literature as well as challenges for the future. The book
should be especially useful for students and mathematicians
interested in pursuing further research in this rapidly expanding
field.
Table of contents
Witt groups, Deloopings in Algebraic K-theory, Bivariant K- and
cyclic theories, Motivic Complexes of Suslin and Voevodsky, Semi-topological
K-theory, Motivic cohomology, K-theory and topological cyclic
homology, K-theory and intersection theory, Regulators, The
motivic spectral sequence, K-theory of truncated polynomial
algebras, La conjecture de Milnor (d'apres V. Voevodsky),
Algebraic K-theory, algebraic cycles and arithmetic geometry,
Bott periodicity in topological, algebraic and Hermitian K-theory,
Mixed motives, The Baum-Connes and the Farrell-Jones Conjectures
in K- and L-theory, Equivariant K-theory, K(1)-local homotopy
theory, Iwasawa theory and algebraic K-theory, The K-theory of
Triangulated Categories, K-theory and geometric topology,
Comparison between algebraic and topological K-theory for Banach
algebras and C*-algebras, Algebraic K-theory of rings of integers
in local and global fields, Quadratic K-theory and Geometric
Topology
Series : Graduate Texts in Mathematics , Preliminary entry 229
2005, Approx. 245 p. 18 illus., Hardcover
ISBN: 0-387-22215-4
ISBN: 0-387-22232-4(soft cover)
Due: November 2004
About this textbook
Algebraic Geometry often seems very abstract, but in fact it is
full of concrete examples and problems. This side of the subject
can be approached through the equations of a variety, and the
syzygies of these equations are a necessary part of the study.
This book is the first textbook-level account of basic examples
and techniques in this area. It illustrates the use of syzygies
in many concrete geometric considerations, from interpolation to
the study of canonical curves. The text has served as a basis for
graduate courses by the author at Berkeley, Brandeis, and in
Paris. It is also suitable for self-study by a reader who knows a
little commutative algebra and algebraic geometry already. As an
aid to the reader, the appendices provide summaries of local
cohomology and commutative algebra, tying together examples and
major results from a wide range of topics.
Table of contents
Preface: Algebra and Geometry * Free Resolutions and Hilbert
Functions * First Examples of Free Resolutions * Points in P^2 *
Castelnuovo?Mumford Regularity * The Regularity of Projective
Curves * Linear Series and 1-Generic Matrices * Linear Complexes
and the Linear Syzygy Theorem * Curves of High Degree * Clifford
Index and Canonical Embedding * Appendix 1: Introduction to Local
Cohomology * Appendix 2: A Jog Through Commutative Algebra *
References * Index
Series : Springer Monographs in Mathematics
2005, Approx. 160 p., Hardcover
ISBN: 1-85233-888-1
Due: January 2005
About this book
The book presents variational methods combined with boundary
integral equation techniques in application to a model of dynamic
bending of plates with transverse shear deformation. The emphasis
is on the rigorous mathematical investigation of the model, which
covers a complete study of the well-posedness of a number of
initial-boundary value problems, their reduction to time-dependent
boundary integral equations by means of suitable potential
representations, and the solution of the latter in Sobolev spaces.
The analysis, performed in spaces of distributions, is applicable
to a wide variety of data with less smoothness than that required
in the corresponding classical problems, and is very useful for
constructing error estimates in numerical computations. This
illustrative model was chosen because of its practical importance
and some unusual mathematical features, but the solution
technique can easily be adapted to many other hyperbolic systems
of partial differential equations arising in continuum mechanics.
Table of contents
Formulation of the Problems and their Nonstationary Boundary
Integral Equations.- Problems with Dirichlet Boundary Conditions.-
Problems with Neumann Boundary Conditions.- Boundary Integral
Equations for Problems with Dirichlet and Neumann Boundary
Conditions.- Transmission Problems and Multiply Connected Plates.-
Plate Weakened by a Crack.- Initial-Boundary Value Problems with
Other Types of Boundary Conditions.- Plate on a Generalized
Elastic Foundation.- Problems with Nonhomogeneous Equations and
Nonhomogeneous Initial Conditions.- Appendix A: The Fourier and
Laplace Transforms of Distributions.- References.- Index.
Series : Springer Texts in Statistics
2005, Approx. 500 p. 120 illus., Hardcover
ISBN: 1-85233-896-2
Due: January 2005
About this textbook
Probability and Statistics are studied by most science students.
Many current texts in the area are just cookbooks and, as a
result, students do not know why they perform the methods they
are taught, or why the methods work. The strength of this book is
that it readdresses these shortcomings; by using examples, often
from real-life and using real data, the authors show how the
fundamentals of probabilistic and statistical theories arise
intuitively. A Modern Introduction to Probability and Statistics
has numerous quick exercises to give direct feedback to students.
In addition there are over 350 exercises, half of which have
answers, of which half have full solutions. A website gives
access to the data files used in the text, and, for instructors,
the remaining solutions. The only pre-requisite is a first course
in calculus; the text covers standard statistics and probability
material, and develops beyond traditional parametric models to
the Poisson process, and on to modern methods such as the
bootstrap.
Table of contents
Why Probability and Statistics?- Outcomes, Events and Probability.-
Conditional Probability and Independence.- Discrete Random
Variables.- Continuous Random Variables.- Simulation.-
Expectation and Variance.- Computations with Random Variables.-
Joint Distributions and Independence.- Covariance and Correlation.-
More Computations with More Random Variables.- The Poisson
Process.- The Law of Large Numbers.- The Central Limit Theorem.-
Exploratory Data Analysis: Graphical Summaries.- Exploratory Data
Analysis: Numerical Summaries.- Basic Statistical Models.- The
Bootstrap.- Unbiased Estimators.- Efficiency and Mean Squared
Error.- Maximum Likelihood.- The Method of Least Squares.-
Confidence Intervals for the Mean.- More on Confidence Intervals.-
Testing Hypotheses: Essentials.- Testing Hypotheses: Elaboration.-
The t-test.- Comparing Two Samples.- Datasets.- Appendix A:
Answers to Selected Exercises.- Appendix B: Solutions to Selected
Exercises.- References.- Index.