Friedlander, Eric M.; Grayson, Daniel R. (Eds.)

Handbook of K-Theory

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

Eisenbud, David

The Geometry of Syzygies
A Second Course in Commutative Algebra and Algebraic Geometry

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

Chudinovich, Igor, Constanda, Christian

Variational and Potential Methods
for a Class of Linear Hyperbolic Evolutionary Processes

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.

Dekking, F.M., Kraaikamp, C., Lopuhaa, H.P., Meester, L.E.

A Modern Introduction to Probability and Statistics
Understanding Why and How

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.