Series: Universitext
2006, XIV, 494 p., 52 illus., Softcover
ISBN: 3-540-35445-X
About this textbook
Just as in its 1st edition, this book starts with illustrations
of the ubiquitous character of optimization, and describes
numerical algorithms in a tutorial way. It covers fundamental
algorithms as well as more specialized and advanced topics for
unconstrained and constrained problems. Most of the algorithms
are explained in a detailed manner, allowing straightforward
implementation. Theoretical aspects of the approaches chosen are
also addressed with care, often using minimal assumptions.
This new edition contains computational exercises in the form of
case studies which help understanding optimization methods beyond
their theoretical, description, when coming to actual
implementation. Besides, the nonsmooth optimization part has been
substantially reorganized and expanded.
Table of contents
2006, VIII, 506 p., 15 illus., Hardcover
ISBN: 3-540-35479-4
About this book
This collection of surveys present an overview of recent
developments in Complex Geometry. Topics range from curve and
surface theory through special varieties in higher dimensions,
moduli theory, Kahler geometry, and group actions to Hodge theory
and characteristic p-geometry.
Written by established experts this book will be a must for
mathematicians working in Complex Geometry.
Keywords:
Characteristic p-geometry
Complex Geometry
Hodge Theory
Kahler Geometry
Moduli Spaces
Varieties in higher Diemsions
Table of contents
Series: Universitext
Volume package: Comprehensive Mathematics for Computer Scientists
2006, XIV, 388 p., 118 illus., Softcover
ISBN: 3-540-36873-6
About this textbook
This two-volume textbook Comprehensive Mathematics for Computer
Scientists is a self-contained comprehensive presentation of
mathematics including sets, numbers, graphs, algebra, logic,
grammars, machines, linear geometry, calculus, ODEs, and special
themes such as neural networks, Fourier theory, wavelets,
numerical issues, statistics, categories, and manifolds. The
concept framework is streamlined but defining and proving
virtually everything. The style implicitly follows the spirit of
recent topos-oriented theoretical computer science. Despite the
theoretical soundness, the material stresses a large number of
core computer science subjects, such as, for example, a
discussion of floating point arithmetic, Backus-Naur normal
forms, L-systems, Chomsky hierarchies, algorithms for data
encoding, e.g., the Reed-Solomon code. The numerous course
examples are motivated by computer science and bear a generic
scientific meaning.
For the second edition the entire text has been carefully reread,
and many examples have been added, as well as illustrations and
explications to statements and proofs which were exposed in a too
shorthand style. This makes the book more comfortable for
instructors as well as for students to handle.
Written for:
Students in Computer Science
Keywords:
Algebra
Formal Logic
Graphs
Linear Geometry
Mathematics for Computer Scientists
Sets Print version
Recommend to others
Table of contents
Series: Texts in Applied Mathematics , Vol. 37
2007, XVIII, 657 p., 135 illus., Hardcover
ISBN: 3-540-34658-9
About this textbook
Numerical mathematics is the branch of mathematics that proposes,
develops, analyzes and applies methods from scientific computing
to several fields including analysis, linear algebra, geometry,
approximation theory, functional equations, optimization and
differential equations. Other disciplines, such as physics, the
natural and biological sciences, engineering, and economics and
the financial sciences frequently give rise to problems that need
scientific computing for their solutions.
As such, numerical mathematics is the crossroad of several
disciplines of great relevance in modern applied sciences, and
can become a crucial tool for their qualitative and quantitative
analysis.
One of the purposes of this book is to provide the mathematical
foundations of numerical methods, to analyze their basic
theoretical properties (stability, accuracy, computational
complexity) and demonstrate their performances on examples and
counterexamples which outline their pros and cons. This is done
using the MATLAB software environment which is user-friendly and
widely adopted. Within any specific class of problems, the most
appropriate scientific computing algorithms are reviewed, their
theoretical analyses are carried out and the expected results are
verified on a MATLAB computer implementation. Every chapter is
supplied with examples, exercises and applications of the
discussed theory to the solution of real-life problems.
This book is addressed to senior undergraduate and graduate
students with particular focus on degree courses in Engineering,
Mathematics, Physics and Computer Sciences. The attention which
is paid to the applications and the related development of
software makes it valuable also for researchers and users of
scientific computing in a large variety of professional fields.
In this second edition, the readability of pictures, tables and
program headings have been improved. Several changes in the
chapters on iterative methods and on polynomial approximation
have also been added.
Table of contents
Series Preface.- Preface.- I Getting Started.- 1. Foundations of
Matrix Analysis.- 2 Principles of Numerical Mathematics.- II
Numerical Linear Algebra.- 3 Direct Methods for the Solution of
Linear Systems.- 4 Iterative Methods for Solving Linear Systems.-
5 Approximation of Eigenvalues and Eigenvectors.- III Around
Functions and Functionals.- 6 Rootfinding for Nonlinear Equations.-
7 Nonlinear Systems and Numerical Optimization.- 8 Polynomial
Interpolation.- 9 Numerical Integration.- IV Transforms,
Differentiation and Problem Discretization.- 10 Orthogonal
Polynomials in Approximation Theory.- 11 Numerical Solution of
Ordinary Differential Equations.- 12 Two-Point Boundary Value
Problems.- 13 Parabolic and Hyperbolic Initial Boundary Value
Problems.- References.- Index of MATLAB Programs.- Index.
Series: Statistics for Social Science and Behavorial Sciences
2007, Approx. 490 p., 5 illus., Hardcover
ISBN: 0-387-32917-X
About this book
We live in the information age. Statistical surveys are used
every day to determine or evaluate public policy and to make
important business decisions. Correct methods for computing the
precision of the survey data and for making inferences to the
target population are absolutely essential to sound decision
making. Now in its second edition, Introduction to Variance
Estimation has for more than twenty years provided the definitive
account of the theory and methods for correct precision
calculations and inference, including examples of modern, complex
surveys in which the methods have been used successfully.
The book provides instruction on the methods that are vital to
data-driven decision making in business, government, and academe.
It will appeal to survey statisticians and other scientists
engaged in the planning and conduct of survey research, and to
those analyzing survey data and charged with extracting
compelling information from such data. It will appeal to graduate
students and university faculty who are focused on the
development of new theory and methods and on the evaluation of
alternative methods. Software developers concerned with creating
the computer tools necessary to enable sound decision-making will
find it essential.
Prerequisites include knowledge of the theory and methods of
mathematical statistics and graduate coursework in survey
statistics. Practical experience with real surveys is a plus and
may be traded off against a portion of the requirement for
graduate coursework.
This second edition reflects shifts in the theory and practice of
sample surveys that have occurred since the content of the first
edition solidified in the early 1980fs. Additional replication
type methods appeared during this period and have featured
prominently in journal publications. Reflecting these
developments, the second edition now includes a new major chapter
on the bootstrap method of variance estimation. This edition also
includes extensive new material on Taylor series methods,
especially as they apply to newer methods of analysis such as
logistic regression or the generalized regression estimator. An
introductory section on survey weighting has been added. Sections
on Hadamard matrices and computer software have been
substantially scaled back. Fresh material on these topics is now
readily available on the Internet or from commercial sources.
Kirk Wolter is a Senior Fellow at NORC, Director of the Center
for Excellency in Survey Research, and Professor in the
Department of Statistics, University of Chicago. He is a Fellow
of the American Statistical Association and a Member of the
International Statistical Institute. He is a past president of
the International Association of Survey Statisticians and a past
chair of the Survey Research Methods Section of the American
Statistical Association. During the last 35 years, he has
participated in the planning, execution, and analysis of large-scale
complex surveys and has provided instruction in survey statistics
both in America and around the world.
Table of contents
Introduction.- The method of random groups.-Variance estimation
based on balanced half-samples.- The jackknife method.- The
bootstrap method.- Taylor series methods.- Generalized variance
functions.- Variance estimation for systematic sampling.-Summary
of methods for complex surveys.
2006. 618 Pages, Softcover
ISBN-10: 3-527-40527-5
ISBN-13: 978-3-527-40527-5 - Wiley-VCH, Berlin
Short description
This comprehensive textbook on the novel and growing field of
quantum computing introduces the readers to the fundamental
concepts of information theory and quantum entanglement. It then
moves on to the state of the art of implementations of quantum
computing and communication protocols.
From the contents
1. Classical Information Theory
- Classical Information Theory and Classical Error Correction (M.
Grassl)
- Computational Complexity (S.Mertens)
2. Foundations of Quantum Information Theory
- Discrete Quantum States versus Continuous Variables (J. Eisert)
- Approximate Quantum Cloning (D. Bruss, C. Macchiavello)
- Channels and Maps (M. Keyl, R. Werner)
- Quantum Algorithms (J. Kempe)
- Quantum Error Correction (M. Grassl)
3. Theory of Entanglement
- The Seperability versus Eentanglement Problem (A. Sen (De), U.
Sen, M. Lewenstein, A. Sanpera)
- Entanglement Theory with Continuous Vvariables (P. van Loock)
- Entanglement Measures (M. Plenio, S. Virmani)
- Purifiaction and Distillation (H.-J. Briegel, W. Durr)
- Bound Entanglement (P. Horodecki)
- Multi-Particle Entanglement (J. Eisert, D. Gross)
4. Quantum Communication
- Teleportation (L. C. Davila Romero, N. Korolkova)
- Quantum Communication Experiments with Discrete Variables (H.
Weinfurter)
- Continuous Variable Quantum Communication (U. L. Andersen, G.
Leuchs)
5. Quantum Computing: Concepts
- Requirements for a Quantum Computer (A. Ekert, A. Kay)
- Probabilitistic Quantum Cumputation and Linear Optical
Realization (N. Lutkenhaus)
- One-way Quantum Computation ( D. E. Browne, H.-J. Briegel)
- Holonomic Quantum Computing (A. C. M. Carollo, V. Vedral)
6. Quantum Computing: Implementations
- Quantum Computing with Cold Ions and Atoms: Theory (D. Jaksch,
J. J. Garca-Ripoll, J. I. Cirac, P. Zoller)
- Quantum Computing with Cold Ions and Atoms: Experiments with
Ion Traps (F. Schmidt-Kaler)
- Quantum Computing with Solid State Systems ( G. Burkart, D.
Loss)
- Quantum Computing Implemented via Optimal Control: Theory and
Application to Spin and Pseudo-Spin Systems (T. Schulte-Herbruggen,
A. K. Sporl, R. Marx, N. Khaneja, J. M. Myers, A. F. Fahmy, S. J.
Glaser)
7. Transfer of Quantum Information between Different Types of
Implementations
- Quantum Repeater (W. Dur, H.-J. Briegel, P. Zoller)
- Quantum Interface between Light and Atomic Ensembles (E. S.
Polzik, J. Fiurasek)
- Cavity Quantum Electrodynamics: Quantum Information Processing
with Atoms and Photons (J.-M. Raimond, G. Rempe)
- Quantum Electrodynamics of a Qubit (G. Alber, G. M.
Nikolopoulos)
8. Towards Quantum Technology Applications
- Quantum Interferometry (O. Gockl, U. L. Andersen, G. Leuchs)
- Quantum Imaging (C. Fabre, N. Treps)