Bonnans, J.F., Gilbert, J.C., Lemarechal, C., Sagastizabal, C.A.

Numerical Optimization, 2nd ed.
Theoretical and Practical Aspects

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


Catanese, F.; Esnault, H.; Huckleberry, A.T.; Hulek, K.; Peternell, T. (Eds.)

Global Aspects of Complex Geometry

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

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Mazzola, Guerino, Milmeister, Gerard, Weissmann, Jody

Comprehensive Mathematics for Computer Scientists 1, 2nd ed.
Sets and Numbers, Graphs and Algebra, Logic and Machines, Linear Geometry

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

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Quarteroni, Alfio M., Sacco, Riccardo, Saleri, Fausto

Numerical Mathematics, 2nd ed.

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.

Wolter, Kirk

Introduction to Variance Estimation, 2nd ed.

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 1980fs. 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.

Bruss, Dagmar / Leuchs, Gerd (eds.)

Lectures on Quantum Information

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)