24 x 17 cm. XI, 317 pages. Cloth.
ISBN 3-11-018341-2
Series: de Gruyter Series in Logic and Its Applications 7
Subjects: Mathematics / Basics of Logic, Set Theory
Social Sciences, Economics / Computer Science / Introduction,
Theory
Language: English
to be published November 2004
In this volume the author develops and applies methods for
proving, from large cardinals, the determinacy of definable games
of countable length on natural numbers. The determinacy is
ultimately derived from iteration strategies, connecting games on
natural numbers with the specific iteration games that come up in
the study of large cardinals.
The games considered in this text range in strength, from games
of fixed countable length, through games where the length is
clocked by natural numbers, to games in which a run is complete
when its length is uncountable in an inner model (or a pointclass)
relative to the run. More can be done using the methods developed
here, reaching determinacy for games of length $\omega_1$.
The book is largely self-contained. Only graduate level knowledge
of modern techniques in large cardinals and basic forcing is
assumed. Several exercises allow the reader to build on the
results in the text, for example connecting them with universally
Baire and homogeneously Suslin sets. Overall it is intended that
the book should be accessible both to specialists and to advanced
graduate students in set theory.
- Important contribution to one of the main features of current
set theory, as initiated and developed by Jensen, Woodin, Steel
and others.
Zurich Lectures in Advanced Mathematics
ISBN 3-03719-006-X
October 2004, 100 pages, softcover, 17.0 cm x 24.0 cm.
Non-linear elliptic partial differential equations are an
important tool in the study of Riemannian metrics in differential
geometry, in particular for problems concerning the conformal
change of metrics in Riemannian geometry. In recent years the
role played by the second order semi-linear elliptic equations in
the study of Gaussian curvature and scalar curvature has been
extended to a family of fully non-linear elliptic equations
associated with other symmetric functions of the Ricci tensor. A
case of particular interest is the second symmetric function of
the Ricci tensor in dimension four closely related to the
Pfaffian.
In these lectures, starting from the background material, the
author reviews the problem of prescribing Gaussian curvature on
compact surfaces. She then develops the analytic tools (e.g.
higher order conformal invariant operators, Sobolev inequalities,
blow-up analysis) in order to solve a fully nonlinear equation in
prescribing the Chern-Gauss-Bonnet integrand on compact manifolds
of dimension four.
ISBN: 0-471-66983-0
Hardcover
480 pages
January 2005
Description
The second edition of Matrix Analysis for Statistics provides in-depth,
step-by-step coverage of the most common matrix methods now used
in statistical applications, including eigenvalues and
eigenvectors; the Moore-Penrose inverse; matrix differentiation;
the distribution of quadratic forms; and more. The subject matter
is presented in a theorem/proof format, and every effort has been
made to ease the transition from one topic to another. Proofs are
easy to follow, and the author carefully justifies every step.
Accessible even for readers with a cursory background in
statistics, the text uses examples that are familiar and easy to
understand. Key features that make this the ideal introduction to
matrix analysis theory and practice include: self-contained
chapters for flexibility in topic choice, extensive examples and
chapter-end practice exercises, and optional sections for
mathematically advanced readers.
Table of Contents
Preface.
1. A Review of Elementary Matrix Algebra.
2. Vector Spaces.
3. Eigenvalues and Eigenvectors.
4. Matrix Factorizations and Martrix Norms.
5. Generalized Inverses.
6. Systems of Linear Equations.
7. Partitioned Matrices.
8. Special Matrices and Matrix Operations.
9. Matrix Derivatives and Related Topics.
10. Some Special Topics Related to Quadratic Forms.
References.
Index.
ISBN: 0-471-66379-4
Hardcover
336 pages
January 2005
Description
Now in its third edition, this popular book is a concise,
accessible guide to the methods of applied linear regression.
Focusing on model building, assessing fit and reliability, and
drawing conclusions, it develops estimation, confidence, and
testing procedures mostly using least squares. Throughout, the
importance of assumptions and their relevance in specific
problems is stressed. Updated to reflect enormous progress in the
area since the previous edition in 1985, the Third Edition
includes new problems, figures, and completely revised chapters
on multiple regression, diagnostics, and generalizations of
regression.
Table of Contents
Preface.
1. Scatterplots and Regression.
2. Simple Linear Regression.
3. Multiple Regression.
4. Drawing Conclusions.
5. Weights, Lack of Fit, and More.
6. Polynomials and Factors.
7. Transformations.
8. Regression Diagnostics: Residuals.
9. Outliers and Influence.
10. Variable Selection.
11. Nonlinear Regression.
12. Logistic Regression.
Appendix A.1. Web Site.
Appendix A.2. Means and Variances of Random Variables.
Appendix A.3. Least Squares for Simple Regression.
Appendix A.4. Means and Variances of Least Squares Estimates.
Appendix A.5. Estimating E(Y/X) Using a Smoother.
Appendix A.6. A Brief Introduction to Matrices and Vectors.
Appendix A.7. Random Vectors.
Appendix A.8. Least Squares Using Matrices.
Appendix A.9. The QR Factorization.
Appendix A.10. Maximum Likelihood Estimates.
Appendix A.11. The Box-Cox Method for Transformations.
Appendix A.12. Case Deletion in Linear Regression.
References.
ISBN: 0-471-71813-0
Hardcover
704 pages
March 2005
Description
Statistics for Experimenters: Design, Innovation and Discovery,
Second Edition focuses on applications in the physical,
engineering, biological, and social sciences.
Written with the non-mathematician in mind, only knowledge of
elementary mathematics is required for use. The book is based on
the scientific method and provides the tools needed for the
investigator to make the research as effective as possible
through proper choice and conduct of experiments and appropriate
analysis of data. After a problem is stated, appropriate
statistical methods of design and analysis are discussed.
The Second Edition is an ideal reference book for practicing
engineers, scientists, and statisticians in a broad range of
disciplines. It is also ideal as a textbook for courses in
experimental design at the upper-undergraduate and beginning-graduate
levels.
This fully revised industry standard features:
Reorganized sections, fully revised chapters, and updated
methodologies
New material including graphical analyses of variance, a new
classification for fractionals, transmission of error, components
of variance, split-plot designs, and discussions related to
Taguchi
A lucid introduction to the basic statistical methods needed for
research
Worked examples in the text with frequent exercises and answers,
and specific, thought-provoking questions at the end of each
chapter.
Advanced topics selected for their special interest to scientific
investigators are introduced in readily understood language.
These topics include time series analysis, response surface
methods, regression analysis, study of error transmission, and
mechanistic model building.
Table of Contents
1. Catalizing the Generation of Knowledge.
2. Basics: probability, Parameters and Statistics.
3. Comparing Two Entities: Relevant Reference Distributions,
Tests and Confidence Intervals.
4. Comparing a Number of Entities: Randomized Blocks and Latin
Squares.
5. Factorial Designs at Two Levels: Advantages of Experimental
Design.
6. Fraction Factorial Designs: Economy in Experimentation.
7. Other Fractionals, Analysis and Choosing Follow-up Runs.
8. Factorial Designs and Data Transformation.
9. Multiple Sources of Variation: Split Plot Designs, Variance
Components and Error Transmission.
10. Least Squares and Why You Need to Design Experiments.
11. Modelling Relationships, Sequential Assembly: Basics for
Response Surface Methods.
12. Some Applications of Response Surface Methods.
13. Designing Robust Products: An Introduction.
14. Process Control, Forecasting and Times Series: An
Introduction.
15. Evolutionary Process Operation.
Appendices.
Index.
ISBN: 0-471-27246-9
Hardcover
640 pages
March 2005
Description
This new Third Edition addresses the latest advances in discrete
distributions theory including the development of new
distributions such as q-series and generalized zeta-function
distributions and new families of distributions including
Langrangian-type distributions offering and a better
understanding of their theoretical and practical
interrelationships. New derivations of discrete distributions via
stochastic processes and random walks are introduced without
turning the book into a treatise on the subject. Emphasis on the
increasing relevance of Bayesian inference to discrete
distribution, especially with regard to the binomial and Poisson
distributions is maintained. All chapters have been updated to
make them user-friendly and coherent and extensive information on
the increased use of the computer has been added without changing
or compromising the mathematical integrity.
Table of Contents
1. Preliminary Information.
2. Families of Discrete Distributions.
3. Binomial Distributions.
4. Poisson Distributions.
5. Neggative Binomial Distributions.
6. Hypergeometric Distributions.
7. Logarithmic and Lagrangian Distributions.
8. Mixture Distributions.
9. Stopped-Sum Distributions.
10. Matching, Occupancy, Runs, and q-Series Distributions.
11. Parametric Regression Models and Miscellanea.