ISBN: 0-471-08601-0
Hardcover
304 Pages
January 2003
Table of Contents
Introduction.
Cannonballs and Tomatoes.
The Puzzle of the Dozen Spheres.
Parasols, Water Hydrants, and Soccer Players.
Thue's Two Attempts and Fejes-Toth's Achievement.
Twelve's Company, Thirteen's a Crowd.
Nets and Knots.
Twisted Boxes.
No Dancing at this Congress.
The Race for the Upper Bound.
Right Angles for round Spaces.
Wobbly Balls and Hybrid Stars.
Simplex, Cplex, and Symbolic Mathematics.
Bit Is It Really a Proof?
Beehives Again
This Is Not An Epilogue.
Mathematical Appendices.
Bibliography.
Index.
The fascinating story of a problem that perplexed mathematicians
for nearly 400 years
In 1611, Johannes Kepler proposed that the best way to pack
spheres as densely as possible was to pile them up in the same
way that grocers stack oranges or tomatoes. This proposition,
known as Kepler’s Conjecture, seemed obvious to everyone except
mathematicians, who seldom take anyone’s word for anything. In
the tradition of Fermat’s Enigma, George Szpiro shows how the
problem engaged and stymied many men of genius over the
centuries?Sir Walter Raleigh, astronomer Tycho Brahe, Sir Isaac
Newton, mathematicians C. F. Gauss and David Hilbert, and R.
Buckminster Fuller, to name a few?until Thomas Hales of the
University of Michigan submitted what seems to be a definitive
proof in 1998.
George G. Szpiro (Jerusalem, Israel) is a mathematician turned
journalist. He is currently the Israel correspondent for the
Swiss daily Neue Zurcher Zeitung.
ISBN: 0-471-36091-0
Hardcover
736 Pages
May 2003
Table of Contents
Chapter 1. Introduction.
Chapter 2. The Multivariate Normal Distribution.
Chapter 3. Estimation of the Mean Vector and the Covariance
Matrix.
Chapter 4. The Distributions and Uses of Sample Correlation
Coefficients.
Chapter 5. The Generalized T2-Statistic.
Chapter 6. Classification of Observations.
Chapter 7. The Distribution of the Sample Covariance Matrix and
the Sample Generalized Variance.
Chapter 8. Testing the General Linear Hypothesis: Multivariate
Analysis of Variance.
Chapter 9. Testing Independence of Sets of Variates.
Chapter 10. Testing Hypotheses of Equality of Covariance Matrices
and Equality of Mean Vectors and Covariance Matrices.
Chapter 11. Principal Components.
Chapter 12. Cononical Correlations and Cononical Variables.
Chapter 13. The Distributions of Characteristic Roots and Vectors.
Chapter 14. Factor Analysis.
Chapter 15. Pattern of Dependence; Graphical Models.
Appendix A: Matrix Theory.
References.
Index.
The Second Edition of An Introduction to Multivariate Statistical
Analysis has become a standard in the field. Since its
publication, several advances have been made in multivariate (MV)
statistical analysis. Maintaining the previous editions
mathematically rigorous development of statistical models, the
Third Edition substantially revises and adds to the original text
to bring statisticians up to date with recent developments in the
field.
ISBN: 0-471-41137-X
Hardcover
488 Pages
February 2003
Table of Contents
Preface.
Acknowledgements.
What is Statistics? How is it Applied in the Health Sciences?
Defining Populations and Selecting Samples.
Systematic Organization and Display of Data.
Summary Statistics.
Basic Probability.
The Normal Distribution.
Sampling Distribution for Means.
Estimating Population Means.
Tests of Hypotheses.
Inferences Regarding Proportions. Correlation, Simple Linear
Regression and Logistic Regression.
One Way Analysis of Variance.
Nonparametric Methods.
Analysis of Survival Times.
Software Packages.
Appendix A. Percentage Points, F-Distribution (α=0.05).
Appendix B. Studentized Range Statistics: Upper 5 Percent Points.
Appendix C. Quantiles of the Wilcoxon Signed Rank Test Statistic.
Appendix D. χ2 Distribution.
Appendix E. Table of Standard Normal Distribution.
Appendix F. Percentage Points, Student's t Distribution.
Appendix G. Answers to Selected Exercises.
Introductory Biostatistics for the Health Sciencesprovides a
basic but thorough introduction to biostatistics and its
applications. Stressing practical applications, the book
interweaves recent advances in the bootstrap, outliers, and meta-analysis
throughout the book in an effort to modernize the subject matter.
These are topics not typically covered in the competition.
Practical applications are stressed, along with the necessary
theory to accompany them, in view of the fact that both an
academician and an industrialist have combined their talents and
know-how.
ISBN: 0-471-23222-X
Hardcover
776 Pages
February 2003
Table of Contents
PART I: REGRESSION MODELS.
Introduction to Linear Models.
Regression on Functions of One Variable.
Transforming the Data.
Regression of Functions of Several Variables.
Collinearity in Multiple Linear Regression.
Influential Observations in Multiple Linear Regression.
Polynomial Models and Models with Qualitative Predictors.
Additional Topics.
PART II: ANALYSIS OF VARIANCE MODELS.
Introduction to Analysis of Variance Models.
Fixed Effects Models !: One-Way Classification of Means.
Fixed Effects Models II: Two-Way Classification of Means.
Fixed Effects Models II: Multiple Crossed and Nested Factors.
Mixed Models I: The AOV Method with Balanced Data.
Mixed Model II: The AVE Method with Balanced Data.
Mixed Models III: Unbalanced Data.
PART II: THE MATHEMATICAL THEORY OF LINEAR METHODS.
The Distribution of Linear and Quadratic Forms.
Estimation and Inference for Linear Models.
Simulation Inference: Tests and Confidence Intervals.
Appendix A. Mathematics.
Appendix B. Statistics.
Appendix C. Statistical Tables.
Appendix D. Data.
References.
Index.
The popular First Edition of this book provided a thorough
treatment of the concepts and methods of linear model analysis
and illustrated them with numerical and conceptual examples.
Revised to enhance its value as a teaching text, the Second
Edition presents the material in a conceptually simple way so
that users could more easily understand the applications of the
methods and be able to use the appropriate computer applications
to perform the analysis.
ISBN: 0-471-41540-5
Hardcover
564 Pages
March 2003
Table of Contents
Preface.
Vectors of Random Variables.
Multivariate Normal Distribution.
Linear Regression: Estimation and Distribution Theory.
Hypothesis Testing.
Confidence Intervals and Regions.
Applications: Straight Line Regression.
Polynomial Regression.
Analysis of Variance.
Departures from Underlying Assumptions.
Departures from Assumptions: Diagnosis and Remedies.
Computational Algorithms for Fitting a Regression.
Prediction and Model Selection.
Appendix A. Some Matrix Algebra.
Appendix B. Orthogonal Projections.
Appendix C. Tables.
Outline Solutions to Exercises.
References.
Index.
Regression analysis is an often used tool in the statisticians
toolbox. This new edition takes into serious consideration the
furthering development of regression computer programs that are
efficient, accurate, and considered an important part of
statistical research. The book provides up-to-date accounts of
computational methods and algorithms currently in use without
getting entrenched in minor computing details.