Anirban Dasgupta, Editor

A Festschrift to Honor Herman Rubin

This volume is a collection of 32 original papers and two biographical accounts put together as a Festschrift to Herman Rubin to honor his diverse and many deep contributions to mathematical sciences over more than 50 years. The topics of the original articles touch on the main themes in which Professor Rubin has contributed, as well as other topics of intense current activity. This volume contains innovative new methodological articles on cluster analysis, goodness of fit, likelihood inference, classification algorithms, and meta analysis. On the purely theoretical side, there are a number of comprehensive review articles on fractional Brownian motion, stochastic integration, de Finetti theorems, admissibility, and estimation under constraints. Each of these review articles provides readable glimpses into the current state of the art. Some notable classic unsolved problems in number theory and random permutations provide attractive additions to the interesting landscape of this volume.

The IMS Lecture Notes - Monograph Series vol.45

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Persi Diaconis and Susan Holmes, Editors

Stein's Method: Expository Lectures and Applications

Stein's method is one of the most powerful tools for proving limit theorems with sharp, explicit errors for complex dependent problems. It is curiously hard to grasp how and why it works since it avoids both characteristic functions and higher moments. This book consists of tutorial and survey papers aimed at teaching Stein's method to non specialists. The book provides a self contained development with motivation and full proofs. As a unifying theme, all papers use Stein's approach of exchangeable pairs. In addition to the usual Poisson and Normal approximations the book gives applications to convergence of Markov chains on finite state spaces, to birth and death chains and to empirical process convergence for the bootstrap. One novel feature is the development of Stein's method as an adjunct to simulation via Monte Carlo. Usually, the identities underlying the method give an explicit error term which is bounded. With the present version using exchangeable pairs, the error is given as an explicit expectation for the reversible Markov chain. It can thus be easily simulated to give improvements to classical approximations. The authors of various chapters, Persi Diaconis, Jason Fulman, Gesine Reinert, Susan Holmes, Mark Huber and Charles Stein have used common notation and worked together to achieve a unified treatment.

The IMS Lecture Notes - Monograph Series vol.46

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Y. Benjamini, F. Bretz and S. Sarkar, Editors

Recent Developments in Multiple Comparison Procedures

This volume is based on the NSF-CBMS Conference in Mathematical Sciences "New Horizons in Multiple Comparison Procedures" held in August 2001at Temple University, Philadelphia, with Yosef Hochberg as the key speaker. The conference was organized in response to the sudden upsurge of research that has taken place in the area of multiple comparisons. A number of newer ideas have emerged from the recent research activities that could generate a steady stream of new research. This volume is a collection of 11 papers, covering a broad range of topics in Multiple Comparisons, which were invited for the conference. The goal of this volume is to gain deeper understanding of these ideas and to promote further research activities in this area.

The IMS Lecture Notes - Monograph Series vol.47

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Nan Laird, Harvard University

Analysis of Longitudinal and Cluster-Correlated Data

The analysis of data with outcomes measured repeatedly on each subject has experienced several transforming developments in the last twenty years. This monograph presents a unified treatment of modern methods for longitudinal and/or correlated data that have developed during this period. The basic approach that the author takes to modeling longitudinal data is to extend familiar univariate regression models to multivariate or correlated outcomes. The author deals with linear models for measured data and generalized linear models for binary and count data. The author shows how methods can accommodate missing outcomes and/or unbalanced designs. Both likelihood and moment methods of estimation are covered, as are random effects approaches to data modeling and parameter estimation. The monograph assumes that the reader has a solid foundation in statistical inference, linear and generalized linear regression models, and a basic knowledge of multivariate methods. It is appropriate for second year doctoral students or postdoctoral fellows in Statistics/Biostatistics as well as researchers or faculty interested in learning about the field.

NSF-CBMS Regional Conference Series in Probability and Statistics,vol.8.

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Michael J. Crawley

Statistics: An Introduction using R

ISBN: 0-470-02298-1 Paperback
ISBN: 0-470-02297-3 Hardcover
304 pages,May 2005

Description

Statistics: An Introduction Using R offers a concise introduction to statistical methods, stressing the graphical investigation of data, and features step-by-step instructions to help the non-statistician to understand fully the methodology. The computing is done in R, the freeware version of S-Plus, which is globally recognised as one of the most powerful and flexible statistical software packages. This book is the first available title on the market to cover a broad array of statistical methods at a suitable level for a wide range of disciplines.

Table of Contents

Preface.
Chapter 1 Fundamentals.
Chapter 2 Dataframes.
Chapter 3 Central Tendency.
Chapter 4 Variance.
Chapter 5 Single Samples.
Chapter 6 Two Samples.
Chapter 7 Statistical Modelling.
Chapter 8 Regression.
Chapter 9 Analysis of Variance.
Chapter 10 Analysis of Covariance.
Chapter 11 Multiple Regression.
Chapter 12 Contrasts.
Chapter 13 Count Data.
Chapter 14 Proportion Data.
Chapter 15 Death and Failure Data.
Chapter 16 Binary Response Variable.
Appendix 1: Fundamentals of the R Language.


Eugene Herman, Michael Pepe

Visual Linear Algebra

ISBN: 0-471-68299-3 Hardcover
560 pages January 2005

Description

Following an innovative approach to learning, this text integrates paper and pencil skill building and the theoretical development of ideas with geometric exploration and conceptual understanding.
Tutorials and traditional text. Visual Linear Algebra covers the topics in a standard one-semester introductory linear algebra course in forty-seven sections arranged in eight chapters. In each chapter, some sections are written in a traditional textbook style and some are tutorials designed to be worked through using either Maple or Mathematica.
About the tutorials Each tutorial is a self-contained treatment of a core topic or application of linear algebra that a student can work through with minimal assistance from an instructor. The thirty tutorials are provided on the accompanying CD both as Maple worksheets and as Mathematica notebooks. They also appear in print as sections of the textbook.
Geometry is used extensively to help students develop their intuition about the concepts of linear algebra.
Applications. Students benefit greatly from working through an application, if the application captures their interest and the materials give them substantial activities that yield worthwhile results. Ten carefully selected applications have been developed and an entire tutorial is devoted to each of them.
Active Learning. To encourage students to be active learners, the tutorials have been designed to engage and retain their interest. The exercises, demonstrations, explorations, visualizations, and animations are designed to stimulate studentsa ? interest, encourage them to think clearly about the mathematics they are working through, and help them check their comprehension.

Table of Contents

Chapter 1. Systems of Linear Equations.
Chapter 2. Vectors.
Chapter 3. Matrix Algebra.
Chapter 4. Linear Transformations.
Chapter 5. Vectors Spaces.
Chapter 6. Determinants.
Chapter 7. Eigenvalues and Eigenvectors.
Chapter 8. Orthogonality.
Appendix A: Glossary of Linear Algebra Definitions.
Appendix B: Linear Algebra Theorems.
Appendix C: Advice for Using Maple with Visual Linear Algebra.
Appendix D: Commands Used in Maple Tutorials.
Appendix E: Appendix with Visual Linear Algebra.
Appendix F: Commands Used in Mathematic Tutorials.
Appendix G: Answers and Hints for Selected Pencil and Paper Problems.

Roger Cooke

The History of Mathematics: A Brief Course, 2nd Edition

ISBN: 0-471-44459-6 Hardcover
626 pages April 2005

Description

Written by one of the foremost experts in the field, The History of Mathematics: A Brief Course is substantially revised in the second edition. This acclaimed text now reorganized topically rather than geographically begins with first applications of counting and numbers in the ancient world, and continues with discussions of geometry, algebra, analysis, probability, logic, and more. Discussions of women in the history of mathematics make this a very thorough, inclusive resource.

Table of Contents

Preface to the Second Edition.
PART 1: THE WORLD OF MATHEMATICS AND THE MATHEMATICS OOF THE WORLD.
Chapter 1. The OPrigin and Prehistory of Mathematics.
Chapter 2. Mathematical Cultures I.
Chapter 3. Mathematical Cultures II.
Chapter 4. Women Mathematicians.
PART 2: NUMBERS.
Chapter 5.Counting.
Chapter 6. Calculation.
Chapter 7. Ancient Number Theory.
Chapter 8. Numbers and Number Theory in Modren Mathematics.
PART 3: COLOR PLATES.
PART 4: SPACE.
Chapter 9. Measurement.
Chapter 10. Euclidean Geometry.
Chapter 11. Post-Euclidean Geometry.
Chapter 12. Modern Geometries.
PART 5: ALGEBRA.
Chapter 13. Prolems Leading to Algebra.
Chapter 14. Equations and Methods.
Chapter 15. Modern Algebra.
PART 6: ANALYSIS.
Chapter 16. The Calculus.
Chapter 17. Real and Complex Aanlysis.
PART 7: MATHEMATICAL INFERENCES.
Chapter 18. Probability and Statistics.
Chapter 19. Logic and Set Theory.
Literature.
Subject Index.
Name Index.