ISBN: 0-471-22066-3
Paperback
199 pages
February 2004
Author Information
A colorful tour through the intriguing world of mathematics
The world of modern mathematics abounds with fascinating, unusual
ideas?ideas and concepts even seasoned mathematicians often
wonder about. Mathematical Journeys takes you on a grand tour of
the best of modern math?its most elegant solutions, most clever
discoveries, most mind-bending propositions, and most impressive
personalities.
Writing with a light touch while showing the real mathematics,
author Peter Schumer introduces you to the history of
mathematics, number theory, combinatorics, geometry, graph
theory, and "recreational mathematics." Requiring only
high school math and a healthy curiosity, Mathematical Journeys
helps you explore all those aspects of math that mathematicians
themselves find most delightful. Youfll discover brilliant,
sometimes quirky and humorous tidbits like how to compute the
digits of pi, the Josephus problem, mathematical amusements such
as Nim and Wythofffs game, pizza slicing, and clever twists on
rolling dice. For a glimpse of the minds that gave birth to the
math, read the profiles of such great thinkers as Paul Erdos and
Leonhard Euler.
Each chapter of the book focuses on some interesting piece of
mathematics, giving the history and requisite math background,
the solution of a problem or two, and some indication of natural
generalizations and related areas of study. Whether youfre a
math novice curious to learn what your calculus class left out or
a math lover ready for the green chicken contest (Whatfs that?
Read the book!), Mathematical Journeys will give you a true taste
of what mathematicians themselves find most exciting about math.
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ISBN: 0-471-52638-X
Hardcover
504 pages
January 2004
Key Features:
Contains plenty of examples, clear proofs, and significant
motivation for the crucial concepts.
Includes numerous exercises of varying levels of difficulty, both
computational and more proof-oriented.
Exercises are arranged in order of increasing difficulty.
Table of Contents
Preface.
Chapter 1. Vectors and Matrices.
Chapter 2. Functions, Limits, and Continuity.
Chapter 3. The Derivative.
Chapter 4. Implicit and Explicit Solutions of Linear Systems.
Chapter 5. Extremum Problems.
Chapter 6. Solving Nonlinear Problems.
Chapter 7. Integration.
Chapter 8. Differential Forms and Integration on Manifolds.
Chapter 9. Eigenvalues, Eigenvectors, and Applications.
Glossary of Notations and Results from Single-Variable Calculus.
For Further Reading.
Answers to Selected Exercises.
Index.
ISBN: 0-471-68029-X
Paperback
489 pages
April 2004
Table of Contents
PART ONE. SURVEY OF PROBABILITY THEORY.
Chapter 1. Introduction.
Chapter 2. Experiments, Sample Spaces, and Probability.
Chapter 3. Random Variables, Random Vectors, and Distributions
Functions.
Chapter 4. Some Special Univariate Distributions.
Chapter 5. Some Special Multivariate Distributions.
PART TWO. SUBJECTIVE PROBABILITY AND UTILITY.
Chapter 6. Subjective Probability.
Chapter 7. Utility.
PART THREE. STATISTICAL DECISION PROBLEMS.
Chapter 8. Decision Problems.
Chapter 9. Conjugate Prior Distributions.
Chapter 10. Limiting Posterior Distributions.
Chapter 11. Estimation, Testing Hypotheses, and linear
Statistical Models.
PART FOUR. SEQUENTIAL DECISIONS.
Chapter 12. Sequential Sampling.
Chapter 13. Optimal Stopping.
Chapter 14. Sequential Choice of Experiments.
References.
Supplementary Bibliography.
Name Index.
Subject Index.
ISBN: 0-471-21487-6
Hardcover
536 pages
June 2004
A rigorous, systematic presentation of modern longitudinal
analysis
Longitudinal studies, employing repeated measurement of subjects
over time, play a prominent role in the health and medical
sciences as well as in pharmaceutical studies. An important
strategy in modern clinical research, they provide valuable
insights into both the development and persistence of disease and
those factors that can alter the course of disease development.
Written at a technical level suitable for researchers and
graduate students, Applied Longitudinal Analysis provides a
rigorous and comprehensive description of modern methods for
analyzing longitudinal data. Focusing on General Linear and Mixed
Effects Models for continuous responses, and extensions of
Generalized Linear Models for discrete responses, the authors
discuss in detail the relationships among these different models,
including their underlying assumptions and relative merits. The
book features:
A focus on practical applications, utilizing a wide range of
examples drawn from real-world studies
Coverage of modern methods of regression analysis for correlated
data
Analyses utilizing SAS
Multiple exercises and "homework" problems for review
An accompanying Web site features twenty-five real data sets used
throughout the text, in addition to programming statements and
selected computer output for the examples.
ISBN: 0-470-86697-7
Hardcover
328 pages
August 2004
Regression analysis has been one of the most widely used
statistical tools for many years, and continues to be developed
and applied to new applications. Generalized least squares
estimation (GLSE) based on Gauss-Markov theory plays a key role
in understanding theoretical and practical aspects of statistical
inference in general linear regression models. GLSE can be
applied to problems encountered in many disciplines, particularly
statistics, econometrics, and biometrics.
Provides a self-contained introduction to GLSE.
Includes detailed coverage of the 'lower and upper bounds'
approach, pioneered by the authors.
Adopts a concise yet mathematically rigorous approach.
Includes applications to statistics, econometrics, and biometrics.
Contains exercises at the end of each chapter, enabling use as a
course text or for self-study.
Includes a comprehensive bibliography.
Generalized Least Squares provides an accessible introduction to
GLSE suitable for researchers and graduate students from
statistics, econometrics, and biometrics. It provides an
excellent source of reference, can be used as a course text, and
will help to stimulate further research into this flourishing
topic.
Table of Contents
Preliminaries.
Generalized Least Squares Estimators.
Nonlinear Gauss-Markov Theorem.
SUR and Heteroscedastic Models.
Serial Correlation Model.
Normal Approximation.
Extension of Gauss-Markov Theorem.
Some Further Extensions.
Growth Curve Model.
Appendix.
Bibliography.