0-534-40518-5
450 pages Case Bound 6 3/8 x 9 1/4
2004 Available Now
the title indicates, this text is intended for courses aimed at
bridging the gap between lower level mathematics and advanced
mathematicstransition to advanced mathematics presented is
discrete since continuous functions are not studiedprovides a .
The careful to techniques for writing proofs and a logical
development of topics based on intuitive understanding of . The
text introduction conceptsThe authors writing style and a wealth
of examples to develop an understanding of discrete mathematics
and critical . utilize a clear thinking skillsIncluding than can
be covered in one semester, the text offers innovative material
throughout, particularly in the last . more topics three chapters
Numbers and Pascal's Triangle). This allows flexibility for the
instructor and the ability to teach a deeper, richer (e.g.
Fibonacci course.
Table of Contents
1. SETS AND LOGIC.
Sets. Set Operations. Partitions. Logic and Truth Tables.
Quantifiers. Implications.
2. PROOFS.
Proof Techniques. Mathematical Induction. The Pigeonhole
Principle.
3. NUMBER THEORY.
Divisibility. The Euclidean Algorithm. The Fundamental Theorem of
Arithmetic. Divisibility Tests. Number Patterns.
4. COMBINATORICS.
Getting from Point A to Point B. The Fundamental Principle of
Counting. A Formula for the Binomial Coefficients. Combinatorics
with Indistinguishable Objects. Probability.
5. RELATIONS.
Relations. Equivalence Relations. Partial Orders. Quotient Spaces.
6. FUNCTIONS AND CARDINALITY.
Functions. Inverse Relations and Inverse Functions. Cardinality
of Infinite Sets. An Order Relation for Cardinal Numbers.
7. GRAPH THEORY.
Graphs. Matrices, Digraphs, and Relations. Shortest Paths in
Weighted Graphs. Trees.
8. SEQUENCES.
Sequences. Finite Differences. Limits of Sequences of Real
Numbers. Some Convergence Properties. Infinite Arithmetic.
Recurrence Relations.
9. FIBONACCI NUMBERS AND PASCAL'S TRIANGLE.
Pascal's Triangle. The Fibonacci Numbers. The Golden Ratio.
Fibonacci Numbers and the Golden Ratio. Pascal's Triangle and the
Fibonacci Numbers.
10. CONTINUED FRACTIONS.
Finite Continued Fractions. Convergents of a Continued Fraction.
Infinite Continued Fractions. Applications of Continued Fractions.
0-534-4097-76
672 pages Case Bound 7 3/8 x 9 1/4
2005 Available Now
Awarded Outstanding Academic Book by CHOICE magazine in its first
edition, FORECASTING, TIME SERIES, AND REGRESSION: AN APPLIED
APPROACH now appears in a fourth edition that illustrates the
vital importance of forecasting and the various statistical
techniques that can be used to produce them. With an emphasis on
applications, this book provides both the conceptual development
and practical motivation students need to effectively implement
forecasts of their own. Bruce Bowerman, Richard O'Connell, and
Anne Koehler clearly demonstrate the necessity of using forecasts
to make intelligent decisions in marketing, finance, personnel
management, production scheduling, process control, and strategic
management. In addition, new technology coverage makes the latest
edition the most applied text available on the market.
New to the Edition
New modernized, high-resolution computer graphics and output
reflect the latest software releases and illustrate practical
tools and applications.
The exercises have been expanded and updated to include recent
data and realistic scenarios.
Regression is more thoroughly addressed with expanded sections on
the topic as well as an optional appendix on matrix algebra.
The totally re-written exponential smoothing chapter emphasizes
modern techniques, models, and spreadsheets.
Clearer discussion of Box-Jenkins models enables students to
better understand this important topic.
New balanced organization allows the book to be used in a variety
of course syllabi. Whether you wish to focus exclusively on
Forecasting, Time Series or even Regression, or cover some of
each, this text provides all the topics you'll need in one book.
0-534-42441-4
512 pages Case Bound 6 3/8 x 9 1/4
c 2005 Available Now
Modern and measure-theory based, this text is intended primarily
for the first-year graduate course in probability theory. The
book focuses attention on examples while developing theory. There
is an emphasis on results that can be used to solve problems in
the hopes that those who apply probability to work will find this
a useful reference.
Table of Contents
INTRODUCTORY LECTURE.
1. LAWS OF LARGE NUMBERS.
Basic Definitions. Random Variables. Expected Value. Independence.
Weak Laws of Large Numbers. Borel-Cantelli Lemmas. Strong Law of
Large Numbers. Convergence of Random Series. Large Deviations.
2. CENTRAL LIMIT THEOREMS.
The De Moivre-Laplace Theorem. Weak Convergence. Characteristic
Functions. Central Limit Theorems. Local Limit Theorems. Poisson
Convergence. Stable Laws. Infinitely Divisible Distributions.
Limit theorems in Rd.
3. RANDOM WALKS.
Stopping Times. Recurrence. Visits to 0, Arcsine Laws. Renewal
Theory.
4. MARTINGALES.
Conditional Expectation. Martingales, Almost Sure Convergence.
Examples. Doob's Inequality, LP Convergence. Uniform
Integrability, Convergence in L1 / Backwards Martingales.
Optional Stopping Theorems.
5. MARKOV CHAINS.
Definitions and Examples. Extensions of the Markov Property.
Recurrence and Transience. Stationary Measures. Asymptotic
Behavior. General State Space.
6. ERGODIC THEOREMS.
Definitions and Examples. Birkhoff's Ergodic Theorem. Recurrence.
Mixing. Entropy. A Subadditive Ergodic Theorem. Applications.
7. BROWNIAN MOTION.
Definition and Construction. Markov Property, Blumenthal's 0-1
Law. Stopping Times, Strong Markov Property. Maxima and Zeros.
Martingales. Donsker's Theorem. CLT's for Dependent Variables.
Empirical Distributions, Brownian Bridge. Laws of the Iterated
Logarithm.
APPENDIX: MEASURE THEORY.
REFERENCES.
NOTATION.
NORMAL TABLE.
INDEX.
0-534-38778-0
498 pages Case Bound 7 3/8 x 9 1/4
c 2005 Available Now
MULTIVARIATE STATISTICAL METHODS fills a void in the marketplace,
striking a crucial balance between the technical information and
real-world applications of multivariate statistics. Donald
Morrison has taught this course at the Wharton School for 33
years, and he has integrated his demonstrably successful teaching
style into this textbook.
Table of Contents
1. SOME ELEMENTARY STATISTICAL CONCEPTS.
Introduction. Random Variables. Normal Random Variables. Random
Samples and Estimation. Tests of Hypothesis for the Parameters of
Normal Populations. Testing the Equality of Several Means: The
Analysis of Variance.
2. MATRIX ALGEBRA.
Introduction. Some Definitions. Elementary Operations with
Matrices and Vectors. The Determinant of a Square Matrix. The
Inverse Matrix. The Rank of a Matrix. Simultaneous Linear
Equations. Orthogonal Vectors and Matrices. Quadratic Forms. The
Characteristics Roots and Vectors of a Matrix. Partitioned
Matrices. Differentiation with Vectors and Matrices. Further
Reading.
3. SAMPLES FROM THE MULTIVARIATE NORMAL POPULATION.
Introduction. Multidimensional Random Variables. The Multivariate
Normal Distribution. Conditional and Marginal Distributions of
Multinormal Random Variables. Samples from the Multinormal
Population. Correlation and Regression. Simultaneous Inference
about Regression Coefficients. Inferences about the Correlation
Matrix. Samples with Incomplete Observations. Exercises.
4. TESTS OF HYPOTHESES ON MEANS.
Introduction. Tests on Means and the T2 ?Statistic. Simultaneous
Inferences for Means. The Case of Two Samples. The Analysis of
Repeated Measurements. Groups of Repeated Measurements: The
Paired T2 Test. Profile Analysis for Two Independent Groups. The
Power of Tests on Mean Vectors. Some Tests with Known Covariance
Matrices. Tests for Outlying Observations. Testing the Normality
Assumption. Exercises.
5. MULTIVARIATE ANALYSIS OF VARIANCE.
Introduction. The Multivariate General Linear Model. The
Multivariate Analysis of Variance. MANOVA for Unbalanced Two-Way
Layouts. The Multivariate Analysis of Covariance. Multiple
Comparisons in the Multivariate Analysis of Variance. Profile
Analysis. Power and Sample Size Determination. Curve Fitting for
Repeated Measurements. MANOVA Robustness. Exercises.
6. CLASSIFICATION BY DISCRIMINANT FUNCTIONS.
Introduction. The Linear Discriminant Function for Two Groups.
Classification with Known Parameters. The Case of Unequal
Covariance Matrices. Estimation of the Misclassification
Probabilities. Classification for Several Groups. Exercises.
7. INFERENCES FROM COVARIANCE MATRICES.
Introduction. Hypothesis Tests for a Single Covariance Matrix.
Tests for Two Special Patterns. Testing the Equality of Several
Covariance Matrices. Testing the Independence of Sets of Variates.
Canonical Correlation. Exercises.
8. THE PRINCIPLE COMPONENTS OF MULTIVARIATE DATA.
Introduction. The Principal Components of Multivariate
Observations. The Geometrical Meaning of Principal Components.
The Interpretation of Principal Components. Biplots. Some
Patterned Matrices and Their Principal Components. The Sampling
Properties of Principal Components. Further Extensions. Exercises.
9. THE FACTOR STRUCTURE OF MULTIVARIATE DATA.
Introduction. The Mathematical Model for Factor Structure.
Estimation of the Factor Loadings. Testing the Goodness of Fit of
the Factor Model. Examples of Factor Analysis. Factor Rotation.
An Alternative Model for Factor Analysis. The Evaluation of
Factors. Sampling Properties of Factor Model Estimates. Models
for the Dependence Structure of Ordered Responses. Clustering
Sample Units. Multidimensional Scaling. Exercises.
REFERENCES.
TABLES AND CHARTS.
DATA SETS.
NAME INDEX.
SUBJECT INDEX.
New to the Edition
The book shows students how to perform multivariate analyses
using SPSS, MINITAB, JMP, Systat and APL.
References reflect the most recent statistical literature.
New discussions of MANOVA for Unbalanced Two-Way Layouts, Power
and Sample Size Determination, and MANOVA Robustness appear in
Chapter 3.
0-534-41805-8
486 pages Case Bound 7 3/8 X 9 1/4
c 2005 Available Now
This introductory text on the design and analysis of sample
surveys emphasizes the practical aspects of survey problems. It
begins with brief chapters on the role of sample surveys in the
modern world. Thereafter, each chapter introduces a sample survey
design or estimation procedure by describing the pertinent
practical problem. The authors describe the methodology proposed
for solving the problem and provide the details of the estimation
procedure, including a compact presentation of the formulas
needed to complete the analysis. Then, a practical example is
worked out in complete detail. At the end of each chapter, a
wealth of exercises gives students ample opportunity to practice
the techniques and stretch their grasp of ideas.
Table of Contents
1. INTRODUCTION.
2. ELEMENTS OF THE SAMPLING PROBLEM.
Introduction. Technical Terms. How to Select the Sample: The
Design of the Sample Survey. Sources of Errors in Surveys.
Designing a Questionnaire. Planning a Survey. Summary.
3. SOME BASIC CONCEPTS OF STATISTICS.
Introduction. Summarizing Information in Populations and Samples:
The Infinite Population Case. Summarizing Information in
Populations and Samples: The Finite Population Case. Sampling
Distributions. Covariance and Correlation. Estimation. Summary.
4. SIMPLE RANDOM SAMPLING.
Introduction. How to Draw a Simple Random Sample. Estimation of a
Population Mean and Total. Selecting the Sample Size for
Estimating Population Means and Totals. Estimation of a
Population Proportion. Comparing Estimates. Summary.
5. STRATIFIED RANDOM SAMPLING.
Introduction. How to Draw a Stratified Random Sample. Estimation
of a Population Mean and Total. Selecting the Sample Size for
Estimating Population Means and Totals. Allocation of the Sample.
Estimation of a Population Proportion. Selecting the Sample Size
and Allocating the Sample to Estimate Proportions. Additional
Comments on Stratified Sampling. An Optimal Rule for Choosing
Strata. Stratification after Selection of the Sample. Double
Sampling for Stratification. Summary.
6. RATIO, REGRESSION, AND DIFFERENCE ESTIMATION.
Introduction. Surveys that Require the Use of Ratio Estimators.
Ratio Estimation Using Simple Random Sampling. Selecting the
Sample Size. Ratio Estimation in Stratified Random Sampling.
Regression Estimation. Difference Estimation. Relative Efficiency
of Estimators. Summary.
7. SYSTEMATIC SAMPLING.
Introduction. How to Draw a Systematic Sample. Estimation of a
Population Mean and Total. Estimation of a Population Proportion.
Selecting the Sample Size. Repeated Systematic Sampling. Further
Discussion of Variance Estimators. Summary.
8. CLUSTER SAMPLING.
Introduction. How to Draw a Cluster Sample. Estimation of a
Population Mean and Total. Equal Cluster Sizes; Comparison to
Simple Random Sampling. Selecting the Sample Size for Estimating
Population Means and Totals. Estimation of a Population
Proportion. Selecting the Sample Size for Estimating Proportions.
Cluster Sampling Combined with Stratification. Cluster Sampling
with Probabilities Proportional to Size. Summary.
9. TWO-STAGE CLUSTER SAMPLING.
Introduction. How to Draw a Two-Stage Cluster Sample. Unbiased
Estimation of a Population Mean and Total. Ratio Estimation of a
Population Mean. Estimation of a Population Proportion. Sampling
Equal-Sized Clusters. Two-Stage Cluster Sampling with
Probabilities Proportional to Size. Summary.
10. ESTIMATING THE POPULATION SIZE.
Introduction. Estimation of a Population Size Using Direct
Sampling. Estimation of a Population Size Using Inverse Sampling.
Choosing Sample Sizes for Direct and Inverse Sampling. Estimating
Population Density and Size from Quadrat Samples. Estimating
Population Density and Size from Stocked Quadrats. Adaptive
Sampling. Summary.
11. SUPPLEMENTAL TOPICS.
Introduction. Interpenetrating Subsamples. Estimation of Means
and Totals over Subpopulations. Random-Response Model. Use of
Weights in Sample Surveys. Adjusting for Nonresponse. Imputation.
Selecting the Number of Callbacks. The Bootstrap. Summary.
12. SUMMARY.
Summary of the Designs and Methods. Comparisons among the Designs
and Methods.
Appenidices.
References and Bibliography Tables. Derivation of Some Main
Results. Macros for MINITAB. Macros for SAS. Data Sets.
Selected Answers.
Index.
New to the Edition
This edition bridges the gap between classroom and practice in
the area of sample survey design and analysis. This begins with
the discussion of weights in Chapter 3 and continues through the
new sections on weights in unequal probability sampling and
adjustments for nonresponse in Chapter 11, which now includes the
use of imputation as a technique for handling some types of
nonresponse.
A modern technique for establishing margins of error and
confidence intervals in complex designs, the bootstrap, is
introduced, as is an adaptive sampling technique for improving
estimates while the field work is in progress.
Data sets have been updated and new exercises appear throughout.
An effort was made to make the computations compatible with
modern statistical software; hand calculation formulas have been
de-emphasized.
Simulations to demonstrate key statistical concepts have been
added, along with suggestions on how the student might expand on
these.
Hardback (ISBN-0-521-83540-2)
Publication is planned for April 2005 | 368 pages | 260 x 183 mm
Textbook
Lecturers can request inspection copies of this title.
Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov’s inequality, Chevyshev’s inequality, Chernoff bounds, balls and bins models, the probabilistic method, and Markov chains. In the second half, the authors delve into more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods, coupling, martingales, and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.
Contents
Preface; 1. Events and probability; 2. Discrete random variables and expectation; 3. Moments and deviations; 4. Chernoff bounds; 5. Balls, bins and random graphs; 6. The probabilistic method; 7. Markov chains and random walks; 8. Continuous distributions and the Poisson process; 9. Entropy, randomness, and information; 10. The Monte Carlo method; 11. Coupling of Markov chains; 12. Martingales; 13. Pairwise independence and universal hash functions; 14. Balanced allocations; References.