Jacob Bernoulli
translated with an introduction and notes by Edith Dudley Sylla

The Art of Conjecturing,
together with "Letter to a Friend on Sets in Court Tennis"

hardcover
0-8018-8235-4
December 2005 528 pp. 3 line drawings

Description

Jacob Bernoulli's Ars Conjectandi, published posthumously in Latin in 1713 by the Thurneysen Brothers Press in Basel, is the founding document of mathematical probability. Here, Edith Dudley Sylla offers the first complete English translation of this monumental work.

Part I reprints and reworks Huygens's On Reckoning in Games of Chance. Part II offers a thorough treatment of the mathematics of combinations and permutations, including the numbers since known as "Bernoulli numbers." In Part III, Bernoulli solves more complicated problems of games of chance using that mathematics. In the final part, Bernoulli's crowning achievement in mathematical probability is manifest: he applies the mathematics of games of chance to the problems of epistemic probability in civil, moral, and economic matters, proving what we now know as the weak law of large numbers.

Sylla provides an extensive introduction and detailed translator's notes. She includes as supplemental texts Bernoulli's "Letter to a Friend on Sets in Court Tennis" and "Thesis 32" of Theses Logicae de conversione et oppositione enunciationum.

Reviews

"Bernoulli's The Art of Conjecturing has always been recognized as one of the outstanding texts in the history of probability, marking a dramatic development in the theory. The lack of a complete translation has hampered an understanding of the exact nature of its achievement. With Sylla's translation, it becomes clear what a comprehensive and revolutionary work it was."--James Franklin, University of South Wales

Author Information
Edith Dudley Sylla is a professor of history at North Carolina State University.

Edited by: G. Pfister, S. Cojocaru and V. Ufnarovski

Computational Commutative and Non-Commutative Algebraic Geometry

Volume 196 NATO Science Series: Computer & Systems Sciences
April 2005, 336 pp., hardcover
ISBN: 1-58603-505-3 NEW


This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in Commutative and Non-Commutative Algebraic Geometry and Algebra. The contributors to this publication present the most recent and state of the art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.

table of contents


Peter Olofsson

Probability, Statistics, and Stochastic Processes

ISBN: 0-471-67969-0
Hardcover
486 pages
May 2005

This text begins with chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions. The next sections introduce limit theorems and simulation. Also included is a chapter on statistical inference, with a section on Bayesian statistics which is an important, though often neglected, topic for undergraduate-level texts. Markov chains in discrete and continuous time is also discussed within the book. More than 400 examples are interspersed throughout the text to help illustrate concepts and theory and to assist the reader to develop an intuitive sense of the subject. Readers will find many of the examples to be both entertaining and thought provoking. This is also true for the carefully selected problems that appear at the end of each chapter.

Contents

Preface.
1. Basic Probability Theroy.
2. Random Variables.
3. Joint Distributions.
4. Limit Theorems.
5. Simulation.
6. Statistical Inference.
7. Stochastic Processes.
Appendix A: Tables.
Appendix B: Answers to Selected Problems.
References.

Granville Sewell

The Numerical Solution of Ordinary and Partial Differential Equations,
2nd Edition

ISBN: 0-471-73580-9
Hardcover
352 pages
June 2005

Description

The Second Edition of this popular text provides an insightful introduction to the use of finite difference and finite element methods for the computational solution of ordinary and partial differential equations. Readers gain a thorough understanding of the theory underlying themethods presented in the text. The author emphasizes the practical steps involved in implementing the methods, culminating in readers learning how to write programs using FORTRAN90 and MATLAB(r) to solve ordinary and partial differential equations.

The book begins with a review of direct methods for the solution of linear systems, with an emphasis on the special features of the linear systems that arise when differential equations are solved. The following four chapters introduce and analyze the more commonly used finite difference methods for solving a variety of problems, including ordinary and partial differential equations and initial value and boundary value problems. The techniques presented in these chapters, with the aid of carefully developed exercises and numerical examples, can be easilymastered by readers.

The final chapter of the text presents the basic theory underlying the finite element method. Following the guidance offered in this chapter, readers gain a solid understanding of the method and discover how to use it to solve many problems.

A special feature of the Second Edition is Appendix A, which describes a finite element program, PDE2D, developed by the author. Readers discover how PDE2D can be used to solve difficult partial differential equation problems, including nonlinear time-dependent and steady-state systems, and linear eigenvalue systems in 1D intervals, general 2D regions, and a wide range of simple 3D regions. The software itself is available to instructors who adopt the text to share with their students.

Table of Contents

Direct Solution of Linear Systems.
1. Initial Value Ordinary Differential Equations.
2. The Initial Value Diffusion Problem.
3. The Initial Value Transport and Wave Problems.
4. Boundary Value Problems.
5. The Finite Element Method.
Appendix A: Solving PDEs with PDE2D.
Appendix B: The Fourier Stability Method.
Appendix C: MATLAB Programs.
Appendix D: Can 'Anything' Happen in an Open System?
Appendix E: Answers to Selected Exercises.
References.

Steven J. Janke, Frederick Tinsley

Introduction to Linear Models and Statistical Inference

ISBN: 0-471-66259-3
Hardcover
600 pages
July 2005

Description

Intended for a first course in linear models at either the upper undergraduate or beginning graduate level, Introduction to Linear Models and Statistical Inference provides a basic introduction to probability distribution theory and statistical inference. It includes descriptive methods for building models with an emphasis on linear regression, variance, and covariance. In an effort to extend reader comprehension and intrigue, there is a general discussion of analysis of model fit and modern robust techniques at the end of the book.
* The exercises are a mix of both the theoretical and the practical; some are marked as requiring calculus, linear algebra, or computer skills.
* The text utilizes output from MINITAB to illustrate many of the examples. An appendix introduces the reader to MINITAB.
* The text includes an introduction to matrix algebra in an appendix for those readers who have a weak background in the topic. Optional sections are included at chapter ends for use in courses where the integration of linear algebra techniques is desired. The sections can be omitted without loss of continuity.
* The text can serve as a first course in general statistics for students with some mathematical background at the first-year graduate level or as a second course for those readers pursuing a more quantitative emphasis in the social or natural sciences at the undergraduate level.
* Actual data from readily available (interdisciplinary) sources is used both in-text and on an author-maintained web site.
* Both intuitive and mathematical explanations are given in an effort to balance the overall treatment and comprehension.

Table of Contents

Introduction.
1. Data: Plots and Location.
2. Data: Dispersion and Correlation.
3. Random Variables: Probability.
4. Random Variables: Expectation and Variance.
5. Statistical Inference.
6. Simple Linear Models.
7. Linear Model Diagnostics.
8. Linear Models: Two Independent Variables.
9. Linear Models: Several Independent Variables.
10. Model Building.
11. Extended Linear Models.
Appendix A: Data References.
Appendix B: MINITAB Reference.
Appendix C: Introduction to Linear Algebra.
Appendix D: Statistical Tables.
References.
Index.

Steven Piantadosi

Clinical Trials: A Methodologic Perspective, 2nd Edition

ISBN: 0-471-72781-4
Hardcover
720 pages
July 2005

Description

The previous edition of this title has an excellent track record, and its continued comprehensive coverage is unparalleled by the competition. The author, who is renowned throughout the world, has significantly and thoroughly refined and retooled this edition.
This updated volume continues its straightforward, authoritative review of basic statistical methods for clinical trials. Even though numerous books have appeared on the subject matter, very few of them, except for this title, emphasize accessible coverage of statistical methods -- the crucial building blocks of medical research. The author's hands-on approach, embracing a number of different trial designs and clinical fields, guides readers through the process of planning an experiment, putting together a study cohort, assessing data, and reporting results, and addresses the problems that are likely to confront any such study. Paramount throughout is the effort to strike a common ground between qualitative clinical and rigorous statistical methods.

Covers vital design considerations
Emphasizes experimental designs to search for treatment advances
Focuses on concepts that unify
Explores areas of controversy such as ethics (now greatly expanded) and offers pragmatic information regarding allegations of fraud or misconduct
Includes summaries, revised discussion questions, and updated references in each chapter
Accompanied by an ftp site, dozens of new, redrawn, and/or updated illustrations, a comprehensive bibliography, and multiple indexes
Incorporates new content, including new chapters on contexts, perspectives, transitional trials, and early developmental drug design
Now, extensively class-tested

Table of Contents

1. Preliminaries.
2. Clinical Trails as Research.
3. Why Clinical Trials Are Ethical.
4. Contexts for Clinical Trials.
5. Statistical Perspectives.
6. Clinical Trials as Experimental Designs.
7. Random Error and Bias.
8. Objectives and Outcomes.
9. Translational Clinical Trials.
10. Dose Finding Designs.
11. Sample Size and Power.
12. The Study Cohort.
13. Treatment Allocation.
14. Treatment Effects Monitoring. 15. Counting Patients and Events.
16. Estimating Clinical Effects.
17. Prognostic Factor Analyses.
18. Reporting and Authorship.
19. Factorial Designs.
20. Cross-Over Designs.
21. Meta-Analyses.
22. Misconduct and Fraud in Clinical Research.
Appendix A: Data and Programs.
Appendix B: Notation and Terminology.
Appendix C: Abbreviations.
Appendix D: Nuremberg Code.
Appendix E: Declaration of Helsinki.
Appendix F: NCI Data and Safety Monitoring Policy.
Appendix G: NIH Data and Safety Monitoring Policy.
Appendix H: Royal Statistical Society Code of Conduct.