Bressoud, D.M., Macalester College, Saint Paul, MN, USA
Wagon, S., Macalester College, Saint Paul, MN, USA
A Course in Computational Number Theory
2000. Approx. 415 pp. 28 figs., 3 in color, with CD-ROM.
1-930190-10-7
This text will be a modern introduction to number theory, a course taught at most colleges and universities,
primarily to math and c.s. majors, and will place heavy and continuing emphasis on algorithmic aspects of the
subject. The language of the algorithms used will be the popular Mathematica, and a comprehensive set of
notebooks will be included on a book web site. While the emphasis will be on modern topics like factorization and primality testing techniques, there will be extensive coverage of traditional number theory. Among its features willbe lots of displayed computations, and the inclusion of many computer exercises for students.
Contents: Fundamentals.- Primes and Perfect Numbers.- Fermat, Euler and Pseudoprimes.- Applications.-
Quadratic Residues.- Primitive Roots.- Continued Fractions.- Lucas Sequences.- Prime Imaginaries and Imaginary Primes.
Series: Textbooks in Mathematical Sciences.
University mathematics
Book category: Undergraduate Textbook
Publication language: English
Friedman, L.M., National Heart, Lung, and Blood Institute, Bethesda, MD, USA
Furberg, C.D., Wake Forest University, Winston-Salem, NC, USA
DeMets, D.L., University of Wisconsin, Madison, WI, USA
Fundamentals of Clinical Trials
3rd ed. 1998. Corr. 3rd printing 1999. XVIII, 361 pp.
0-387-98586-7
This standard reference discusses general as well as specific issues involved in the development, management,
and analysis of clinical trials. It serves to update areas in which considerable progress has recently been made,
and to broaden the scope in the light of clinical trials in new areas. The text will assist investigators in academia and industry in improving the quality of clinical trials by discussing fundamental concepts for those with some clinical trial experience as well as for those who plan to conduct a trial for the first time. It may also be used as a textbook in the teaching of clinical trial methodology and to assist members of the scientific and medical community who wish to evaluate and interpret published reports of trials. Although not a technically oriented text, it may equally be used as a reference for a graduate course on statistical methods in clinical trials.
Contents: Introduction to Clinical Trials.- What Is The Question?- Study Population.- Basic Study Design.-
The Randomization Process-.- Blindness.- Sample Size.- Baseline Assessment.- Recruitment of Study
Participants.- Data Collection and Quality Control.- Assessing and Reporting Adverse Effects.- Assessment of
Health-Related Quality of Life.- Participant Adherence.- Survival Analysis.- Monitoring Response Variables.-
Issues in Data Analysis.- Closeout.- Reporting and Interpreting of Results.- Multicenter Trials.
Fields: Statistics, general; Statistics for Life Sciences, Medicine, Health Sciences
Written for: Grad students, practitioners
Book category: Graduate Textbook
Publication language: English
Krause, A., Basle, Switzerland
Olson, M., Geneva, Switzerland
The Basics of S and S-PLUS , 2nd ed.
2000. Approx. 400 pp. 34 figs.
0-387-98961-7
A lucid explanation of the basics of S-PLUS at a level suitable for users with little computing or statistical
knowledge. Unlike the S-PLUS manuals, the book does not strive to be comprehensive, but instead introduces
the most important ideas of S-PLUS through the use of many examples. Each chapter includes a collection of
exercises that are accompanied by fully worked-out solutions and detailed comments, and the whole is rounded off with practical hints on how to work efficiently in S-PLUS, making it well-suited for both self-study and as a textbook. This second edition has been updated to incorporate the completely revised S Language and its implementation in S-PLUS, while new chapters have been added to explain the Windows GUI, how to explore relationships in data using the powerful Trellis graphics system, and how to understand and use object-oriented programming. In addition, the programming chapter has been extended to cover some of the more technical but important aspects of S-PLUS.
Contents: Introduction.- Windows User Interface.- A First Session.- A Second Session.- Graphics.- Trellis
Graphics.- Exploring Data.- Statistical Modeling.- Programming.- Object-Oriented Programming.- Input and
Output.- S-PLUS Internals.- Tips and Tricks.- Information Sources On and Around S-PLUS.- References.
Series: Statistics and Computing.
Fields: Statistics, general
Written for: Practitioners, students
Book category: Handbook
Publication language: English
Majumdar, M., Cornell University, Ithaca, NY, USA
Mitra, T., Cornell University, Ithaca, NY, USA
Nishimura, K., Kyoto University, Kyoto, Japan
(Eds.)
Optimization and Chaos
2000. X, 454 pp. 13 figs.
3-540-67030-0
The book begins with an introduction to some of the basic concepts and results on chaotic dynamical systems.
Next it turns to a detailed self-contained summary of the literature on discounted dynamic optimization. The first two chapters are of particular pedagogical interest. The volume also brings together a number of outstanding advanced research papers on complex behavior of dynamic economic models. These make it clear that complexity cannot be dismissed as "exceptional" or "pathological" and, for explanation and prediction of economic variables, it is imperative to develop models with special structures suggested by empirical studies. Graduate students in economics will find the book valuable for an introduction to optimization and chaos. Specialists will find new directions to explore themes like robustness of chaotic behavior and the role of discounting in generating cycles and complexity.
Keywords: Dynamical Systems, Chaos, Optimization, Non-Linear Systems
Contents: M. Majumdar, T. Mitra: Dynamical Systems: A Tutorial.- T. Mitra: Introduction to Dynamic
Optimization Theory.- M. Majumdar, T. Mitra: Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects.- K. Nishimura, M. Yano: Optimal Chaos, Nonlinearity, and Feasibility Conditions.- R. Becker, C. Foias: The Local Bifurcation of Ramsey Equilibrium.- G. Sorger: On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy and Sunspots.- M. Majumdar, T. Mitra: Robust Ergodic Chaos in Discounted Dynamic Optimization Models.- K. Nishimura, M. Yano: Non-Linear Dynamics and Chaos in Optimal Growth: A Constructive Exposition.- K. Nishimura, G. Sorger, M. Yano: Ergodic Chaos in Optimal Growth Models with Low Discount Rates.- G. Sorger: On the Minimum Rate of Impatience for Complicated Optimal Growth Paths.- T. Mitra: An Exact Discount Factor Restriction for Period-Three Cycles in Dynamic Optimization Models.- K. Nishimura, M. Yano: On the Least Upper Bound of Discount Factors that are Compatible with Optimal Period-Three Cycles.- T. Mitra: On the Relationship between Discounting and Entropy of Dynamic Optimization Models.
Series: Studies in Economic Theory.VOL. 11
Fields: Economics; Optimization and Optimal Control
Written for: Researchers, graduate students
Book category: Monograph
Publication language: English
Nicola, P.C., University of Milano, Italy
Mainstream Mathematical Economics in the 20th Century
2000. XX, 521 pp. 15 figs.
3-540-67084-X
This book presents the contributions of the 20th century to economic theory in a mathematical language and in historical sequence. General equilibrium is the focal point of the book; but also a number of macroeconomic
models, especially with respect to the first half of the century, are considered. Dynamic models are extensively
studied per se, and not merely as extensions of their static counterparts. The book with its extensive bibliography gives a broad view over the developments in mathematical economics and is therefore an invaluable source of information for researchers and students working in this field.
Keywords: Mathematical economics, economic theory, history of mathematical economics
Fields: Economic Theory/Mathematical Methods; Computational Mathematics and Scientific Computing
Written for: Researchers
Book category: Monograph
Publication language: English
Ribes, L., Carleton University, Ottawa, Ont., Canada
Zalesskii, P., University of Brasilia, Brazil
Profinite Groups
2000. Approx 450 pp.
3-540-66986-8
The aim of this book is to serve both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. The book is reasonably self-contained. Profinite groups are Galois groups. As such
they are of interest in algebraic number theory. Much of recent research on abstract infinite groups is related to profinite groups because residually finite groups are naturally embedded in a profinite group. In addition to basic facts about general profinite groups, the book emphasizes free constructions (particularly free profinite groups and the structure of their subgroups). Homology and cohomology is described with a minimum of prerequisites.
Keywords: Profinite group, Galois group, cohomology
Contents: Inverse and Direct Limits.- Profinite Groups.- Free Profinite Groups.- Some Special Profinite
Groups.- Discrete and Profinite Modules.- Homology and Cohomology of Profinite Groups.- Cohomological
Dimension.- Normal Subgroups of Free Pro-C Groups.- Free Constructions.- Open Questions.- Appendix.-
Bibliography.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in
Mathematics.VOL. 40
Fields: Group Theory; Topological Groups, Lie Groups, Lie Algebra; Number Theory
Written for: Group theorists, number theorists, algebraists, topologists
Book category: Monograph
Publication language: English