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Are current testing practices consistent with the goals of the reform movement in school mathematics? If not, what are the alternatives? How can authentic performance in mathematics be assessed? These and similar questions about tests and their uses have forced those advocating change to examine the way in which mathematical performance data is gathered and used in American schools. This book provides recent views on the issues surrounding mathematics tests, such as the need for valid performance data, the implications of the Curriculum and Evaluation Standards for School Mathematics for test development, the identification of valid items and tests in terms of the Standards, the procedures now being used to construct a sample of state assessment tests, gender differences in test taking, and methods of reporting student achievement.
This volume is the Proceedings of the Third Korea-China-Japan Inter national Symposium on Ring Theory held jointly with the Second Korea Japan Joint Ring Theory Seminar which took place at the historical resort area of Korea, Kyongju, June 28-July 3, 1999. It also includes articles by some invited mathematicians who were unable to attend the conference. Over 90 mathematicians from 12 countries attended this conference. The conference is held every 4 years on a rotating basis. The first con ference was held in 1991 at Guilin, China. In 1995 the second conference took place in Okayama, Japan. At the second conference it was decided to include Korea, who hosted this conference of 1999. During the past century Ring Theory has diversified into many subar eas. This is reflected in these articles from over 25 well-known mathemati cians covering a broad range of topics, including: Classical Ring Theory, Module Theory, Representation Theory, and the theory of Hopf Algebras. Among these peer reviewed papers are invited survey articles as well as research articles. The survey articles provide an overview of various areas for researchers looking for a new or related field to investigate, while the research articles give the flavor of current research. We feel that the variety of related topics will stimulate interaction between researchers. Moreover the Open Problems section provides guidance for future research. This book should prove attractive to a wide audience of algebraists. Gary F. Birkenmeier, Lafayette, U. S. A.
This book is a collection of essays on iterative algorithms and their uses. It focuses on the mathematics of medical image reconstruction, with emphasis on Fourier inversion. The book discusses the problems and algorithms in the context of operators on finite-dimensional Euclidean space.
Learn How to Program Stochastic ModelsHighly recommended, the best-selling first edition of Introduction to Scientific Programming and Simulation Using R was lauded as an excellent, easy-to-read introduction with extensive examples and exercises. This second edition continues to introduce scientific programming and stochastic modelling in a clear,
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
This book provides an introduction to the ideas and methods of linear func tional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the ory of metric spaces). Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa tions. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set. In general, such a vector space is infinite-dimensional. This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite dimensional vector spaces, many others do not. For example, in general infinite dimensional vector spaces there is no framework in which to make sense of an alytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now briefly outline the contents of the book.
After an introduction to the subject area and a concise treatment of the technical foundations for the subsequent chapters, this book features 14 chapters on state-of-the-art graph drawing software systems, ranging from general "tool boxes'' to customized software for various applications. These chapters are written by leading experts: they follow a uniform scheme and can be read independently from each other. The text covers many industrial applications.
Cluster Analysis for Applications deals with methods and various applications of cluster analysis. Topics covered range from variables and scales to measures of association among variables and among data units. Conceptual problems in cluster analysis are discussed, along with hierarchical and non-hierarchical clustering methods. The necessary elements of data analysis, statistics, cluster analysis, and computer implementation are integrated vertically to cover the complete path from raw data to a finished analysis. Comprised of 10 chapters, this book begins with an introduction to the subject of cluster analysis and its uses as well as category sorting problems and the need for cluster analysis algorithms. The next three chapters give a detailed account of variables and association measures, with emphasis on strategies for dealing with problems containing variables of mixed types. Subsequent chapters focus on the central techniques of cluster analysis with particular reference to computational considerations; interpretation of clustering results; and techniques and strategies for making the most effective use of cluster analysis. The final chapter suggests an approach for the evaluation of alternative clustering methods. The presentation is capped with a complete set of implementing computer programs listed in the Appendices to make the use of cluster analysis as painless and free of mechanical error as is possible. This monograph is intended for students and workers who have encountered the notion of cluster analysis.
The field of Artificial Intelligence has changed a great deal since the 80s, and arguably no one has played a larger role in that change than Judea Pearl. Judea Pearl's work made probability the prevailing language of modern AI and, perhaps more significantly, it placed the elaboration of crisp and meaningful models, and of effective computational mechanisms, at the center of AI research. This book is a collection of articles in honor of Judea Pearl, written by close colleagues and former students. Its three main parts, heuristics, probabilistic reasoning, and causality, correspond to the titles of the three ground-breaking books authored by Judea, and are followed by a section of short reminiscences. In this volume, leading authors look at the state of the art in the fields of heuristic, probabilistic, and causal reasoning, in light of Judea's seminal contributors. The authors list include Blai Bonet, Eric Hansen, Robert Holte, Jonathan Schaeffer, Ariel Felner, Richard Korf, Austin Parker, Dana Nau, V. S. Subrahmanian, Hector Geffner, Ira Pohl, Adnan Darwiche, Thomas Dean, Rina Dechter, Bozhena Bidyuk, Robert Matescu, Emma Rollon, Michael I. Jordan, Michael Kearns, Daphne Koller, Brian Milch, Stuart Russell, Azaria Paz, David Poole, Ingrid Zukerman, Carlos Brito, Philip Dawid, Felix Elwert, Christopher Winship, Michael Gelfond, Nelson Rushton, Moises Goldszmidt, Sander Greenland, Joseph Y. Halpern, Christopher Hitchcock, David Heckerman, Ross Shachter, Vladimir Lifschitz, Thomas Richardson, James Robins, Yoav Shoham, Peter Spirtes, Clark Glymour, Richard Scheines, Robert Tillman, Wolfgang Spohn, Jian Tian, Ilya Shpitser, Nils Nilsson, Edward T. Purcell, and David Spiegelhalter.
This volume contains the lectures and communications presented at the NATO Advanced Research Workshop (NATO ARW 900857) which was held May 5-10, 1991 at McMaster University, Hamilton, Ontario, Canada. A scientific commitee made up of P.P. Lambropoulos (USC & Crete), P.8. Corkum (NRC, Ottawa), and H. B. vL. van den Heuvell (FOM, Amsterdam) guided the organizers, A.D. Bandrauk (Sherbrooke) and S.C. Wallace (Toronto) in preparing a programme which would cover the latest advances in the field of atom and molecule laser interactions. Since the last meeting held in July 1987 on "Atomic and Molecular Processes with Short Intense Laser Pulses", NATO ASI vol 1718 (Plenum Press 1988), considerable progress has been made in understanding high intensity effects on atoms and the concomitant coherence effects. After four years, the emphasis is now shifting more to molecules. The present volume represents therefore this trend with four sections covering the main interests of research endeavours in this area: i) Atoms in Intense Laser-Fields ii) Molecules in Intense Laser Fields iii) Atomic Coherences iv) Molecular Coherences The experience developed over the years in multiphoton atomic processes has been very useful and is the main source of our understanding of similar processes in molecules. Thus ATI (above threshold ionization) has been found to occur in molecules as well as a new phenomenon, ATD (above-threshold dissociation). Laser-induced avoided crossings of molecular electronic surfaces is also now entering the current language of high intensity molecular processes.