David Breen, Donald House
Cloth Modeling and Animation
Written by leaders in the field of computer clothing design and simulation, Cloth
Modeling and Animation is a vital resource for researchers and developers of cloth
simulation software as well as computer animators and graphics programmers.
Readers will learn about cloths nature and structure, scientific approaches to
understanding its behavior and look, and the latest modeling and simulation
techniques for automatically animating cloth on the computer. Topics covered
include drape models, dynamic models, woven and knit fabrics, and appearance
models. A special section describes the use of simulated cloth in several recent
feature films and animations.
Year: 2000 ISBN: 1-56881-090-3
300 pages. Hardcover.
Curtis McKnight, Andy Magid, and Teri J. Murphy
Mathematics Education Research: A Guide for the Research Mathematician
Description
Mathematics education research in undergraduate mathematics has increased significantly in the last decade and shows no signs of abating in the near future. Thus far, this research has often been associated with innovations in curriculum such as calculus reform, statistics education, and the use of computational and graphing technology in instruction.
Carefully conducted mathematics education research is something far more fundamental and widely useful than might be implied by its use by the advocates of innovation in undergraduate mathematics education. Most simply, mathematics education research is inquiry by carefully developed research methods aimed at
providing evidence about the nature and relationships of many mathematics learning and teaching phenomena. It seeks to clarify the phenomena, illuminate them, explain how they are related to other phenomena, and explain how this may be related to undergraduate mathematics course organization and teaching.
This book--the collaborative effort of a research mathematician, mathematics education researchers who work in a research mathematics department and a professional librarian--introduces research mathematicians to education research. The work presents a non-jargon introduction for educational research, surveys the
more commonly used research methods, along with their rationales and assumptions, and provides background and careful discussions to help research mathematicians read or listen to education research more critically.
This guide is of practical interest to university-based research mathematicians. It introduces the methodology of quantitative and qualitative research in education, provides critical guidelines for assessing the reliability and validity of mathematics education research, and explains how to use online database resources to locate
education research. The book will also be valuable to graduate students in mathematics who are planning academic careers, and to mathematics department chairs and their deans.
Contents
Evidence-based pedagogy
Recognizing research
Quantitative research
Critiquing quantitative research
Reliability and validity in quantitative research
A survey of statistical methods
Qualitative research
Critiquing qualitative research
Reliability and validity in qualitative research
A survey of qualitative methods
Using mathematics education research appropriately
Teaching experiments, quasi-experimental research, and threats to validity
Evaluation, assessment, and research
Finding research: The literature search
From consumer to producer
References
Details:
Publication Year: 2000
ISBN: 0-8218-2016-8
Paging: 106 pp.
Binding: Softcover
Judy L. Walker, University of Nebraska, Lincoln, NE
Codes and Curves
Description
When information is transmitted, errors are likely to occur. This problem has become increasingly important as tremendous amounts of information are transferred electronically every day. Coding theory examines efficient ways of packaging data so that these errors can be detected, or even corrected.
The traditional tools of coding theory have come from combinatorics and group theory. Since the work of Goppa in the late 1970s, however, coding theorists have added techniques from algebraic geometry to their toolboxes. In particular, by re-interpreting the Reed-Solomon codes as coming from evaluating functions
associated to divisors on the projective line, one can see how to define new codes based on other divisors or on other algebraic curves. For instance, using modular curves over finite fields, Tsfasman, Vladut, and Zink showed that one can define a sequence of codes with asymptotically better parameters than any previously
known codes.
This monograph is based on a series of lectures the author gave as part of the IAS/PCMI program on arithmetic algebraic geometry. Here, the reader is introduced to the exciting field of algebraic geometric coding theory. Presenting the material in the same conversational tone of the lectures, the author covers linear codes, including cyclic codes, and both bounds and asymptotic bounds on the parameters of codes. Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. The construction of algebraic geometric codes is given, and the Tsfasman-Vladut-Zink result mentioned above is
discussed.
No previous experience in coding theory or algebraic geometry is required. Some familiarity with abstract algebra, in particular finite fields, is assumed. However, this material is reviewed in two appendices. There is also an appendix containing projects that explore other codes not covered in the main text.
Contents
Introduction to coding theory
Bounds on codes
Algebraic curves
Nonsingularity and the genus
Points, functions, and divisors on curves
Algebraic geometry codes
Good codes from algebraic geometry
Abstract algebra review
Finite fields
Projects
Bibliography
Details:
Series: Student Mathematical Library, Volume: 7
Publication Year: 2000
ISBN: 0-8218-2628-X
Paging: 66 pp.
Binding: Softcover
Edited by: Decio Levi, University of Rome I, Italy,
and Orlando Ragnisco, University of Rome III, ItalySIDE III--Symmetries and Integrability of Difference Equations
Description
This volume contains the proceedings of the third meeting on "Symmetries and Integrability of Difference Equations" (SIDE III). The collection includes originalresults not published elsewhere and articles that give a rigorous but concise overview of their subject, and provides a complete description of the state of the art.
Research in the field of difference equations--often referred to more generally as discrete systems--has undergone impressive development in recent years. In this collection the reader finds the most important new developments in a number of areas, including: Lie-type symmetries of differential-difference and
difference-difference equations, integrability of fully discrete systems such as cellular automata, the connection between integrability and discrete geometry, the isomonodromy approach to discrete spectral problems and related discrete PainlevEequations, difference and q-difference equations and orthogonal polynomials, difference equations and quantum groups, and integrability and chaos in discrete-time dynamical systems.
The proceedings will be valuable to mathematicians and theoretical physicists interested in the mathematical aspects and/or in the physical applications of discrete nonlinear dynamics, with special emphasis on the systems that can be integrated by analytic methods or at least admit special explicit solutions. The research in this volume will also be of interest to engineers working in discrete dynamics as well as to theoretical biologists and economists.
Details:
Series: CRM Proceedings & Lecture Notes, Volume: 25
Publication Year: 2000
ISBN: 0-8218-2128-8
Paging: 444 pp.
Binding: Softcover
Lindsay N. Childs, State University of New York at Albany, NY
Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory
Description
This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory.
Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether's theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness
and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic
extensions of local fields of degree $p$ and $p^2$; and Kummer theory of formal groups.
Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory. From there, this exposition serves as an excellent resource and motivation for further work in the field.
Contents
Introduction
Hopf algebras and Galois extensions
Hopf Galois structures on separable field extensions
Tame extensions and Noether's theorem
Hopf algebras of rank $p$
Larson orders
Cyclic extensions of degree $p$
Non-maximal orders
Ramification restrictions
Hopf algebras of rank $p^2$
Cyclic Hopf Galois extensions of degree $p^2$
Formal groups
Principal homogeneous spaces and formal groups
Bibliography
Index
Details:
Series: Mathematical Surveys and Monographs, Volume: 80
Publication Year: 2000
ISBN: 0-8218-2131-8
Paging: 215 pp.
Binding: Hardcover
Michael E. Taylor, University of North Carolina, Chapel Hill, NC
Tools for PDE: Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials
Description
This book develops three related tools that are useful in the analysis of partial differential equations (PDEs), arising from the classical study of singular integral operators: pseudodifferential operators, paradifferential operators, and layer potentials.
A theme running throughout the work is the treatment of PDE in the presence of relatively little regularity. The first chapter studies classes of pseudodifferential operators whose symbols have a limited degree of regularity; the second chapter shows how paradifferential operators yield sharp estimates on the action of various nonlinear operators on function spaces. The third chapter applies this material to an assortment of results in PDE, including regularity results for elliptic PDE with rough coefficients, planar fluid flows on rough domains, estimates on Riemannian manifolds given weak bounds on Ricci tensor, div-curl estimates, and results on
propagation of singularities for wave equations with rough coefficients. The last chapter studies the method of layer potentials on Lipschitz domains, concentrating on applications to boundary problems for elliptic PDE with variable coefficients.
Michael Taylor is the author of several well-known books on topics in PDEs and pseudodifferential operators. His "Noncommutative Harmonic Analysis", Volume 22 in the Mathematical Surveys and Monographs series published by the AMS, is a good introduction to the use of Lie groups in linear analysis and PDEs.
The present book, Tools for PDE, is suitable as a text for advanced graduate students preparing to concentrate in PDE and/or harmonic analysis.
Contents
Pseudodifferential operators with mildly regular symbols
Paradifferential operators and nonlinear estimates
Applications to PDE
Layer potentials on Lipschitz surfaces
Bibliography
List of symbols
Index
Details:
Series: Mathematical Surveys and Monographs, Volume: 81
Publication Year: 2000
ISBN: 0-8218-2633-6
Paging: 257 pp.
Binding: Hardcover