Series: Algorithms and Computation in Mathematics, Vol. 2
1st ed. 1998. Corr. 2nd printing, 2004, XIII, 408 p., Softcover
ISBN: 3-540-21311-2
This ACM volume deals with tackling problems that can be
represented by data structures which are essentially matrices
with polynomial entries, mediated by the disciplines of
commutative algebra and algebraic geometry. The discoveries stem
from an interdisciplinary branch of research which has been
growing steadily over the past decade. The author covers a wide
range, from showing how to obtain deep heuristics in a
computation of a ring, a module or a morphism, to developing
means of solving nonlinear systems of equations - highlighting
the use of advanced techniques to bring down the cost of
computation. Although intended for advanced students and
researchers with interests both in algebra and computation, many
parts may be read by anyone with a basic abstract algebra course.
Table of contents
Fundamental Algorithms.- Toolkit.- Principles of Primary
Decomposition.- Computing in Artin Algebras.- Nullstellensatze.-
Integral Closure.- Ideal Transforms and Rings of Invariants.-
Computation of Cohomology (by David Eisenbud).- Degrees of
Complexity of a Graded Module.- Appendix A. A Primer on
Commutative Algebra.- Appendix B. Hilbert Functions (by Jurgen
Herzog).- Appendix C. Using Macaulay 2 (by David Eisenbud, Daniel
Grayson and Michael Stillman).- Bibliography.- Index.
Series: Algorithms and Computation in Mathematics, Vol. 1
2004, approx. 330 p. 3 illus., Hardcover
ISBN: 3-540-21493-3
Symbolic Integration I is destined to become the standard
reference work in the field. Manuel Bronstein is a leading expert
on this topic and his book is the first to treat the subject both
comprehensively and in sufficient detail - incorporating new
results along the way. The book addresses mathematicians and
computer scientists interested in symbolic computation,
developers and programmers of computer algebra systems as well as
users of symbolic integration methods. Many algorithms are given
in pseudocode ready for immediate implementation, making the book
equally suitable as a textbook for lecture courses on symbolic
integration. This second edition offers a new chapter on the
Risch-Norman algorithm, a number of other improvements and a
couple of additional exercises. From the reviews of the first
edition: "... The writing is excellent, and the author
provides a clear and coherent treatment of the problem of
symbolic integration of transcendental functions…" F.
Winkler, Computing Reviews 1997
Table of contents
Preface.- Algebraic Preliminaries.- Integration of Rational
Functions.- Differential Fields.- The Order Function.-
Integration of Transcendental Functions.- The Risch Differential
Equations.- Parametric Problems.- The Coupled Differential System.-
Structure Theorems; References.- Index.- Plus Chapter on Risch-Noman
Algorithm
2004, Approx. 190 p., Hardcover
ISBN: 3-211-20995-6
The papers in this book originate from lectures which were held
at the ?Vienna Workshop on Nonlinear Models and Analysis“ ? May
20?24, 2002. They represent a cross-section of the research field
Applied Nonlinear Analysis with emphasis on free boundaries,
fully nonlinear partial differential equations, variational
methods, quasilinear partial differential equations and nonlinear
kinetic models.
Table of contents
On the Curvature of the Free Boundary for the Obstacle Problem in
Two Dimensions (B. Gustafsson, M. Sakai) Nonlinear Free Boundary
Problems with Singular Source Terms (A. Hakobyan, A. Karakhanyan)
Behavior of the Free Boundary Near Contact Points with the Fixed
Boundary for Nonlinear Elliptic Equations (N. Matevosyan, P.
Markowich) Global Solutions of an Obstacle-Problem-Like Equation
With Two Phases (H. Shahgholian, N. Uraltseva, G. S. Weiss)
Entropies and Equilibria of Many-Particle Systems: An Essay on
Recent Research (A. Arnold, J. A. Carrillo, L. Desvillettes, A.
Jungel, C. Lederman, P. A. Markowich, G. Toscani, C. Villani) On
the Blow-Up Set for ut = (um)xx, m > 1, with Nonlinear
Boundary Conditions (M. C. Cortazar, M. Elgueta, O. Venegas) A
Phase Plane Analysis of the “Multi-Bubbling” Phenomenon in
Some Slightly Supercritical Equations (M. del Pino, J. Dolbeault,
M. Musso) The Dirichlet Problem for the Porous Medium Equation in
Bounded Domains. Asymptotic Behavior (J. L. Vazquez) A Note on
Deformations of 2D Fluid Motions Using 3D Born-Infeld Equations (Y.
Brenier) Kinetic Models for Chemotaxis and their Drift-Diffusion
Limits (F. A. C. C. Chalub, P. Markowich, B. Perthame, C.
Schmeiser) Rotating Charge Coupled to the Maxwell Field:
Scattering Theory and Adiabatic Limit (V. Imaikin, A. Komech, H.
Spohn) On Hyperbolic Variational Inequalities of First Order and
Some Applications (J. F. Rodrigues) Kinetic and Hydrodynamic
Models of Nearly Elastic Granular Flows (G. Toscani)