DIMACS: Series in Discrete Mathematics and Theoretical Computer Science 2003; 219 pp; hardcover Volume: 60 ISBN10: 0821828630 ISBN13: 9780821828632 List Price: US$80 Member Price: US$64 Order Code: DIMACS/60
 Algorithmic and quantitative aspects in real algebraic geometry are becoming increasingly important areas of research because of their roles in other areas of mathematics and computer science. The papers in this volume collectively span several different areas of current research. The articles are based on talks given at the DIMACS Workshop on "Algorithmic and Quantitative Aspects of Real Algebraic Geometry". Topics include deciding basic algebraic properties of real semialgebraic sets, application of quantitative results in real algebraic geometry towards investigating the computational complexity of various problems, algorithmic and quantitative questions in real enumerative geometry, new approaches towards solving decision problems in semialgebraic geometry, as well as computing algebraic certificates, and applications of real algebraic geometry to concrete problems arising in robotics and computer graphics. The book is intended for researchers interested in computational methods in algebra. Copublished with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 17 were copublished with the Association for Computer Machinery (ACM). Readership Graduate students and research mathematicians interested in algebra and algebraic geometry and their applications. Table of Contents  C. Andradas  Characterization and description of basic semialgebraic sets
 D. Bailey and V. Powers  Constructive approaches to representation theorems in finitely generated real algebras
 I. Bonnard  Combinatorial characterizations of algebraic sets
 P. Bürgisser  Lower bounds and real algebraic geometry
 B. Chevallier  The Viro method applied with quadratic transforms
 A. Gabrielov and T. Zell  On the number of connected components of the relative closure of a semiPfaffian family
 C. McCrory  How to show a set is not algebraic
 P. A. Parrilo and B. Sturmfels  Minimizing polynomial functions
 B. Reznick  Patterns of dependence among powers of polynomials
 F. Rouillier  Efficient algorithms based on critical points method
 F. Sottile  Enumerative real algebraic geometry
 I. Streinu  Combinatorial roadmaps in configuration spaces of simple planar polygons
 T. Theobald  Visibility computations: From discrete algorithms to real algebraic geometry
