Contemporary Mathematics 1994; 405 pp; softcover Volume: 155 ISBN10: 0821851543 ISBN13: 9780821851548 List Price: US$50 Member Price: US$40 Order Code: CONM/155
 The papers in this volume grew out of a yearlong program in "Real Algebraic Geometry and Quadratic Forms", held at the University of California at Berkeley during the 19901991 academic year. This valuable collection of research articles by top workers serves as a record of current developments in these areas and as a tribute to the fruitful interaction between them. Students and researchers alike will find this book a useful reference, with articles ranging from the technical to the expository. Also included are summaries of the current developments in several subdisciplines and indications of new research directions. Readership Graduate students and researchers in computational algebra and applications of real algebraic geometry. Table of Contents  T. Recio and C. Andradas  D. W. Dubois and the pioneer days of real algebraic geometry
 Papers on real algebraic geometry
 S. Akbulut  On algebraic structures of manifolds
 C. Andradas and J. M. Ruiz  On local uniformization of orderings
 R. Berr  Real algebraic geometry over \(p\)real closed fields
 L. Bröcker  On the reduction of semialgebraic sets by real valuations
 T. C. Craven  Orderings for noncommutative rings
 C. N. Delzell  Nonexistence of analytically varying solutions to Hilbert's 17th problem
 M. A. Dickmann  A combinatorial geometric structure on the space of orders of a field II
 M. J. GonzálezLopez and T. Recio  Formal determination of polynomial consequences of real orthogonal matrices
 R. Huber and M. Knebusch  On valuation spectra
 M. Marshall  Minimal generation of basic sets in the real spectrum of a commutative ring
 A. Pfister  A new proof of the homogeneous nullstellensatz for \(p\)fields, and applications to topology
 M. J. de la Puente  The compatible valuation rings of the coordinate ring of the real plane
 G. Stengle  Estimates for parametric nonuniformity in representations of a definite polynomial as a sum of fourth powers
 Papers on quadratic forms
 J. Kr. Arason, R. Elman, and B. Jacob  On generators for the Witt ring
 E. Becker and T. Wöermann  On the trace formula for quadratic forms
 W. Bichsel and M.A. Knus  Quadratic forms with values in line bundles
 M. Krüskemper  On annihilators in graded Witt rings and in Milnor's \(K\)theory
 K. H. Leung  An application of the theory of order completions
 D. B. Leep and A. S. Merkurjev  Growth of the \(u\)invariant under algebraic extensions
 J. Mináč  Remarks on Merkurjev's investigations of the \(u\)invariant
 R. Parimala and W. Scharlau  On the canonical class of a curve and the extension property for quadratic forms
 R. Parimala and R. Sridharan  Reduced norms and pfaffians via BrauerSeveri schemes
 R. Perlis, K. Szymiczek, P. E. Conner, and R. Litherland  Matching Witts with global fields
 J. Shick  On Wittkernels of function fields of curves
 V. Suresh  On the canonical class of hyperelliptic curves
