The papers in this volume grew out of a year-long program in "Real Algebraic Geometry and Quadratic Forms", held at the University of California at Berkeley during the 1990--1991 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 sub-disciplines and indications of new research directions.
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