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 Contemporary Mathematics 2013; 185 pp; softcover Volume: 604 ISBN-10: 0-8218-9150-2 ISBN-13: 978-0-8218-9150-6 List Price: US$76 Member Price: US$60.80 Order Code: CONM/604 Not yet published.Expected publication date is January 6, 2014. This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluís Santaló Summer School on "Recent Advances in Real Complexity and Computation", held July 16-20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: "Can a zero of $$n$$ complex polynomial equations in $$n$$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?" These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving. This book is published in cooperation with Real Sociedad Matemática Española (RSME). Readership Graduate students and research mathematicians interested in the complexity of computation. Table of Contents M. Baartse and K. Meer -- Topics in real and complex number complexity theory B. Bank, M. Giusti, and J. Heintz -- Polar, bipolar and copolar varieties: Real solving and algebraic varieties with intrinsic complexity C. Beltrán and M. Shub -- The complexity and geometry of numerically solving polynomial systems M. Giusti and J.-C. Yakoubsohn -- Multiplicity hunting and approximating multiple roots of polynomials systems J. Heintz, B. Kuijpers, and A. R. Paredes -- On the intrinsic complexity of elimination problems in effective algebraic geometry G. Malajovich -- Newton iteration, conditioning and zero counting