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“Near-Optimal Time-Space Tradeoff for Element Distinctness,”

The raw material for this book is the fruit of the labors of many hundreds of people who have sought to understand computation. It is a great privilege to have the opportunity to convey this exciting body of material to a new audience. Because the writing of a book involves years of solitary work, it is far too easy for authors to lose sight of their audience. For this reason I am indebted to a number of individuals who have read my book critically. Jose G. Casta ´ nos, currently a Brown Ph.D. candidate and my ˜ advisee, has been of immense help to me in this regard. He has read many drafts of the book and has given me the benefit of his keen sense of what is acceptable to my readers. Jose has ´ also served as a teaching assistant for the undergraduate theory course for which this book was used and contributed importantly to the course and the book in this capacity. Dimitrios Michailidis, also a Brown Ph.D. candidate, has also been a great help; he has read several drafts of the book and has spotted many errors and lacunae. Bill Smart, a third Brown Ph.D. candidate, also carefully read the first nine chapters. I have also benefited greatly from the evaluations done for my publisher by Richard Chang, University of Maryland, Baltimore County; Michael A. Keenan, Columbus State University; Philip Lewis, State University of New York, Stony Brook; George Lukas, University of Massachusetts at Boston; Stephen R. Mahaney, Rutgers University; Friedhelm Meyer auf der Heide, University of Paderborn, Germany; Boleslaw Mikolajczak, University of Massachusetts, Dartmouth; Ramamohan Paturi, University of California, San Diego; Professor Gabriel Robins, and Jeffery Westbrook, AT&T Labs–Research. Others, including Ray Greenlaw of the University of New Hampshire, read an early version of the manuscript for other publishers and offered valuable advice. Gary Rommel of the Eastern Connecticut State College and the Hartford Graduate Center provided feedback on classroom use of the book. Finally, I am indebted to students in my undergraduate and graduate courses at Brown whose feedback has been invaluable