Cos 594d: a Theorist’s Toolkit
نویسنده
چکیده
These are edited lecture notes from a graduate course at the Computer Science department of Princeton University in Fall 2002. The course was my attempt to teach first year graduate students students many mathematical tools useful in theoretical computer science. Of course, the goal was too ambitious for a course with 12 three hour lectures. I had to relegate some topics to homework; these include online algorithms, Yao’s lemma as a way to lowerbound randomized complexity, Madhu Sudan’s list decoding algorithm (useful recently in complexity theory and pseudorandomness), and pseudorandom properties of expander graphs. If I had time for another lecture I would have covered basic information theory. To put the choice of topics in context, I should mention that our theory grads take a two semester course sequence on Advanced Algorithm Design and Complexity Theory during their first year, and I did not wish to duplicate topics covered in them. Inevitably, the choice of topics —especially the final two chapters— also reflected my own current research interests. The scribe notes were written by students, and I have attempted to edit them. For this techreport I decided to reshuffle material for coherence, and so the scribe names given with each chapter does not completely reflect who wrote that chapter. So I will list all the scribes here and thank them for their help: Tony Wirth, Satyen Kale, Miroslav Dudik, Paul Chang, Elad Hazan, Elena Nabieva, Nir Ailon, Renato F. Werneck, Loukas Georgiadis, Manoj M.P., and Edith Elkind. I hope the course was as much fun for them as it was for me. Sanjeev Arora March 2003
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