CIS 615 | Design and Analysis of Algorithms | Spring 2007 |
Monday 4:40-7:10pm | Tuttleman 302 |
Teacher and media critic John Maguire wrote:
I think many kids (speaking of freshmen I have taught) today "understand" that the world is an untrustworthy place, that their own minds are untrustworthy, that they must rely on others to explain things to them and the explanations are wormy with self-interest, and that someone else is in charge of everything that matters, and that the truth is not inside them but "out there" and endlessly evasive.I suspect that many of my students (even graduate students) feel the same way. No authority (including me) has a monopoly on truth. At the same time, a small dose of self-doubt is good for healthy thought. Learn to check your own work and criticize your own thinking. Master logic and apply it carefully; then you will be able to find the truth inside yourself, and you won't need anyone to tell you when you are right.
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Define h_{b}(x) = (Σx_{i}b^{i}) mod p. Prove that for every pair of distinct x and y, the probability that h_{b}(x) = h_{b}(y) is less than n/p when b is chosen at random.