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Midterm Review. CSC 172 SPRING 2002 LECTURE 15. Diversity.
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Midterm Review CSC 172 SPRING 2002 LECTURE 15
Diversity The Faculty of the College affirms that diversity, pluralism, and respect for difference are fundamental values in our community. Learning cannot advance in an atmosphere of prejudice or intimidation. All members of our community -- regardless of culture, religion, gender, or sexual orientation -- are entitled to learn and work in an environment of civility, dignity, fairness, and mutual respect. As a faculty, we condemn recent events on campus that exhibit bigotry, insensitivity to life, and hostility toward people on the basis of their ethnicity, religion, or sexual orientation. These malevolent behaviors and attitudes undermine our collective work and have no place in our community of learning. As scholars, we encourage one another -- and as teachers we encourage our students -- to reject these expressions of intolerance and work together to build the kind of open community that makes authentic learning possible. We cannot afford to be indifferent. We must speak out against these deplorable expressions. We must expect better of ourselves and of one another. Thank you, Sanford L. Segal Chair of the Faculty Council Steering Committee
Freedom of thought Do people have the right to hold wrong opinions? Do we tolerate intolerance? Treating people decently does not imply approval.
Professionalism People have both public and private lives Sort of like public and private interfaces public life provides a context for social interaction public life is to some degree regulated (laws, cultures) We often deal with people with whom we disagree because we can share purposes with people Professionalism allows us to maintain a workable public interface with diverse people Tolerance (public) does not imply that you agree (private) So, it is possible to maintain both workable social relationships and individual freedom of thought
Scholarship Being a member of the university community implies a shared objective – a public society The tradition of scholarship is a tradition of openness This implies having the courage to take credit for your statements Having to take credit for your statements tends to “raise the level of discussion”
General Recurrence Relations The solution to T(n) = aT(n/b) + O(nk)
Proof Assume T(1) = 1 Assume n is a power of b n = bm n/b = bm-1 nk = (bm)k = bmk = bkm = (bk)m So, T(bm) = aT(bm-1) + (bk)m
a>bk The sum is a geometric series with ratio < 1 Since the sum of such an infinite series would converge to a constant, the finite sum is also bound by a constant
a=bk Each term of the sum is 1 The sum contains 1+logbn terms a=bk implies logba = k
a<bk The sum is a geometric series with ratio > 1
(Aside) Prove by induction on n:
Chuck-a-Luck Show that in Chuck-a-Luck, the probability of any event in which all three dice have different values is twice the probability of any event where one number appears exactly twice and six times the probability of any event in which all three dice show the same number.
Chuck-a-Luck Show that in Chuck-a-Luck, the probability of any event in which all three dice have different values is twice the probability of any event where one number appears exactly twice and six times the probability of any event in which all three dice show the same number.
Chuck-a-Luck An event is a unique throw of the dice There are 6 different events of all the same number P(all 1s) = 1/216 P(all 2s) = 1/216 … P(all 6s) = 1/216
Chuck-a-Luck There are 120 events where all the numbers are distinct 6*5*4 But some are indistinguishable There are 6 ways to arrange 3 items P(any event where all numbers different) = 6/216 So,
Chuck-a-Luck There are 30 different ways of getting the same number exactly twice 6*5 For each event (say 2 “1s”, and one “2”) there are 3 ways to get it ((1,1,2),(1,2,1),(2,1,1)) P(any event where one number appears twice) = 3/216
Error Correcting Codes If no two strings in a code differ in fewer than three positions, then we can actually correct a single error, by finding the unique string in the code that differes from the received string in only one position. It turns out that there is a code of 7 bit string that corrects single errors and contains 16 strings. Find such a code.
Error Correcting Codes 0000 and 0001 differ by 1 0000 and 0011 differ by 2 0000 and 0111 differ by 3 So, if I only allowed 0000 and 0111 and there was only one “error”, then I could always recover 0001,0010,0100,1000 -> 0000 1111,0011,0101,0110 -> 0111
Linked Lists (code) Stacks (algs) Queues (algs) Proof by induction (section) Recurrence Relations (math) Big-Oh (section) Run time of code segments Combinatorics (section) Probability Recursion (QS,MS, etc) So, what’s on the exam? (180 min)
Homework Solutions http://www.cs.rochester.edu/~pawlicki/lectures/CSC172
When and where is the exam Friday March 8th 8AM-11AM, 632 CSB – 4 students 2PM-5PM, 115 Harkness
