15 251 Great Theoretical Ideas in Computer Science 15 251 Course Evaluations Student Comments sadistic 251 is like we re gonna kick your ass and you re gonna enjoy it And we did Awesome despite soul crushing homework Von Ahn mocked Intelligent Design in one of the first lectures which deeply offended me von Ahn Chuck Norris 15 251 Some Great Theoretical Ideas in Computer Science for www cs cmu edu 15251 Course Staff Instructors TAs Luis von Ahn Anupam Gupta Anton Bachin Drew Besse Michelle Burroughs Andrew Krieger Alan Pierce Daniel Schafer Nicholas Tan David Yang Grading Homework 35 Final 25 Participation 5 3 In Recitation Tests 30 In Class Quizzes 5 Dr von Ahn I know my grade is a 42 100 and according to the class Web site that is an F Is there an alternative grading scheme by which I can get a C Dear X As a matter of fact there are infinitely many alternative grading schemes by which you would get a C with a 42 100 Unfortunately for you I will not use any of them Weekly Homework Homework will go out every week and be due the next week Ten points per day late penalty No homework will be accepted more than three days late Homework MUST be typeset Collaboration Cheating You may NOT share written work You may NOT use Google or solutions to previous years homework You MUST sign the class honor code Textbook There is NO textbook for this class We have class notes in wiki format You too can edit the wiki Feel free to ask questions Bits of Wisdom on Solving Problems Writing Proofs and Enjoying the Pain How to Succeed in This Class Lecture 1 January 13 2009 What did our brains evolve to do What were our brains intelligently designed to do What kind of meat did the Flying Spaghetti Monster put in our heads Our brains did NOT evolve to do math Over the last 30 000 years our brains have essentially stayed the same The human mind was designed by evolution to deal with foraging in small bands on the African Savannah faulting our minds for succumbing to games of chance is like complaining that our wrists are poorly designed for getting out of handcuffs Steven Pinker How the Mind Works Our brains can perform simple concrete tasks very well And that s how math should be approached Substitute concrete values for the variables x 0 x 100 Draw simple pictures Try out small examples of the problem What happens for n 1 n 2 I don t have any magical ability I look at the problem and it looks like one I ve already done When nothing s working out then I think of a small trick that makes it a little better I play with the problem and after a while I figure out what s going on Terry Tao Fields Medalist considered to be the best problem solver in the world Novice Expert The better the problem solver the less brain activity is evident The real masters show almost no brain activity Simple and to the point Use a lot of paper or a board Quick Test Count the green squares you will have three seconds How many were there Hats with Consecutive Numbers A B 1 Alice Alice starts Bob Hats with Consecutive Numbers I don t know what my number is round 1 Alice Bob A B 1 and A B 0 Alice starts Hats with Consecutive Numbers I don t know what my number is round 2 Alice Bob A B 1 and A B 0 Alice starts Hats with Consecutive Numbers I don t know what my number is round 3 Alice Bob A B 1 and A B 0 Alice starts Hats with Consecutive Numbers I don t know what my number is round 4 Alice Bob A B 1 and A B 0 Alice starts Hats with Consecutive Numbers I know what my number is round 251 Alice Bob A B 1 and A B 0 Alice starts Hats with Consecutive Numbers I know what my number is round 252 Alice Bob A B 1 and A B 0 Alice starts Question What are Alice and Bob s numbers Imagine Alice Knew Right Away I know what my number is round 1 Alice Bob A B 1 and A B 0 Then A 2 and B 1 1 2 N Y 2 1 Y 2 3 N Y 3 2 N N Y 3 4 N N N Y 4 3 N N Y 4 5 N N N Y Inductive Claim Claim After 2k NOs Alice knows that her number is at least 2k 1 After 2k 1 NOs Bob knows that his number is at least 2k 2 Hence after 250 NOs Alice knows her number is at least 251 If she says YES her number is at most 252 If Bob s number is 250 her number must be 251 If his number is 251 her number must be 252 Exemplification Try out a problem or solution on small examples Look for the patterns A volunteer please Relax I am just going to ask you a Microsoft interview question Four guys want to cross a bridge that can only hold two people at one time It is pitch dark and they only have one flashlight so people must cross either alone or in pairs bringing the flashlight Their walking speeds allow them to cross in 1 2 5 and 10 minutes respectively Is it possible for them to all cross in 17 minutes Get The Problem Right Given any context you should double check that you read heard it correctly You should be able to repeat the problem back to the source and have them agree that you understand the issue Four guys want to cross a bridge that can only hold two people at one time It is pitch dark and they only have one flashlight so people must cross either alone or in pairs bringing the flashlight Their walking speeds allow them to cross in 1 2 5 and 10 minutes respectively Is it possible for them to all cross in 17 minutes Intuitive But False 10 1 5 1 2 19 so the four guys just can t cross in 17 minutes Even if the fastest guy is the one to shuttle the others back and forth you use at least 10 1 5 1 2 17 minutes Vocabulary Self Proofing As you talk to yourself make sure to tag assertions with phrases that denote degrees of conviction Keep track of what you actually know remember what you merely suspect 10 1 5 1 2 19 so it would be weird if the four guys could cross in 17 minutes even if we use the fastest guy to shuttle the others they take too long If it is possible there must be more than one guy doing the return trips it must be that someone gets deposited on one side and comes back for the return trip later Suppose we leave 1 for a return trip later We …
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