15-251Great Theoretical Ideas in Computer Science“Von Ahn mocked Intelligent Design in one of the first lectures , which deeply offended me”251 is like: “we’re gonna kick your ass and you’re gonna enjoy it”.“Awesome, despite soul-crushing homework”15-251 Course Evaluations: Student CommentsAnd we did!“sadistic”“von Ahn > Chuck Norris”15-251Great Theoretical Ideas in Computer ScienceforSomewww.cs.cmu.edu/~15251Course StaffInstructorsLuis von AhnAnupam GuptaTAsAnton BachinDrew BesseMichelle BurroughsAndrew KriegerAlan PierceDaniel SchaferNicholas TanDavid YangHomework35%Final25%In-Class Quizzes5%3 In-Recitation Tests 30%Participation5%GradingDr. 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 HomeworkTen points per day late penaltyNo homework will be accepted more than three days lateHomework will go out every week and be due the next weekHomework MUST be typesetCollaboration + CheatingYou may NOT share written workYou may NOT use Google, or solutions to previous years’ homeworkYou MUST sign the class honor codeTextbookThere is NO textbook for this classWe have class notes in wiki formatYou too can edit the wiki!!!((( )))Feel free to ask questionsBits 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 handcuffsSteven Pinker“How the Mind Works”Our brains can perform simple, concrete tasks very wellAnd that’s how math should be approached!Draw simple picturesTry out small examples of the problem: What happens for n=1? n=2?Substitute concrete values for the variables: x=0, x=100, …Terry Tao (Fields Medalist, considered to be the best problem solver in the world)“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.”ExpertNoviceThe better the problem solver, the less brain activity is evident. The real masters show almost no brain activity!Simple and to the pointUse 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 NumbersAlice BobAlice starts: …| A - B | = 1Hats with Consecutive NumbersAlice BobAlice starts: …| A - B | = 1 and A, B > 0I don’t know what my number is(round 1)Hats with Consecutive NumbersAlice BobAlice starts: …| A - B | = 1 and A, B > 0I don’t know what my number is(round 2)Hats with Consecutive NumbersAlice BobAlice starts: …| A - B | = 1 and A, B > 0I don’t know what my number is(round 3)Hats with Consecutive NumbersAlice BobAlice starts: …| A - B | = 1 and A, B > 0I don’t know what my number is(round 4)…Hats with Consecutive NumbersAlice BobAlice starts: …| A - B | = 1 and A, B > 0I know what my number is!!!!!!!!(round 251)Hats with Consecutive NumbersAlice BobAlice starts: …| A - B | = 1 and A, B > 0I know what my number is!!!!!!!!(round 252)Question: What are Alice and Bob’s numbers?Imagine Alice Knew Right AwayAlice BobI know what my number is!!!!!!!!Then A = 2 and B = 1| A - B | = 1 and A, B > 0(round 1)1,2 N,Y2,1 Y2,3 N,Y3,2 N,N,Y3,4 N,N,N,Y4,3 N,N,Y4,5 N,N,N,YInductive ClaimClaim: 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, pleaseRelaxI am just going to ask you a Microsoft interview questionFour 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 issueFour 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-ProofingAs you talk to yourself, make sure to tag assertions with phrases that denote degrees of convictionKeep 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 laterWe start with 1 and X and then X returns Total time:Thus, we start with 1,2 go over and 2 comes back….2X1 2 5 101 2 5 101 2 5 105 10 2 11 2 5 105 10 2 11 2 5 105 102 5 102 111 2 5 105 102 5 102 111 2 5 105 102 5 1022 111 5 101 2 5 105 102 5 1022
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