tag:blogger.com,1999:blog-8890204.post1483441642133564574..comments2024-03-10T05:26:42.148-04:00Comments on My Biased Coin: Writing a Chapter, and Answering Some QuestionsMichael Mitzenmacherhttp://www.blogger.com/profile/06738274256402616703noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-8890204.post-49918647796415120002008-04-26T07:59:00.000-04:002008-04-26T07:59:00.000-04:00High school sophomores can be highly perceptive if...High school sophomores can be highly perceptive if you give them a problem that is meaningful. I had to work on some trigonometry homework problems with my niece (HS Junior) a couple of weeks back.<BR/><BR/>I wrote something similar to this on <A HREF="http://godplaysdice.blogspot.com" REL="nofollow">Isabel's</A> blog the other day. The idea is that you start with an interesting problem, construct the meaningful abstractions, reason about them, then come back to answer about your concrete problem.<BR/><BR/>In this case, if you want to encourage kids to investigate and understand theory, it might be useful to construct a problem, derive the abstractions, then map those abstractions to [same|[near|not] similar] problems. This demonstrates the two important things, bijective abstract-concrete reasoning, and the importance of looking for the abstract [refactoring your comprehension base].Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8890204.post-80712965881023805372008-04-25T09:20:00.000-04:002008-04-25T09:20:00.000-04:00I think there are completely untapped markets you ...I think there are completely untapped markets you haven't mentioned. By aiming at high school sophomores you are writing at a level that is accessible by anyone vaguely interested in the subject. This includes leagues of business people, older engineers, and those generally interested in problem solving. Lastly, as a graduate student, I would probably grab a copy for my parents to better explain my interests in the form of interesting/meaningful problems. By increasing the general awareness of problems computer scientists are interested in, you still will likely achieve your goal of attracting younger people to the field. Personally I believe explaining the subject via analogy to everyday problems (e.g. TSP) you can make it accessible to many. If you would like a small audience of potential high school students I would be glad to help where possible.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8890204.post-70532534823213186382008-04-24T22:52:00.000-04:002008-04-24T22:52:00.000-04:00anonymous -- I just looked at what I could of the ...anonymous -- I just looked at what I could of the Turning omnibus online. It looks cool. But it looks much more mathematical/deep than I'm expecting. From my quick peek, it looks like it's at the level of college sophomores (in particular, college sophomores who have probably had some CS already!). I'd like to aim for high school sophomores.Michael Mitzenmacherhttps://www.blogger.com/profile/02161161032642563814noreply@blogger.comtag:blogger.com,1999:blog-8890204.post-80864062187084333762008-04-24T22:50:00.000-04:002008-04-24T22:50:00.000-04:00Harry --I agree with your sentiment. The point of...Harry --<BR/><BR/>I agree with your sentiment. The point of what I'm aiming for is not to cover every area of CS (or even of theory). It's to spark that curiosity. <BR/><BR/>I guess I just think there are problems in most areas of CS (and in particular TCS) that are interesting. I'm not interested in starting with problems. I'm interested in starting with <I>people</I> -- people who think they have something interesting to write about and who are interested in writing -- and I assume that the exciting problems will come from there. <BR/><BR/>So I don't want to make a laundry list of "topics to covered". (Though, from my own personal bias, of course I think there are topics that are really exciting and should be covered.)Michael Mitzenmacherhttps://www.blogger.com/profile/02161161032642563814noreply@blogger.comtag:blogger.com,1999:blog-8890204.post-27770611309546568462008-04-24T21:18:00.000-04:002008-04-24T21:18:00.000-04:00Here's a problem - let's say you have codes to lau...Here's a problem - let's say you have codes to launch a nuclear missile. You'd like to divide the codes between two people, so that neither one can launch the missile alone. (Think the opening scene from WarGames.)<BR/><BR/>How do you do it? <BR/><BR/>Answer: draw a line that crosses the Y-axis at the coordinate equal to the launch codes. Give each person one point on the line. <BR/><BR/>Can then bring up issues of how best to represent "points" and "lines" on a computer. This leads to secret sharing over finite fields, which ties into the Reed-Solomon codes you described in the sample chapter.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8890204.post-49068204686833472322008-04-24T18:32:00.000-04:002008-04-24T18:32:00.000-04:00Something I keep wondering when I see your posts o...Something I keep wondering when I see your posts on this subject: have you seen Dewney's <I>The (New) Turing Omnibus</I>? How would your project differ from that book?<BR/><BR/>D. Eppstein (for some reason locked out of OpenID today)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8890204.post-20683571351618185472008-04-24T17:48:00.000-04:002008-04-24T17:48:00.000-04:00I wonder if this is the right way to think about t...I wonder if this is the right way to think about the problem you are trying to solve. Do it this way and you will wind up with the framework for the theory quals (of schools that, unlike Harvard, actually have theory quals). You're not actually trying to crate a foundation on which a superstructure can be built, nor to visit all the squares of a neatly stitched quilt. You are trying to get students to say OK, I get the problem, dunno how to solve it ... Wow! that's really neat! I wonder what else there is like that?<BR/><BR/>So maybe you'd be better off thinking of PROBLEMS first, problems anyone can understand and have "elementary" solutions but have the characteristic that solving them exposes interesting principles. You may have to pause to develop some substructure on the way to the solution, or you may solve the problem and then explain the generalized structure later. Some areas, such as PL semantics, might get omitted entirely because there are no problems you can state to a 15 year old that are likely to seem natural.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8890204.post-58624962567367434732008-04-24T13:16:00.000-04:002008-04-24T13:16:00.000-04:00Programming language semantics are closer to theor...Programming language semantics are closer to theory than a lot of AI. The problem, of course, is that the entire field is ungodly boring!<BR/><BR/>But certainly:<BR/>Cryptography<BR/>Learning Theory<BR/>Game Theory<BR/>Complexity Theory<BR/>Approximation Algorithms<BR/><BR/>all have the potential to lend themselves to sexy chapters and captivating problems.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8890204.post-280218681904498982008-04-24T12:22:00.000-04:002008-04-24T12:22:00.000-04:00I'm curious about the range of subjects you'd like...I'm curious about the range of subjects you'd like to see included. How broad of a net are you using to define "theory"? I'm assuming that it would include machine learning and AI ... what about things like programming language semantics, or database theory? If you posted a list of proposed topics it would undoubtedly generate some interesting discussion here.Anonymousnoreply@blogger.com