The note-taker for the 9/24 meeting was Jim. Jim had everyone go around and say a bit about their (non-mathematical) selves. "What are you passionate about outside of math? What's something that people wouldn't know about you just by looking at you?" Then he discussed his expectations (and the contracts, which he lost but will hand out on Thursday): Student commitments ------------------- "Attend weekly group meetings" "Help create a comfortable intellectual atmosphere": We're here to have fun at the frontier of knowledge Attending to content and process; how we say what we say Two goals: * advance my research agenda (things I *really* want to know the answer to) * advance your educations We're going to form a community of inquiry People are at different levels It's a microcosm of the mathematical community at large I'm still learning how to run a group like this Think about the impact you have on others and they have on you Avoiding interuptions and imbalances in level of participation Remember: REACH will be more exciting in the long run if we invest some time at the beginning to make sure everyone's finding a niche. And: explaining stuff that's old can be almost as much fun as explaining stuff you just figured out. "Arrive on-time and stay until end": 3-5 p.m. "Notify in advance in cases of unavoidable lateness or absence" "Participate actively": questions; lectures What are the things some people know and other people don't? "Teach what you know, learn what you don't, document everything." "Share note-taking duties": I'll provide my notes; the note-taker records everything that wasn't planned. The note-taker's job is to fill in the gaps (e.g., don't copy down the programs!) In particular, the note taker records people's statements of what they intend to do. As in when I say: "By this weekend, I'll make sure that you've all been added to the email lists for the domino and bilinear forums". Expectation: Note taker should post draft of minutes on her/his REACH site later that evening or the next morning; Jim will send his corrections "Spend 6 hours per week on REACH outside of meetings": Everything counts: background reading; infrastructure (email, web-sites), even "homework" Suggest you keep a research notebook Get Mathematica or Maple NOW "Create a term project (document or software)" Mention previews of unwritten articles (to be posted soon) Stress that the theorems announced in the previews may be false! "Write an end-of-term report" Helps me get more grants (e.g., if we need extra money for the spring!) Helps me remember what you did when you're looking for a letter of recommendation "Stay in contact with Supervisor and other group-members": "Call me Jim or Prof. Propp" send email to reach@math.harvard.edu (don't send big files on it, give people a webpage URL instead!) "Create and maintain a personal REACH web-page": avoid unintentional duplication of effort update every couple of weeks "Report on hours and activities every week": keep track! ("What counts?") weekly one-paragraph report sent on Friday, Saturday, or Sunday starting THIS WEEK [give them examples] To be posted on your private web-page (or, if something is private, via email) Primary missions (every week): What you've done (e.g., computations, summary of what you've read) How many hours you spent (hours spent at meetings count!) (Don't assume I've taken attendance; include all hours.) Secondary missions (every two or three weeks): What you're planning to do How your're feeling about your involvement with REACH (overwhelmed? understimulated? bored with the problems? left out because you don't know other people in the group?) Suggestions for how REACH could better serve your needs Billable time: Attending meetings counts (also Weds.) Avoid blind alleys: send me an email every 10 hours of research time "Communicate and cooperate with other students working on the same project": buddy system? importance of listening, debugging, proof-reading "Read email regularly and respond promptly": read every day (preferably) "Follow through on tasks" "Exercise initiative": e.g., MECCAH; tee-shirts; if you want some meeting-time to be devoted to something or other, propose it to me in email! Jim's commitments ----------------- "Give students interesting topics to think about" What I offer that most REU programs don't is a network of interconnected problems "Help students develop skills in solving problem and inventing new ones" "Help students obtain publishable results" I need to get better at this; "previews" may help "Maintain a central clearinghouse for exchange of information": www.math.harvard.edu/~propp/reach/ (public stuff) Elsewhere (minutes of meetings; software links) Minutes: I can edit and return; it gets sent out about 24 hours after the meeting Other sources of information are www.math.wisc/~propp/tiling/, the domino forum and the bilinear forums. (Don't be disturbed if you don't follow the postings!) Privacy issues (security through obscurity) "Provide funds for needed books and software": Library can grow (manuals). Money from the grant can also be spent on supplies. Want to learn C? Maple? Mathematica? We can buy a book that you can borrow. (Catch: it ends up belonging to the REACH Library, not to you.) Maybe buy software too: send me email if you need something. "Pay salary (or submit grades) promptly": $10/hour; salary cap currently $500/term Where the money is coming from: NSF personal grant, through VIGRE, an REU supplement (NSF encouraging vertical integration), and the NSA. Non-US citizens are funded via Jim's start-up funds at the University of Wisconsin; non-U.S.: I-94; passport/visa "Write letters of recommendation for students": your final report comes in handy! In the second half of the meeting, Jim showed the group: www.math.harvard.edu/~propp/reach www.math.harvard.edu/~propp/192/: Students helped each other set up web pages, get access to Maple or Mathematica, etc. First homework -------------- A matching of a graph is a (possibly empty) set of disjoint edges in the graph (i.e., no two edges in the set share a vertex). There are 22 matchings of the 2-by-3 grid (including the empty matching): o o o o o o o--o o o o--o o o o o o--o | | | | o o o o o--o o--o o o o o o o o o o--o o--o o o o o o--o o o o o o o o o o o | | | | | | | o o o o o o o o--o o o--o o o o o o o o o--o o o o o o--o o--o o o o o | | | | o o o o o o o--o o o o o o o o o o o o o o o o--o o o o o--o o | | | o--o o o o o o o--o o--o o o--o o Show that if we let a(n) denote the number of matchings of the 2-by-n grid, the terms a(n) satisfy the recurrence a(n) = 3a(n-1) + a(n-2) - a(n-3) or equivalently, show that the generating function sum_{n=0}^{infinity} a(n) t^n is the power series for the rational function (1-t)/(1-3t-t^2+t^3). David Offner agreed to be the note-taker for the 9/26 meeting.