SSL Notes for meeting #1 (9/9)
Martin is the notetaker for today
Introductions, including outside interests
Martin  Music, comics, computer science
Hal  Did SSL before.
Abby  Music, movies, fashion, Students for a Free Tibet
Emily  Minnesota Twins, skiing, read, math
Josh  Music (recording, synth), fables, job?
Sam  Modern European and American literature, jazz, backgammon
Paul  Golf, guitar/piano, music, reading
Steven  Basketball (dislocated shoulder), sail
Jeremy  sailing, snowboarding, hiphop music
Jim  Cafes. Cambridge is home of the best cafe but at least Madison has
wireless cafes (Muddy Waters, Electric Earth, Mother Fool's).
Acapella/choral singing.
Jeremy: EVP Coffee has wireless? But at least good coffee.
This is the smallest group I've run in a long time (maybe 7 years!)
This year, more of a focus on process (as well as outcome)
One part of that is giving me feedback on how things are going for you,
for others, or for the group as a whole (even more than usual).
Another part is, there may be some formal assessment (via questionnaires).
Distribute contracts
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
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 SSL
site later that evening or the next morning; Jim will send his
corrections
Notetaker should anticipate problems. "Wendy, I'm not going to be
able to copy that all down. Can you email it to me for inclusion
in the notes?"
Spend 6 hours per week on SSL outside of meetings. Some weeks more, some
weeks less. You'll get more out of it if you put in more time.
This room will be available 2 hours a day. In midOctober, a
webaccessible cluster of computers can let you run Maple wherever you
are. For now, less on computers and more on math background. The reading
will be on articles by other undergraduates. Hal's article? Hal will
send the link to the list when it is up (will wait for the test message).
Last year, lots of students wrote papers but not enough read and critiqued
each other's papers. WHen you find a passage you don't understand, can be
fixed.
"Spend 6 hours per week on SSL outside of meetings":
You'll get more out of it if you put in more time
Everything counts: background reading; infrastructure
(email, websites), even "homework"
Suggest you keep a research notebook
Get Mathematica or Maple NOW
(salary cap: $700 for students who buy Maple/Mathematica/whatever;
$600 for students who don't)
Related: What to do
This room (B107 w/ Maple computers) will be available 2 hours a day
In midOctober, a webaccessible cluster of computers can let you
run Maple wherever you are
For now, less on computers and more on math background
The reading will be on articles by other undergraduates. Hal's?
 Hal will send the link to the list when it is up
Last year, lots of students wrote papers but not enough read and
critiqued each other's papers.
"Create a term project (document or software)"
Could even be a tshirt!
"Write an endofterm report"
Only a few paragraphs, maybe an hour of time max.
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 groupmembers":
"Call me Jim or Prof. Propp"
send email to ssl@math.wisc.edu (?)
(don't send big files on it, give people a webpage URL
instead!)
"Create and maintain a personal SSL webpage":
avoid unintentional duplication of effort
update every couple of weeks
keep track of hours (no particular format, but should be clear)
What does Wisconsin provide? SIT (Student Information
Technology).
Notoriously bad service  losing password means everything is
gone?
Everything is automated. www.sit.wisc.edu.
CS and engineering have similar systems.
Hal can help out if necessary.
"Report on hours and activities every week": keep track! ("What counts?")
weekly oneparagraph report sent on Friday, Saturday, or Sunday
starting THIS WEEK [give them examples]
To be posted on your private webpage (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 you're feeling about your involvement with SSL
(overwhelmed? understimulated? bored with the
problems? left out because you don't know other
people in the group?)
Suggestions for how SSL 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, proofreading
"Read email regularly and respond promptly":
read every day (preferably)
"Follow through on tasks"
"Exercise initiative": e.g., teeshirts;
if you want some meetingtime 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; lowered teach load may help
"Maintain a central clearinghouse for exchange of information":
jamespropp.org/SSL/ (public stuff)
(minutes of meetings; software links)
jamespropp.org/... (keep this private)
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/,
jamespropp.org/reach/,
the domino forum and the bilinear forums.
(Bilinear stuff is related to the talk that was on 9/8)
(Don't be disturbed if you don't follow the postings!)
Privacy issues (security through obscurity)
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 SSL 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 $600/term or $700/term.
Where the money is coming from: VIGRE, (NSF encouraging
vertical integration).
"Write letters of recommendation for students":
your final report comes in handy!
A room for food in the break time will hopefully be reserved for next
time.
We take turns bringing refreshment.
In the second half of the meeting, Jim showed the group:
www.math.harvard.edu/~propp/reach/
www.math.harvard.edu/~propp/192/
"In the next few weeks, I'll do something like this for SSL."
Students helped each other set up web pages, get access to Maple or
Mathematica, etc.
What I want: people learning, teaching, reading, writing, creating
pictures, creating models, creating software, running experiments,
enjoying themselves
What I also want: articles to get written (with or without my name on
them)
What I offer: good problems; an overview of groupmembers and the ability
to connect people with each other; some individual support
Stephen will be augmenting the amount of support I can offer
(in addition to participating in specific groups)
What I also want: logistical support for my own work (e.g., if I'm giving
a talk, I could use people to proofread my slides)
(Talk about puzzles and their relation to tilings)
For Thursday: An understanding of snake graphs, which are a bunch of
boxes. Each box is to the right of or above the last box.
Good procedures for counting perfect matchings of these snake graphs. A
two box snake graph:
.__.__.
  
.__.__.
A perfect matching: Each vertex is paired up with exactly one other vertex
by selecting edges in the graph. Here's an example:
. . .
  
. . .
If we select the first vertical, there's another way:
. .__.

. .__.
Or we could pair the upperleft vertex with the vertex to its right,
in which case the other choices are forced:
.__. .

.__. .
Work on: Various small snakes, counting matchings other than brute force
elimination. Systematic.
Interested in both solid ways "you can count on" to count these, as well
as conjectured ways that seem to work better but you haven't proven it
yet. Jim feels that he knows how to do this efficiently. Here is the
pattern:
.__.__.__.
   
.__.__.__.
Again, for the first (upper left) vertex we have two choices, down and
right. After having matched first vertex down, what remains is the
other graph we looked at. So 3 perfect matchings of that type:
. . . .
   
. . . .
. . .__.
 
. . .__.
. .__. .
 
. .__. .
Or, we can pair the first vertext to the right. If we do this,
there are two more possibilities:
.__. .__.
.__. .__.
and
.__. . .
 
.__. . .
.__.__.__.__.
     has 5+3=8 perfect matchings
.__.__.__.__.
Fibonacci numbers: (1,1),2,3,5,8,13,21...
Or we can alternate: 1, 2, 5, 13, ... vs 1, 3, 8, 13, ...
1+5 is thrice 2. 2+13 is thrice 5.
1+8 is thrice 3. 3+21 is thrice 8.
F_{n2}+F_{n+2}=3F_n
Find a combinatorial proof. (Let O^k be the snake graph of k segments,
e.g. OOOO is the graph with 8 perfect matchings shown above.)
M(graph) = # of matchings of the graph.
.
U is disjoint union.
. . .
M(OOOOOO) U M(OO) = M(OOOO) U M(OOOO) U M(OOOO)
Since disjoint sets, the union has cardinality equal to the product
of their respective sizes.
How do we process the left side to generate the right side? A bijection
between the sets.
A bijective proof you already know. Examine
.
M(OOOOOO) = M(OOOOO) U M(OOOO).
21 is the number of pefect matchings of OOOOOO.
We've already given this. Either the first vertex is matched below or to
the right. Cardinality of the straight snake follows the fibonacci
recurrence and begins like fibonacci, therefore is equal to the fibonacci
sequence (aside from the 1's).
Not only a multiplicative but an additive relation between c and c'. It's
like 3 copies of the same set.
Disjoint union: Sums of the cardinalities, ignoring the intersection.
"Nothing as complicated" as taking the cardinality of the multiset.
.
{1,0} U {0,1} = {1,0_1,0_2,1}
.
#(A U B) = #(A) + #(B) Ignore the metaphysical issue of taking 2 copies of
the element 0.
Want to see a variety of answers. Get started for Thursday. Want to know
what our steps have been. More interested in examining matchings of small
snakes. (Straight snakes are simple. Zigzag snakes are going to be
harder.
Winding snakes may be the next step.)
If you had only 5 minutes, how would you work out this snake:
OOOO
O What about only 30 seconds?
OO
Jim will post his Markoff notes from the talk yesterday.
Next notetaker is Paul.
Notetaker should remind Jim to ask for the next notetaker at the end of
the meeting.
Notetaker should also remind Jim to ask for the next snackbringer.
Abby is bringing the snack.