At 11:29 PM 11/6/02 -0700, you wrote:

I've moved the Math-Fun mailing list to another system that does spam filtering. Everyone should have recently received a "Welcome" message to the new list. The message includes a personal password that you'll need to "manage" your mailing list options. Interesting options include echoing of posts and a digest option. [I think I've turned off the monthly password reminders.] I think the initial setting is for single messages (non-digest) and echoing ON. Another good feature is archiving. The URL for reaching the archive in the message headers seems broken, but you can get there from the generic list page at

http://mailman.xmission.com/mailman/listinfo/math-fun

The new posting address is

math-fun@mailman.xmission.com

I think sending to the old address (math-fun@cs.arizona.edu) should still work, if I've got the forwarding right.

The list is set to "members only" for posting. This will have two annoying consequences: (a) if you post from a different address, or (b) if someone else temporarily joins our discussion; then the message is placed on hold for me to approve or reject. I'll try to notice these and whitelist the extra addresses.

The old reminders about preferring plain vanilla ascii, no Mime, no attachments, pictures, binary files, etc. still apply.

Undoubtedly there will be glitches; please report them to me at my usual address below. With luck, this will be the last hand- edited digest.

Rich rcs@cs.arizona.edu

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From: "Mike Stay" <staym@datawest.net> To: rcs@CS.Arizona.EDU Subject: analysis question Date: Tue, 5 Nov 2002 20:10:52 -0700

sum is to integral as prod is to what?

I.e. is there a name for exp(integral(log(f(x)),dx))? Where do I worry about branch cuts in that expression? -- Mike Stay staym@datawest.net

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[editorial comment: Gosper calls these Prodigals. I don't think they have any non-obvious proerties, but it is strange there's no "official" name. --Rich]

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From: James Propp <propp@math.wisc.edu> Date: Tue, 5 Nov 2002 23:51:15 -0600 (CST) To: math-fun@CS.Arizona.EDU Subject: PSL(2,F_7), SL(3,F_2), and the Fano plane

What's a good way to see that PSL(2,F_7) is isomorphic to SL(3,F_2)?

More concretely, what's a good way to see PSL(2,F_7) as being the symmetry group of the Fano plane?

(The Fano plane is the projective plane over F_2, so it's easy to see why its symmetries are described by a linear group over F_2.)

Also: What's the easiest way to see that the group in question is simple?

Jim Propp

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Date: Wed, 6 Nov 2002 10:12:56 -0800 (PST) From: "R. William Gosper" <rwg@spnet.com> To: math-fun@CS.Arizona.EDU Subject: Silver, purple rhymes

The CDROM version reveals that Webster's big old Third International has all along defined CHILVER as a ewe lamb. And Roger Miller's heroic effort:

Roses are red. Violets are purple. Sugar is sweet; And so's maple syrple.

Roses are red. Violets are purple. I won't shoot you, But Wyatt Earp'll. -A