Happenings – 2011 July 30

Let me start easy and warm up.

Thursday was a very surprising day on the blog. In 4 of the last 7 full days, I’ve had fewer than 100 hits; but Thursday had 230 hits – 51 on my home page (high, but not that unusual) and 49 on the 3–5–8 puzzle about splitting 8 gallons of wine into 2 four-gallon shares.

49 hits is unusually large for any single post. It may well be a single-day record for one post. I have no idea what caused that flurry of activity.

Since today is the final diary post for July, let me go way out on a limb and predict that there will be at least one earthquake of magnitude 7 or higher somewhere on earth in August. It would be more prudent to say one such quake in the next 2 months, but I’m bored from being safe with my forecasts.

I decided to go through John Stillwell’s “Naïve Lie Theory” instead of Baker’s “Matrix Groups” – Stillwell is simpler, and I don’t know everything in it yet. Much, yes… which is why I’m already through Chapter 6 of 9.

Don’t misunderstand me… there are a lot of things I still want to work out in Stillwell… but the book flows well for me.

Incidentally, he’s a good author – good enough that I buy every book he writes. Go check him out on Amazon.

As I have said before, the days of my disdaining undergraduate math books are way in my past. This is how I find people talking about math instead of just organizing it. Organization is essential, but so are insight and context, and I find more of both in undergraduate books.

There were, as you might expect, a few books in his bibliography which I wanted. Since I trust his recommendations – and they were cheap books – I ordered three. They came in Wednesday and Thursday.

One of them was “a notable book that conducts lie theory at the group level…”; it got shelved after I flipped through it – it’s a reference book. I wasn’t surprised.

The other two were overviews. “The story of the sporadic simple groups is a long one, filled with so many amazing episodes that it is impossible to sketch it here. Instead, I recommend the book [by] Ronan for an overview, and Thompson… for a taste of the mathematics.”

That is, one of the other two books was “From Error Correcting Codes Through Sphere Packings to Simple Groups” by Thomas M. Thompson. The part about error correcting codes was pretty readable… sphere packings got hairy… the introduction to simple groups wasn’t bad… but the detailed derivation of the structure of one of the sporadic groups was over the top.

Maybe someday. I’m glad I have it, but its final chapter will keep for a while.

And the 3rd book, I’m still reading: “Symmetry and the Monster” by Mark Ronan. It’s the easiest of the three… in fact, he avoids technical terminology, but fortunately he has a glossary at the back, so I know that what he refers to as a “cross-section” in the narrative is technically an “involution centralizer”. I have no idea what that is, but at least I know what he’s referring to in the story. (I was a bit frustrated until I looked for and found the glossary: I didn’t want to know the gory details, but I did want to know where I might find them.)

Oh, reading Stillwell this week was serendipitous. It looks like I’m going to be talking about matrix norms this Monday – that is, measures of the size of the elements of a matrix… a desirable property of matrix norms is that the norm of a product be less than or equal to the product of the norms…

\parallel A B \parallel \le \parallel A \parallel\ \parallel B \parallel\ .

My favorite book on norms calls that a consistency condition. But Stillwell calls it the submultiplicative property – and that's the term I'll use, too, when I get there.

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