Thursday, November 15, 2007

Math is Hard... and Then You Die: Chapter 6

If I were going to make this a longer series, I certainly have more folks and topics I would talk about from my undergraduate career. Back in the 1970s, I was very glad that I took courses from Ken Rebman, Ed Keller, John Summers, Dan Jurca, Art Simon, Russ Merris and many others. But I'm going to jump ahead to my graduate career, which starts in 1999 and continues for about three years until I get my master's degree.

Once again, I had a lot of good teachers during my second stay at Cal State Hayward, including Keller and Merris (again), Edna Reiter and Massoud Malek. It was also great to reconnect with old friends like Dan Jurca and Gary Lippman, as well as meeting and getting to know folks who weren't there in the 1970's like Tom Roby, Julie Glass and Don Wolitzer. But if I'm going to make this the last post in the series, it has to be about Dr. Stuart Smith, known at Cal State as the one man graduate program.

I took at least two classes a quarter during my second stay at Cal State, all of it math or computer science. I took at least one class a quarter from Stu Smith and sometimes two. He is simply amazing. I've never met anyone who knows more math than Stu, or does a better job presenting it.

(If any voters from the MacArthur Foundation stumble upon this humble blog, let me just say... Dr. Stuart Smith! Throw some cash his way. He deserves it.)

The first class I took from Stu when I got back into the program was Group Representation Theory, which is the major 20th Century addition to the greatness that is group theory. If group theory is about symmetry, group representation theory is symmetry meets orthogonality. If two lines meet at 90 degrees, we call them perpendicular. When we jump up into three dimensions (or beyond), mathematicians use the word orthogonal instead of perpendicular. Group representation theory was terrific fun. Filling in a character table is kind of like a sudoku problem, though with a little trickier rules involving both real and imaginary numbers, which when combined are called complex numbers. The great thing about a class from Stu Smith is that you get to find out where this very abstract stuff is actually being used, and group representation theory is very important to the study of atomic and sub-atomic physics. It's what brought the mathematicians and physicists back together after a decades long rift.

At Cal State, you have to pass the comprehensive exams to get your degree, so many classes were aimed at the stuff every grad student should know about algebra, topology, real and complex analysis. But Stu also taught classes in topics he found interesting, so I learned about Lie algebras and Lie groups, differential topology, algebraic topology, Lebesgue measure, Ferrers diagrams (another fun sudoku like field), spectral analysis and more. We learned the math that underlies relativity and the stuff that makes quantum theory so goofy, and why either relativity or quantum theory is wrong, though we don't know which one right now.

Stu told great stories about the people of mathematics, so we find out about a guy following a soliton wave while riding a horse beside a canal in England, about the great Von Hemholtz asking the muckymucks at Yale "Where's Gibbs?", about Sophus Lie and Felix Klein deciding over dinner one night that they would figure out everything about group theory between them, Lie taking the infinite groups and Klein the finite. (Lie got the easy half.)

I remember my classmate Jeremy Gross bringing up something Carl Sagan said, and Stu, casting some skepticism, said. "Well, Sagan smoked pot."

"Feynman smoked pot." Jeremy replied.

"Sagan smoked a lot of pot." was Stu's reply.

I could go on and on about my graduate classes, but I will end this chapter with my small contribution to the education of Cal State students to this day. We were studying simplicial complexes, which can be classified by their Betti numbers and the torsion that is found in the maps from one dimension of their component parts to the next smallest dimension. The method for doing this is creating a series of matrices and then reducing these to Smith Normal Form. (Not Stu Smith, some other Smith.) It's a labor intensive process, so I wrote a little C program I call sc_classify, where sc stands for simplicial complex. I showed it to Stu and he was impressed. It worked so fast that he thought I might be cheating, that the answer to the problem had been downloaded with the program. He did a second example to see that it in fact answers a difficult math problem in the time it takes to hit the enter button.

A colleague at Laney is taking classes up at Cal State this quarter, and he told me that Stu is still giving his students sc_classify to use in the classes where he teaches about simplicial complexes (and an important subcategory called pseudomanifolds). I'm happy and proud that I'm able to make people's work in this field a little easier, so they might have time to study the fascinating field more deeply.

This is the last chapter for now of Math Is Hard... And Then You Die. I may come back to the memoir at a later date.

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