As with so many things, the post explaining where those miscellaneous facts about wavelets come from is getting longer and more complicated. I do, however, know how to fix that: break it into pieces.
Last weekend was “Seminar Day” at Caltech; that is our reunion weekend. Other schools may have parties — we have lectures.
I drove down to Pasadena Friday afternoon, arriving at about 8 PM. Lectures ran Saturday from 9 AM to 5 PM, with a long break for lunch and a “general session” for honoring alumni and for someone to speak on a more general topic.
I habitually use that general session to hit the bookstore. Alas, it looks like this was my last serious visit to it. The bookstore is going out of business — as a bookstore. It will continue to sell clothing, coffee cups, and supplies, but it will make official what is at present de facto: the students buy their textbooks from Amazon.
It occurs to me that the loss of the technical bookstore just might cut back on my showing up for Seminar Day.
As it happens, I did not make it down to Caltech last year, and so I did not make my customary purchase of many interesting books. I want to joke that they went out of business because I missed a year of purchases.
Which lectures did I attend? Quantum mechanics, the Phoenix lander on Mars, human genetics, the large hadron collider, and quantum information science.
The quantum mechanics was fascinating. Something about replacing a small quantum mechanical system by an infinite limit with the same statistics (so I think they’re going from one system to an ensemble of identical systems); then treat the infinite ensemble classically! The key phrase is “Ring Polymer Molecular Dynamics”.
The Mars lander and the collider were interesting and straightforward. The genetics went over my head.
The quantum information science started well, and then lost me. (Well, I knew what he was saying but I couldn’t relate it to anything else I knew.) But I might take another look at Merman (see the bibliography and this old post). And I might go look up “anyons”, something about the “fractional quantum Hall Effect”.
Then I drove back Saturday evening and night as soon as the last lecture ended. (OK, I grabbed a cup of coffee first.) I wanted Sunday for myself. I did some mathematics, but not a lot. I had jury duty on Monday.
I made it onto a jury. The judge’s head swiveled sharply at one point. One of the routine questions they ask is, “What do you do for a living?” When I replied, “computer models of power plants”, the judge asked quickly, “What does that mean?”
The end of my answer was to say that I was doing the equivalent of balancing a checkbook, making sure that what went into the plant was equal to what came out of it. Maybe I’m learning something from Charlie Epps on Numbers!
The trial ended unexpectedly Tuesday morning, so I was free to return to work.
One of the nine books I picked up this year was about modular forms (Kilford, L.J.P.; Modular Forms: A classical and computational introduction. Imperial College Press, 2008. ISBN 1 84816 213 8.). One could phrase Andrew Wiles’ proof of Fermat’s last theorem as: every relevant elliptic curve is modular. No, I will not elaborate; but modular forms are what are related to elliptic curves.
Having mentioned as an integral domain where unique factorization does not hold, let me show you a number system where Fermat’s last theorem is false.
The historical overview that opens the book includes the following counterexample for n = 3 in . We have
That is, we have
Of course, those numbers are not integers so this is not a counterexample for the usual Fermat’s last theorem; but I like knowing that it is not true in all number systems.
As for the routine of my blogging, I expect to continue with wavelets; and, more and more, I am being distracted by regression analysis. One of the nine books I bought was about regression diagnostics, and I have already ordered and received the previous book by that author. In fact, I’ve already read — not worked — that previous book, as well as they one I bought Saturday. Now I’m waiting for a third, the follow-up, book. (I have the impression they’re printing it for me.)
… I’ve been doing wavelets this morning, and I guess I’ll take a break to put this out. (I drafted it yesterday.)