On a non-mathematical theme, here are some pictures from Washington (and, soon to come, British Columbia). I’m up here for a conference but I’ll be doing hiking and climbing as well. The conference is at Islandwood, on Bainbridge Island, which is an amazing environmental education center.
Rainier from Puget Sound
Pond at Islandwood Education Center
Treehouse at Islandwood
On the ferry to the Sunshine Coast, north of Vancouver
Atop Mt Baker
Mt Baker climber’s camp
The Strait of Georgia
Wild blackberries all over!
Suspension bridge at Islandwood
As of today the course is up through Part 30, which gets us most of the way through Handout 8. (Note: I edited Handout 8 a bit to streamline it and move some technicalities to the To-Do List–which we will turn to eventually!) The big news is we are now through the proof of (a somewhat restricted version of) Duhamel’s Principle. The proof is almost trivial once we’ve set up the machinery, but in Handout 9 we’ll look carefully at a pretty fundamental issue that we’ve glossed over so far. After a bit more with the story of distributions and convolutions we’ll switch gears a bit to Fourier.
The Motivated Analysis course is up to 7 handouts and 27 videos as of September 14. Pretty soon (I hope) the course will get to a few exciting waypoints:
- Proving Duhamel’s Principle in a general setting, using distributions and convolutions
- Pinning down the precise definition of a distribution (partly motivated by what Duhamel will tell us)
- Going back to the original mass-spring system, but this time forcing with sine waves, not hammers, to start the story of Fourier analysis–a story that will get intimately intertwined with distributions.
I’d love any feedback you have if you are following along (even in a non-serious way). In particular, it would be good to know if there is a desire for more practice-type problem sets (in addition to the problems in the handouts, which develop the ideas). Now, I’m not saying I’ll produce reams of extra problems, but I realize that as it is there might not be quite enough practice for a student to really master the ideas as we go.
My Motivated Analysis course is up to
13 16 videos and 4 5 handouts. Click on the black bar above for the home page. Feel free to comment here if you have responses, questions, or suggestions; of course you can comment on the video pages as well. You may want to follow this blog if you are trying to do the course (either seriously or informally) and want news about major progress.
I’m planning to start a new video series, or really, an informal online course, entitled Motivated Analysis. The goal is to bridge the gap between applications-oriented courses in analysis (mostly differential equations) and theoretical courses, and to show how modern theoretical analysis comes out of practical problems.
Here’s the introduction/advertisement/preview video:
The home page for the course is linked in the black bar just above this post.
And here’s a link to the first discovery handout—I’ll be working through this PDF in the first few videos of the course, but most of it should be doable by someone with the appropriate prerequisites.
Time to brag on my 7-year-old. Adela has been thinking up math problems for me each night. Tonight it was the following. Start with a number, say 2, and do all four operations on it: 2+2=4, 2*2 = 4, 2-2 = 0, and 2/2 = 1. Now add the results all up, getting 4+4+1+0=9.
If you start with 3, you get 3+3=6, 3*3 = 9, 3-3 = 0, and 3/3 = 1. Adding gives 6+9+1+0=16. Hmm…I think I see a pattern here….
Starting with 4 gets you 8+16+1+0=25, which is 5^2 = (4+1)^2.
Of course this is just a cute way of saying that (n+1)^2 = n^2 + 2*n + 1, or more explicitly
(n+1)^2 = n*n + (n+n) + n/n + (n-n)
which I don’t think I had ever thought of in exactly that way. Hurray for kids!
Courtesy of Not Even Wrong, we have news that in addition to awarding a $3M prize to superstring theory founders Green and Schwarz and giving out a number of similar prizes for biomedical research, Yuri Milner is teaming up with Mark Zuckerberg to fund a $3M prize they are calling the Breakthrough Prize in Mathematics. Whether this will be a good thing is already a source of debate, but it will certainly be more fodder for the small set of people (including me) who like to speculate on who will win prizes like this. Will it make People Magazine? Hard to say.