This is a weekend for distractions from mathematics.
For one thing, I’m watching the men’s singles championship at Wimbledon even as I draft this post. As I’ve said before, I’m a staunch fan of Roger Federer, and I’m excited to see him in a grand slam final again. It’s been a while, what with the younger Nadal and Djokovic each in his prime.
For another thing, this post is a day late. Well, yesterday I visited a friend who was in the hospital. He seems to have recovered from a brief crisis that put him into intensive care, but he remains hospitalized.
As for the blog, last Monday’s abstract algebra post about rings followed in the footsteps of the 1st abstract algebra post a few months ago about groups: it got more than 300 hits, and the blog as a whole set a new record on Monday with 542 hits total.
And, as before, there were more than 100 twitter references to my blog. There certainly seems to be a group out there who is interested specifically in abstract algebra… and which quickly spreads the word when I put out an abstract algebra post.
And I’m glad to see that.
I’m not at all sure that a technical post will go out this Monday, because I got no mathematics done yesterday. And even if a technical post does go out this Monday, I’m not at all sure what it will be.
After all, the rings post itself went out because I’m struggling with the next regression post… and I decided, correctly as it turned out, that I could finish off the rings post instead.
While I’ve made very good progress on the 2nd rings post, now I don’t know if I can finish it off in time.
And I did wake up this morning dreaming about the next regression post… so who knows? Maybe I can finish it today.
In other news, there were no earthquakes in my neighborhood on the last day of June, leaving the total at 9 for the month.
Yes! Federer just won the 2nd set, tying the match at one apiece.
As I was saying before that interruption… there was one earthquake in my neighborhood on 1 July, 4 on 4 July, and one on 5 July, for a total of 6 so far in July. In fact, all 4 earthquakes on the 4th were in the same place, about 16 miles from Francisco City Hall. 3 of them occurred within 9 min. and the 4th was 3 hours later. All were less than 3.0 in magnitude.
As for mathematics…
The next regression post should be about probability distributions… normal, t, chi-squared, and F. I’m just having a terrible time getting the t distribution.
The next rings post should be an introduction to integral domains and should demonstrate that the set of numbers of the form
is not a unique factorization domain. I’m just not quite comfortable with all the details.
For autoregressive moving average (ARMA) time series modeling, I think I’ve decided that I will generate timeseries according to known models, and then see how closely our methodology comes to fitting them empirically. I’ve also realized that I can upload Excel files, so I would be able to provide the data.
As I have said, the downside is that the time series package for Mathematica is not free… and many of you will not have it. On the other hand, many of you who are interested in time series analysis itself may very well have it, or something similar.
And, since I’ve been struggling with my intended next posts, I’ve been looking over other things to see what’s required to get them ready.
I still think I really should be able to quickly put out a post about constructing the final tableau of a linear programming problem. I don’t understand everything I want to, but I think the trick is worth showing.
And then there are generalized eigenvectors. They show up whenever we deal with a matrix that cannot be diagonalzed. I understand that every square matrix has a basis of generalized eigenvectors. On the other hand, not every such basis will transform a matrix to Jordan canonical form… and I’m still struggling to identify exactly what it takes to do so.
And then there is dimensional analysis. I think I just want to work a few more problems, and I need to clean things up.
So, we’ll see what happens.
And Roger Federer just broke Andy Murray to go up 4-2 in the third set. Will Murray break back? ….
No! It’s Federer 5-2, with Murray to serve….