The Dean opens it up (talks about 1:30 or so) and introduces me. Then I talk for about 5 minutes, and then the speaker gives an excellent talk about topology, algebra and the mathematics of financial prediction. So if you haven’t met me in person, this is what I sound like.
I have to cover for someone’s class, which cuts into my morning workout. Hence today I ran 5 miles over lunch (about 5.2 actually)
Good news: it was very pretty, though there was a breeze. I did 2 lower Bradley loops (1.22-1.24 miles each) in 21:39 (8:44-8:52 mpm) with the laps being 11:05/10:34. I walked the big hill coming out of the park after these two laps, and then slow jogged it home. Hey, 5 miles are better than zero.
I do have to get new shoes though as my teeth are starting to rattle as I run.
Think of this: suppose you have an ordered list of ingredients of a food stuff (say, water, salt, sugar, gelatin..), the weight of a serving, and the amount of say, protein, fats, sugar (nutritional information on the label).
You can use linear programming (and similar techniques) to determine upper and lower bounds for the various ingredients and have a phone application do this.
Why is this important? Some people have dietary restrictions (e. g. some can’t process phenylalanine) and therefore have maximum amounts of this substance they can have in their daily diet.
Workout notes: 8 mile “run” on the Rivertrail to Glenn Oak Park, up Prospect and into Springdale to the Mausoleum and around that small loop. It was windy and just under freezing; not bad running weather though. The footing was mostly good.
Not shown is the small spur I did on the trail which parallels Perry Ave.; that was iced over so I turned around but I did enough to get 8.
Then I did 10 minutes on the elliptical and a few weightless squats to loosen up.
Note: while out on the “run” I found a dollar bill.
Walk of Shame I took a whole stack of books to the library; they were mostly for a project that didn’t work out. But I did check out a new book to look at something else and what did I find in that book?
I put it on social media but that isn’t exactly “like-bait” But seeing that did remind me that I need to get moving. It has been too long since I’ve had one of these.
I am thinking about things and I have a mystery that I don’t understand…yet. For the mathematically inclined: it has to with speeding up the convergence of an alternating series by using Cesàro summation. For the first two examples I’ve tried (one conditionally convergent, one absolutely convergent), the convergence sped up by a constant multiplicative factor. That isn’t very good for computational purposes, but why “that” factor and not some other one?
Workout notes: 8.3 course in 1:31:10 (about 1:30 slower than last week; but it was 24 F (12 F colder) and I ran a reasonably tough 8 two days ago). I was 43:49 at Heading, 1:22, 46:06 for the last 4+ (10:00 from the Park exit to home).
There were some trees down: a big one that I ran under and a smaller one I ran around (on the way up from the bridges to Cornstalk) and one I stepped over on the way down from Cornstalk to the lower park entrance.
I didn’t feel that good until mile 3 or so.
Then we got take out from Jerusalem restaurant and Tracy came over to watch Notre Dame vs. Ohio State in the Fiesta Bowl.
Though ND moved it well, at times, they were outclassed 44-28. Ohio State had it all: running, short passing, deep threat. But ND didn’t embarrass themselves the way that Iowa is doing in the Rose Bowl (down 35-0 to Stanford at the half).
My goal for 2016: aside from my usual “one marathon or longer” goal, I’ll need to get to work on professional stuff. I don’t want to stagnate. I’ve got 3 ideas to work on, and I need to do it next week. One idea will just result in a dumb blog post that might help with calculus teaching; one will be an exploration of a “long shot” idea and the third is the mostly likely to pay off as a research paper.
Also, I want to read more books; I have one that I want to finish and I need to read some more substantial stuff. My brain is getting lazy.
The night classes are taking a bit out of me; I find myself sleeping in and starting my day later.
Workout notes: lifting only.
pull ups (4 sets of 10 plus a later set of 10) weak today
incline bench presses: 10 x 135, 3 x 160, 7 x 150 (weak on the 160 set)
dumbbell bench press: 10 x 70
military: 3 sets of 10 x 40 standing
pull downs: 3 sets of 10 x 160
rows: 3 sets of 10 x 200 Hammer
yoga (15 minutes worth; really sweated. Was able to headstand)
Math note: I figured out a homework problem that was puzzling to me:
It was to show that (note: refers to an expected value of a random variable of the length of time someone who is years old can expect to live past his/her current age).
It bothered me enough to disrupt my sleep two nights ago, but when I woke up, I was able to figure it out. I did a “happy dance” but in all seriousness, it wasn’t hard. It is just that I am having increasing doubts about my ability to learn new things. These doubts aren’t warranted…yet.
But yes, I bloody well SHOULD have been able to figure it out; it is just that I get mentally lazy at times.
I filled in to teach a class today..and then went to swim:
500 free, 250 of back/fly, 150 of side, 100 IM, 4 x (100 free, 100 pull, 100 fins)
pull ups: 5 sets of 10 (stronger than I had anticipated), super sets with
military (machine, 10 x 100 each arm)
rows( machine, 10 x 110)
Then incline presses: 10 x 135, 10 x 135, 5 x 135 (quit as I was getting tight)
But when I went home, Barbara’s cleaning woman was still there (she had started late), so I walked to the Vietnamese place for a buffet lunch.
It was good, but it was also more food than I was used to.
So when I tried to concentrate on a work topic…..zzzzzzz……and I ended up checking Facebook about 50 times…
There is a reason I eat a light lunch on most days.
FAIL I was looking at a math book (for a class that I am teaching) and read the phrase “…. for integral ” and I didn’t quite get the word “integral” (I had just taught calculus…) until my colleague patiently reminded me of the phrase “for integral multiples of ”
“slow brain + heavy lunch” = “embarrassing fails”.
I got up late (by my standards) and worked out late; today was a lazy summer day. I’ll do some work later today; I have been thinking about a mathematics problem.
Workout notes: weights, then a run.
Weights: surprisingly, I felt relatively strong.
pull ups: 5 sets of 10 (good set today)
incline bench (strong), 10 x 135, 7 x 150, 10 x 140
super set: military: 7 x 45 dumbbell (standing), 10 x 40 dumbbell, 10 x 100 (each arm) seated, machine
rows: 3 sets of 10 x 110
pull downs: 2 sets of 10 x 160 machine 1, 10 x 150 machine two.
run: 11 minutes treadmill, 10:16 mile on the track (aborted a 3 miler), 21:30 treadmill (started slowly, increased the speed); finished feeling better.
my left knee is bothering me and bothered me some yesterday. It is probably a weather ache.
I don’t want to admit that yesterday’s walking workout was harder on me that I thought that it “should” be.
Now to do some thinking; these sort of things will be on my mind:
Workout notes: swam: 2000 straight laps (not timed; counted laps by 5: that is, 8 x 250 with no rests), then 200 pull.
I then took my daughter to Chicago Midway; we left at 9 am, I took her through the boarding pass line and to security; then I drove home and got home at 2:45. That was as fast as I’ve ever made this trip (round trip).
News: John Nash was killed in a traffic accident a couple of days ago. He was the focus of the book/movie A Beautiful Mind. He is known for the Nash equilibrium (in game theory); it was for that he won a Nobel in economics. But he had other great mathematics results; one of these was the Nash Embedding Theorem. The statement is somewhat technical but I think that I can give a flavor of what it was about.
Consider the circle. It is an object known as a “1-manifold” in that, if one examined the circle very “locally”, one would see that it was impossible to distinguish from a straight line. Example: if a tiny, near sided creature lived on a circle, it would look like a line to the creature, just like our spherical earth looks flat to us (locally).
Look at the two closed curves above. Those are “embeddings” (one to one, continuous maps from the circle). The one of the left: two points on the circle itself are “distant” from each other if and only if they are distant from each other as points on the plane. That is said to be an “isometric” embedding of the circle; points on the circle are far away from each other if and only if they are far away from each other in the plane.
Now look at the bent “circle”. See how two points of the circle are “close together” as points on the plane, but if one was forced to go from one of those points to the other point WHILE STAYING ON THE CURVE, one would have to travel a much further distance. That is a non-isometric embedding of the circle as two points are close together as points in the plane but NOT close as points on the circle.
So, the Nash embedding theorem deals with isometric embecdings; he gives a mathematical condition which guarantees that an arbitrary embedding can be approximated by an isometric embedding (as well as a dimensional criteria).
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