Habit

It's certainly best that I'm starting to work "regular" study into my schedule now rather than waiting until school start in the spring because I'm doing a terrible job of it. Studying simply isn't a habit the way going to work or training for running is. I'm sure I can make it one but, for now, I'm really struggling to carve out the time for study.

I'm trying to understand how these habits are formed (aside from the obvious: practice). It's certainly not as simple as schedule. Work is not as routine as one might think. I usually start the day fairly early (between 6 and 7am), but sometimes it's later. I will work nights and weekends when needed. Similarly, my running training moves around quite a bit; some days are morning only, others are morning and afternoon, others will do something just at lunchtime. Yet, the requirements of both work and running are met very consistently.

I don't think it's as obvious as priorities, either. I think it truly is as Aristotle claimed: "We are what we repeatedly do." Before studying can become a regular part of my life, it must become part of my life. A conscious decision needs to be made each day to tend to it.

More Algebra

Busy day at work, so I ended up working through lunch. At home, I decided to break out my Linear Algebra text so I can find more problems to drill on. Spent about half an hour looking through which sections I should work.

Computation

An hour at lunch today working some vector problems. Fairly straightforward stuff, like converting a generic basis to an orthonormal one and decomposing vectors into a subspace member and a member of an orthogonal subspace. Simple enough in concept, but I'm appalled by how rusty I am at actual computation. My daughter has the same problem: she understands the ideas, but really gets hung up on actually running the numbers. I guess she comes by it honestly. I'll just have to take the advice I give her: drill, drill, drill.

Back at it

A very nice weekend (including an age group win at the Alton Half Marathon), but not much time for study. Today was the last day of our iteration at work, which meant we spent a good portion of the day trying to tie up loose ends and plan the next three weeks. As a result, I only had a little time to look at a few vector problems. I'll try to carve out more time tomorrow.

More vectors

1 hour. Finished up my survey of vector algebra at lunch. Picked out some problems to work for my next session.

First proof in about 20 years

Another hour at lunch today. My brief messing with vectors in Python yesterday was enough to convince me I should brush up on linear spaces. You'd think I'd know those pretty well since what we do here at work really boils down to vector arithmetic on very large dimensional spaces. However, optimizing the mechanics of several trillion calculations is a rather independent skill from deriving the theory.

I brought in an old text and read that for a bit and also went through the exercise of proving the Basis Theorem (mainly because it was the first substantive theorem I came across). I didn't see a real elegant way to prove it, so I just brute forced it by decomposing all the basis elements of the larger set into their sums from the smaller set and showed that there had to be enough non-zero coefficients to force dependence. I was thinking I might be missing something slick, so it was with some relief that I found the author's proof to be quite similar.

Bitten by the snake

I got in an hour of study at lunch today. It started as some superficial reading on Markov Chains (no particular reason to choose that topic; just had to start somewhere). Half an hour in, I came across some code that computed Hidden Markov Chains in Python. I haven't written anything in Python in a very long time. I'd forgotten what a delightful little language it is. I spent the remaining half hour messing around with the code. Probably best not to get distracted like that, but it was fun and fun is good at this point.

A little arithmetic for St. Pat's

I really will get around to studying soon, but being mostly Irish, I'll just leave today with a limerick passed down from my great-grandmother (an Irish nun who, upon journeying to the new world, married a Scottish Presbyterian; I bet that went over big back in Dublin).

There once were two cats from Kilkenny
Who thought two was one cat too many.
So they fought and they fit
And they scratched and they bit
'Til instead of two cats, there weren't any!

Cheers!

Optimal stopping rule

I had a brief email conversation with my Thesis Advisor from Cornell, Bruce Turnbull, about the topic of my research. It basically centers around the idea of an Optimal stopping rule for database queries. In a nutshell, the question is, at what point are you beating your head against a wall by bringing back more rows?

At work, I deal with databases that are measured in terabytes. Lots of terabytes. Single queries often bring back several hundred billion rows. Really? Do you really need that many? Of course not. But, how many do you need? Are you sure? With what level of confidence? And, most importantly, how is the best way to select just the rows you do need? That's the problem I'm interested in working on.

To do it, I'm going to need to get myself onto the cutting edge of large database design (that's the easy part, as what we're doing at work is pretty close already) and also take a fresh look at predictive statistics. So, my lesson plan between now and classes starting in the fall is to dust off all my statistics work from 25 years ago.

Time Division Multiplexing

For my first year, I’ll be taking two courses per semester so I can take the Qualifying Exam and get on to real research in my second year. I’m estimating that coursework during my first year will require about 20 hours a week. If it was deep theoretical stuff, I’d expect that to be more like 30 hours a week, but these are core Computer Science courses so I have a lot of context (it is, after all, what I already do 40-50 hours a week).

One way to free that up would be to quit running altogether. I’m not wild about that solution for a couple reasons. First and foremost, running is when I do most of my nurturing of my soul. I’m not sure I could deal with the stresses of this endeavor without that. Secondly, learning is as much passive as it is active. Yes, you need to concentrate and practice. But, you also need to give your mind a break and let it just sort through things on its own. Again, that’s pretty much what happens when I run.

So, I am instead just going to cut running in half. That means I need another 10 hours a week. Kate has agreed to take over cooking duties 2-3 nights a week, so that’s three hours. Sunday evenings are usually free, so I could get another couple hours there. I can probably get in a couple hours a week during my lunch break.

The final 3-4 hours again presents me with a choice I made over 30 years ago. In my late teens, I realized that I could be OK at music or OK at cycling, but if I really wanted to be good at either, I needed to quit one and dump all that effort into the other. Since tenors don't really get their voice until their late 30's, I went with cycling. That played out fairly well, as I did manage to get to the pro level in cycling (albeit, a very marginal pro). However, in retrospect, if I had chosen music, I'd still be good at that whereas my best days as an athlete are long gone.

Still, the physical release is a very much needed thing so, once again, I'm going to jettison music. I'll be quitting my church choir to free up a bit more time. That's a bit sad, as I really do like singing in the choir. It's a sacrifice I'm willing to make, but it's still a sacrifice.

Pi day

Well, it wouldn't be much of a math blog without at least mention of Pi Day. Particularly this year, as you can go to as many digits as you want (3/14/15 9:26:53.358979...). Of course, if you're like me and worked on some Y2K projects in the late 90's, you may still have difficulty writing a 2-digit year.

I'm not much for gimmicky celebrations, but this one really seemed appropriate. So, in for a penny, in for a pound. I served pi (bacon-spinach quiche) for breakfast at 9:26:

Yes, the "6" is backwards. I really am dyslexic and didn't catch it until it was too late. Fortunately, dyslexia and left-handedness have both been linked to proficiency in math, so I'll embrace it.

We had leftover pizza pi (salmon topping and a cream sauce from last night's lenten observance) for lunch. For dinner, it was shepard's pi (ironically, in a non-circular casserole):

And, at 9:26PM, the pumpkin pi was cool enough to cut and top with whipped cream!

Just for the record, I think memorizing digits of pi is about as silly as it gets. If 22/7 isn't good enough, break out a calculator.

Restart

So, it’s back to school for me. I've been accepted at the University of Missouri, St. Louis (UMSL) to finish my PhD in Applied Math (Computer Science Concentration). As I’m doing this while keeping my day job, staying on task will not be a small challenge. I am used to managing similar efforts since I have up to now devoted a significant portion of my free time to running. Extremely helpful in that regard has been keeping a training log. So, that’s really what this blog is: my training log for grad school. It’s written by me and for me but, as with my running log on AttackPoint, some others may find it interesting. So, I’ll post it here.

Also as with my running log, there will be a fair number of orthogonal posts. A training log requires the context of the rest of life. In particular, this will become the new home for my race reports, though I will certainly be posting fewer of those since I won’t have nearly enough time to properly train.