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.