Friday, March 24, 2017

Learning How to Read Again

The reason I started taking math courses in the first place was to learn how to read so that I could learn how to learn. Which is to say, I didn't know about the stuff around me. So I tried to read about stuff. And the books and articles that talked about that stuff had more math in it than I could understand.

Every now and then between classes, I go to the library or search databases to read about that stuff and see how I'm progressing. Firstly, it's interesting that I had a hard time finding the things I originally did. A few years ago, when I was trying to read about infrastructure, energy, society, nutritional studies, and similar things, math eventually, repeatedly, became my roadblock. It's a bit harder to go the other way around. When looking for mathy journals and articles that relate to the stuff around you, it's easier to find things that fit within the designated category right away, but harder to find source material that you'd probably be able to adequately comprehend any time soon.

I guess the eventual goal then, is to funnel things down to journals and sources that cover topics I'm interested in, but still use math to explain that stuff. There are definitely some exceptions. But the math-first stuff will need to come later.

In the past couple months, I've learned a few things like:
  1. Thank God I took pre-calculus (same goes for Algebra)
  2. A lot of these fancy symbols are stand-ins for whatever the writer wants them to mean
  3. Stay away from physics journals until you really know your shit
Pre-calculus was worthwhile because it covers a good deal of the stuff you'll find in books and journals like "Mathematics of Electronics" (actually for electronics, it definitely helps to have taken some linear algebra as well), "Traffic Congestion," "Energy Basics," "Mathematics of Agriculture," (not necessarily actual titles of the books I read, but relevant to what I've skimmed through) etc. Because when I look at equations, instead of seeing some foreign language, I can see how the particular function, scenario, street corner, input-ouput, social trend, physical condition, etc. is expected to change over time based on how the equation is structured.

Something as fundamentally simple as comprehending an equation with a negative exponent used to be a challenge for me. Yes, like 8x *10-5x. Now I just see 8x * (1 / 105x),  or 8x / 105x, which is to say as x gets larger, the result gets a lot smaller very fast.

Very simple. But it was a road block for me nonetheless.

Still, those are just the books you find in the library. It's the journals that seem to have an abundance of crazy-looking symbols and figures that read like a language from some other dimension. It turns out that in a significant number of the journals, it's sometimes explained what these symbols mean. So if you know some things like (a) a subscript attached to the right of a normal looking letter (think capital Z) often represents a function (the Z) based on a parameter represented by the subscript, or (b) what a function might look like, it doesn't look nearly as intimidating.

It's not that I can understand all the stuff in these journals. It's that re-reading them at this point gives me the confidence that I'll eventually be able to get a grasp on much of what's in them.

It's when understanding of all these symbols and relationships are implied that things get more difficult. When there's a common language and understanding of mechanics that you weren't part of prior to reading what's in front you. That's physics journals. I can't even begin to know what the hell they are talking about (not that I expected to). It may take me years to get to a point where I can comprehend them. Maybe not even then. But that's not why I started anyway. Still, I'm intrigued enough to eventually want to get there.

All that brings me back to the classes I am talking now.  Calculus is the most obviously useful.  It's used a lot of places. And it reads and feels like mechanisms in motion, just the way things in the world around you do.

My calculus teacher likes to say "math is a language." And of my current classes, nothing is more representative of the saying than discrete math. It looks and feels really hard at first, because there's so much "vocabulary" to learn in the beginning. And even as you solve problems, it's not necessarily easy to tell whether you've gotten a feel for what's going on. The real learning seems to begin when you go back and read what you've already gone through (as I've learned when studying for tests). All of a sudden, all that disjointed logic and symbolism reads a bit smoother, as if the dots have been linked by lines, that eventually smooth out and curve into an image that reads like a machine or narrative of sorts.

It's not that clear to me yet. Not even close. But I can see where it's going. A lot of benefit can be gained after taking the class and just going back and reading things.

Linear Algebra feels like it's more difficult for me than it should be. But it seems so fundamental as a basis for addressing problems with a lot of moving parts, lots of data, and as a basis for visual representation. So it's something I have a pretty strong interest in learning (I also like the material even though it doesn't come natural to me).

Also, I looked ahead at higher undergrad courses, and I see that what I'm taking is really equivalent to Introduction to Linear Algebra (it may be lower than that). Beyond that is a 300-level Linear Algebra class that assumes you've taken and done well in abstract algebra and real analysis. Beyond that are things like non-linear systems, which I'm guessing are often more representative of what happens in the natural world. And if I haven't gotten the (relatively) simple linear stuff down, how will I find my way through all of the chaos that isn't made of long, straight lines.

Linear Algebra seems so fundamentally important that I think, if I don't come out of this class with a real thorough understanding of the material, then I might just take it again (even if it's the intro class at an undergrad level rather than at community college). Even if by some miracle I happen to squeak out an A (which doesn't seem remotely as likely as it once did).