Tuesday, February 28, 2017

Thursday, February 23, 2017

Wednesday, February 22, 2017

Lost in Translation

Here's what I got so far...

Calculus I: "Change happens."

Discrete Math: "How to Speak Computer: A Beginner's Guide for Humans."

Linear Algebra: "How To Solve a lot of Problems That Look Like Each Other, All at Once, in No Time."

Intro to Databases: "Create order. Prevent chaos."

Backwards, Forwards, and All At Once

I took an online Calculus MOOC course some years ago. The toughest thing about it for me wasn't necessarily the calculus. I got the concept of limits fine enough, until it required factoring polynomials in order to simplify the limit. So I learned there were some algebra basics I had forgotten after years of not using, but I managed to study on the side just enough to stick with it.

The class also introduced trigonometry in both limits and derivatives. Trig was something that drew a blank entirely. Either I had never studied it, didn't pay attention in high school, or simply had long forgotten. At that point I decided to quit, because I had enrolled in the course with the intention of getting the most out of it. Even if I somehow managed to get through it, it was clear to me that what I intended to learn wouldn't stick at this point. When I enrolled back in school and started off in Algebra years down the road, I knew could have started higher, but I also I was there because I really wanted to get a firm grasp of all the important basics that would matter in any future classes I took or self-study I pursued. And I'm glad I did it.

This attempt to learn the basics of math and science seems to very much be about studying some topic, realizing that you have a basic knowledge gap, and going back to shore up your fundamental knowledge base before or while moving forward. This theme seems to only repeat itself, even as I (slowly) move up the ladder.

After that MOOC class I read through a couple (or a few) introductory calculus books on my own over time. I'm not sure how much I absorbed. But I tested it in part by trying to look through books I was interested in reading later. Somewhere along the way, I decided that two of the books I really wanted to not only get through, but to eventually read with ease and understand intuitively, were Mathematics in Nature and A Mathematical Walk Through Nature, by John A. Adams.  It sounds pseudo hippy-dippy corny as can be, but what I wanted to do was read the book, get a really good grasp of what he was saying, then spend some times in the woods, by the beach, or wherever I see more greenery than concrete, and see all the things he wrote about (this is still an eventual goal of mine). Then, I'd follow up with Adams' X and the City: Modeling Aspects of Urban Life and take a stroll through a nearby city to see if all the same things somehow looked different. 

When I tried to read Mathematics in Nature (that must have been some two or three years ago), it was clear I wasn't yet up to the task. But that book, along with a handful of others, did reaffirm the notion that if I was going to get a basic foundation for appreciating the world around me through a basic understanding of the laws of nature that governed it, that it would be important to really get comfortable with calculus and trigonometry.

Just last week, I attempted to get through In Praise of Simple Physics. Turns out, early on, the author mentions the book is really for readers who have already gotten through a class in freshman calculus. I tried anyway, and only made it through something like one-half to two-thirds of the book. But conceptually, I understood what I knew, and got a better sense of the things that I lacked. For one, my current calculus I professor had thankfully introduced implicit differentiation early in the class. So I came to quickly see that implicit differentiation was one of the things that stopped me from understanding calculus in other books I tried to read before. I always used to wonder were that extra term came from - it always felt like it just appeared out of nowhere for no apparent reason. And now the process was somewhat intuitive.

This week, I took on The Theoretical Minimum, which I had also tried to read years before. And it is now already remarkably clearer than my first time around. I could at least understand what was going on. I also learned something new here. Whenever I used to see symbols for partial differentiation, I never knew what the heck I was looking at. Now, the author's explanation seemed straightforward and intuitive.  The book even starts off touching upon concepts related to discrete math, which I'm also currently taking.

In chapter 6, roughly midway through The Theoretical Minimum, the author introduces the concept of The Principle of Least Action. Here, he uses Euler-Langrange equations. Somehow, I can sort of mechanically follow some or most of the mathematics and sort of kind of get what was going on conceptually with out really being able to put it all together. These are equations I could not work out myself as of yet. I stopped after the next chapter, when I realized future portions of the book are built on concepts shared in chapter 6.

I learned something from reading both of these books. One, that there's been some progression for me. Secondly, how important integrals are (I have a reason to look forward to learning about them in detail). Also, while math may be the bedrock for physics, and physics may be the considered the starting point for understanding the theory behind physical science for general, at least for me, understanding the mathematics doesn't necessarily mean understanding the basics of physics. Merging the two seems more like drawing a picture in your head, filtering to through all the mathematical gadgets and gizmos you have in your toolkit to see what might fit, creating new ones if you need to, and rearranging it all together in a way that makes sense and is truly (or at least functionally) representative of.

This makes me think that deriving equations for physical phenomena aren't always intuitive as I'd assumed. Part of doing the hard work of exhaustive and detailed reasoning is making sure you are aren't overcome by faulty assumptions. I get the impression that intuition may get one started in getting from A to B, and help smooth out rough patches in between, but that the end result hardly ever exactly matches what first came to mind. More like the creators learn along the way of trying to figure it all out. Or at least it's safer to assume so.

I don't know that I'll plan to take any physics classes in school (time and money are of concern). But I do know that I plan to use what I learn while taking these math classes to study more about the physical world, starting with concepts in physics before I move onto other things. From reading around, I found that calculus and linear algebra certainly both play a role in physics. So I went looking for books that covered both, hopefully in context of physics, and at a lower level than the two previous I read over the last couple of weeks.

Based on the synopsis and table of contents, No Bullshit Guide To Math and Physics seemed to fit the criteria I was looking for. It shores up pre-calculus fundamentals before going on to basic physics and calculus, vectors, differential and integral calculus, and mechanics. It seems conceptually thorough while still catering to the beginner. Hopefully, it will prove to be a good compliment to current classes, and a decent starting point for similar books I plan to read afterward.

Onward, ho.

Friday, February 17, 2017


Counting crime. At Bloomberg.

Wednesday, February 15, 2017

Sunday, February 5, 2017

Markov Chains for Inventory, Supply Chain, Accounts

Markov Chains were originally in the syllabus for my linear algebra class. However, the teacher announced that he'd always considered it something nice to cover, but that he knew we could skip if we needed to. And so, based on his observations, we are skipping it (why do I get the feeling though, that if I weren't in the class that it would still be covered with confidence? I say this in jest. I'm still catching up to everyone else is all).

However, I'd already started reading ahead just to stay on pace with my more math savvy classmates. I had read the Markov Chains chapter and done the homework. Since we weren't covering Markov Chains in class, it wouldn't be on our first test the following week. In the middle of studying for the test, I re-read the chapter anyway, just to get a grasp of what seemed like an interesting concept whose name I had come a cross a handful of times before I started taking classes.

When I re-read it, I got one of those "ah-hah!" moments. I wish this concept was something I had known while I doing some freelance financial modeling work a year or two ago.

Essentially, I put together two financial spreadsheet models for two different clients that had some combination of physical inventory (and associated multi-faceted cost accounting associated with it), up-front payments (and therefore more complicated accounting), various product lines (more complications), and various market-based outcomes (even more complications).

Both models were monsters in size and breadth. Looking back I always wondered how I could have made them simpler.

Markov Chains essentially do that for you. A chain considers how market conditions or combinations of inputs and outputs might change or transition over the course of a given period in the form of a row-by-column matrix. Each one of these individual transitions are represented by figure between 0 and 1 (0% to 100%), adding up to between 0 and 1 in each column, in the matrix P, called the matrix of transition probabilities. This matrix represents percentage / probability of occurrence in a given period applied to an original market condition X (say X is, for example, is the number of total items sold into a market, with each market represented by a row in X). When you multiply P*X the output Y is your new market condition.

Keep multiplying the same Markov matrix / matrix of transition probabilities and you get the assumed cumulative condition of that market overtime. The one thing I wonder though, is what happens if you have new transition probabilities. I guess instead of multiplying by the same exact matrix of transition probabilities in the given time period, you multiply by a new / adjusted version instead?

Either way, potentially, 10 large tabs in an Excel spreadsheet file could have been reduced to 1-3 more compact ones. Though I'm not sure if Excel can really handle matrices to begin with.

On top of all that, being actually able to apply this method and execute it correctly is a whole other matter.

Still, this feels like adding another compartment/notch to Batman's utility belt. More math seems to give you more options to choose from.

Saturday, February 4, 2017

Free Wi-fi

I don't understand what most of this article is saying. But I now know that for someone with a little know-how or who is willing to learn, free public wi-fi is possible.

"How to get free wifi on public networks." At freeCodeCamp.

Thursday, February 2, 2017

Old Dog, New Math

Some years ago, I decided I didn't know enough about the world. Life kept getting in the way of trying to know more immediately, so I got started a good year or so after that. Reading and reading about the fundamental rules of the physical world. And I came to find one big gap. Many of these books used the language of mathematics. And I barley knew a lick of it.

It was tough trying to learn on my own to start. So I decided I wanted to take a couple classes. Life and bills got in the way. So, finally, a couple years later, I started taking courses at my local community college. Started with intermediate algebra with old folk like me and high school folk alike. Went on to precalculus. More work and catching up (I knew next to nothing about trigonometry). Made it through.

This semester is calculus I, discrete math, and linear algebra. Three weeks in, I feel on pace in some respects and nearly out of my league in others. But I do feel with a bit of hard work that I can make my way to somewhere between the lower ranks and the middle of the pack.

Calculus comes across as the most intuitive for me (but this might be because I spent some time trying to learn it on my own before, with moderate success). Discrete math feels more intuitive than it should be with some work. But that's in part because we've only had some homework so far. When it's just you, a piece of paper, and a question on the test, your mind can start racing. And I can see there is a lot there though and I can already tell that it can catch you off guard of you don't keep up.

Linear algebra is kicking my butt from early. Not in a way that I feel like I'll never be able to catch up. But starting off I'm by far the slowest one in the class.

It's not horribly bad. I came to learn. There's plenty room to do it. And the benefit of going to school for your own sake as non-exceptional adult (more specifically, as someone at least a good 10-15 years older than most of my classmates) is that you are more focused on your own improvement than any insecurities that came with youth or competition. The downside is when you get into a class where everyone moves at twice your speed, if you spend too much time trying to make all the foundational connections your classmates spent making in 6th grade through freshman year in college, by the time you look up everyone else might be miles ahead.

I like to write. Also, I use writing to explain things to myself when I don't understand. Writing is often an exercise of clarification for me.

So I've decided to spend some time using this dormant blog (I think it's been somewhere between 3-4 years since I've written anything here) to explain math to myself.

Maybe it will encourage me to write some other things as well.