Sunday, November 11, 2012

Teach Yourself: Math For Slow People Like Me

I am by no means and never have been a math head. But I took interest in the topic by happenstance. And, as someone who does not have a stratospheric IQ, found it to be a bit more digestible than I remembered from high school.  If you are an Average Joe like me, the hope is, for those who are no genius, but are truly interested in learning the material for its own sake (that's key), this can get you started and help you move a little faster than I was able to:

The Art of Mathematics or another "Mindset" Book -  Essentially, a text that will teach you to think "mathy," I guess.  A fabulous example is the Art of Mathematics by Jerry P. King.  King also happens to be more than a solid writer. This book, for me, just puts things in context. But you'll only appreciate how good it is once you get on to the other stuff.

Proofs - Essential. Get a book on mathematical proofs. Find something slim; if the text is large and hefty you'll be wasting a lot of time. I have two examples in books, one of which I really liked, but will share once I find it. Do not worry if it's a slow read. If you do not understand something stick with it until you do. That's extremely important here. I have an excellent book I read on proofs that I need to share but need to find the name of the title again.

Real Math - I can't say which you'd want to read first: a book on mathematical proofs or a book on "real" mathematics. But once you understand one you'll see why the other is so important. Real Math is based off proofs, and until you understand the thought process behind mathematical proofs, "real" math might look like something from outer space. You'll begin to understand that the math you learn in school assumes a lot of short cuts that "real" math goes through the hard work of proving. That's mostly what makes it look so complicated.

Statistics - I think, for your every day average Joe, statistics represent the bulk of "complicated" math you'll run across on any given day. They are used in marketing, campaigns, financial industry,  decision making... Nearly anytime you are trying to spot trends and make predictions that involves uncertainty and a large group of dynamic bodies that may act differently from one another (those things are often people). I still absolutely, only get this stuff if I happen to be doing it on a fairly regular basis.

The traditional way of learning statistics in school is through repetition and memory, which is fine, but I'm not sure it actually tells you what you are doing. The most enlightening thing for me, in class, was to do a statistics problem using Excel in two ways. First by just running the problem through it's Data Analysis package, which calculates everything for you. Then using the same data in a second spreadsheet to calculate everything yourself, individually, making sure your results match what's on the first. The second exercise is key because you begin to understand some of the assumptions behind the data, why your results are what they are.

Geometry and Physics - These are one of those things that do not necessarily come naturally to me. But reading either may help you do a few things. "Real" math/proofs and statistics aren't necessarily representative of the real world. Using proofs, logic and numbers have to add up, but they don't necessarily have to have any real world applications. Statistics are often entirely assumptions, not fact.

Geometry and physics represent the world around you, and generally, the rules are pretty much "factual" in that the math will accurately reflect what's going on in the real world. If you start reading these along with basic books about real physical world things you know or are in your everyday life (cars and engines, architecture, household heat and water systems) the relationship between math and what you see every day might become clearer. And you might start becoming more curious about mechanics and science as a result.

And... The point of getting a physics book is not to prove how smart you are. It's to get an idea how math is related to the moving physical objects you see everyday, the real world you live in. I'd suggest with a book on the mathematics of physics (I am slowly, painfully working myself through one now) rather than an actual physics book, unless you happen to be in science.

Find People Who Know How To Make Things That Are Complicated Look Simple, While Still Remaining Thorough - I can't explain how to find these things, but I think's videos on exponential functions and natural logarithms are good (but not of the best) examples.