Math, The Way it Should Be (Unit 2.6: Summary and Philosophy)

As you (probably) well know, the final lesson in each unit includes a summary of previous lessons and then some personal philosophy from me.  But before we get to that, I would like to point anyone new to this series to the first post in the series.  I usually also link to the first lesson in the unit, but I'll be getting to that soon enough.

So this unit was pretty much a refresher on geometry and a little bit of what is usually covered in trigonometry classes.  We started with the very of geometry, angles.  The most important thing to take away from that lesson is how radians work.  They're not the most intuitive but once you get used to them, they're well worth it, as you will see later.  After angles came triangles.  The most important thing to remember about those three-sided shapes is that they're the key to doing all kinds of things with vectors.  In fact, you can make an infinite number of triangles with a given vector... it's choosing the right one that is difficult (and the right triangle is usually right!).  Then we covered functions that are basically little machines that turn one thing into another thing.  Trigonometry rounded out July.  The take-away message there regarded the trigonometric functions (most importantly: sine, cosine, and tangent).  The penultimate lesson dealt with areas and volumes.  I wasn't very happy with that lesson but I consider that most of geometry education deals with memorization of formulas that becomes largely obsolete with an understanding of calculus, so I kind of glossed over it, (hopefully) leaving you with exactly enough to understand some of the things that come next.

So here's the philosophy: I don't really like geometry or trigonometry.  My real interests lie elsewhere in mathematics.  Unfortunately, like all of mathematics, those more interesting areas are built on the foundation provided by less complex mathematics, specifically algebra and geometry.  So even though I don't like them, I  have realized that they are necessary to fundamentally understand what is going on in more complex operations.  To me, things like geometry and the multiplication tables are like the alphabet: they're not that interesting in and of themselves, but combine them together and you can form the words that describe the whole universe in a way that very few people understand.

-Lane