More hardcore, actual mathematics will be coming soon. But that requires me to actually have MathJax (the natively installed mathtype software that I've installed on the server) to be up and running and functioning within the blogging software. And then I have to go back and convert all the image based math equations into MathJax typeset. In the mean time - at my last study group, we began talking about symbology. In our last class, we learned that the overbar not only means a repeating decimal, but also means the conjugate of something. Which got me thinking about the below. I don't suggest you try this on your math teacher until I've actually taken over the Mathematical world and imposed my own definitions upon it, but still - take a think about how things you wouldn't normally think of doing can be applied in different ways.

When we see the following equation:

We immediately think - oh! That's a perfect square! Or, at least, maths teachers would desperately hope that's what we think of. And so we factor it:

Now say we see the following equation.

Again, maths teachers would hope we jump up and shout "that's a difference of squares!" And so, we factor it.

But there's no shortcut! But, hang on.

Look! It's an overbar! And an overbar, in this context, could be defined (by me, of course) to mean "take this expression, and multiply it by its conjugate."

So, if we accept the definition of Mathematics by Simon (MbS for short) what would this multiply out to?

A cursory glance of the internet tells me that no-one uses the bar over the exponent to mean something else, but if you know better, please tell me!

And yes, the answer to the superman problem is coming. My problem has been trying to implement the technology behind MathJax, in order to properly display equations and such. The method I was using before (an automatic image generation server) seems to have failed, as you can tell by the lack of equations in my blog. 

Good news is I got an A on my 131 course! Pre-calculus algebra and trigonometry, here I come! I'll be back as soon as the technology is working again. 

Also, elections happened at my college. I took it rather seriously - in fact, probably a bit too seriously, but then democracy, and proper voting, and respect for the voting population matters to me. There was a lot mismanaged about this election, but I think what says it all to me is this:

Last year, 700 students turned out to vote. This year, at least 1200 did. That's awesome. But in Fall 2009, we had 29,709 students enrolled. I don't know if they're all eligible to vote, but let's assume that they are.

To figure out the percentage a number x is of y, you can use a pretty simple formula.  . So, assuming those figures are accurate, and they were all eligible to vote (I couldn't find anything in the bylaws to say that they weren't), that gives us the equation  . So, the voter turnout was 4.04%, assuming that's accurate. It may not be. But even so, out of almost 30,000 students who attend my community college, only 1200 of them voted. It's great that it's better than last year, but it shows that something needs to be done to improve student participation in these elections. And the math proves it.

My next exam is on functions. Doing all sorts of things with em too:

• Operating with functions
  • Adding
  • Subtracting
  • Multiplying
  • Dividing
  • Composing
• Knowing and finding the domain and range of a given function
• Graphing functions and transforming them
• Finding, graphing, and proving inverse functions
• Defining and proving 1-to-1 functions

I don't like functions. Mainly because the two days my tonsils decided to go on painful strike was the day my math professor decided to cover functions. Catching up was difficult. I'm still not quite clear on some of the concepts, especially the inverse functions - I missed an important hour of that this past week because my alarm clock didn't go off. Fortunately, the test was postponed from tomorrow to Wednesday. So I have more time to study. I just hate missing even half a day of class with this course. So much material gets covered it feels impossible to catch up when we're barely keeping pace as it is!

The quadratic formula. High school children learn it all over the globe. I did. I learned it by rote, and I passed my Maths GCSE quite handily by having memorized the formula. Did I have any idea what it meant? Absolutely not. So, when it came time to learn it again, of course I'd completely forgotten about it. All the mathematics teachers I had before my current one taught the formula as something to be uniformly applied and learned. Like the national anthem. I could sing the words to 'Mae Hen Wlad fy Nhadau' as many times as I liked, but it would be years before I actually understood what it meant.

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