Ouch, Analysis-1 is going to be a toughy

2007-11-17 11:55:00

Careful now, this may sting a little... o_O

This semester we're covering Analysis 1, which requires a wholly new way of thinking. Where Statistics 1 was pure maths and calculation, this course requires something additional: insight and a sense of logic.

The thing about this course is that it's all about proving maths. Not using maths to prove stuff, but proving the mathematic equations themselves.

Folks who aren't too hot on math may want to skip the next section :D


For example, the calculation show is above belongs to the question "Prove or disprove that (k^2 -1) is divisible by eight, for all values of K that are integers and odd". "Odd" in this case is opposed to "even".

So, how do you even get started on such a question?! Well, you start filing in bits and pieces, starting out by equating k to (2n + 1). Why? Because one can make -any- odd number by taking integer n, multiplying it by 2 (thus becoming an even number) and then adding 1.

Once all of that is done we're left with 4(n^2 + n). In order for the original theory to be right, this'd mean that any value of (n^2 + n) needs to be even. And that's what I'm testing in the second and third lines: first for even numbers, then for odd numbers. And indeed, both tests come out positive: any value for n will result in an even number.

Pulling this back to the original theory means that any outcome is indeed divisible by eight, because four times any even number is always divisible by eight.


Joy!... I've always sucked at being insightful, so a lot of these "tricks" don't come natural to me. Then again, I used to get good grades for math and even for stuff like this. I ought to be able to get the hang of it again.

I hope ^_^;;

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