math

Okay, I have to admit that I haven’t done much math since high school. With the exception of balancing my checkbook and the grocery store, I haven’t practiced the mathematical skills in about three years. I apologize for the math vocabulary I’ll probably abuse in my explanations; I’ve forgotten a lot of the terms, but I think I remember how to apply them.

First of all, the odd and even numbers. I think the easiest way to prove that the product of two odd numbers is odd and the sum of two odd numbers is even is by factoring out numbers. Here’s the process I used:

2n = even
2n + 1 = odd

odd + odd = even
2n + 1 + 2n + 1 = even
4n + 2 = 2n
2(2n + 1) = 2n [factor out a 2 and you get 2 times an integer]

odd * odd = odd
(2n + 1)(2n + 1) = odd
4n² + 4n + 1 = 2n + 1
2(2n² + 2n) + 1 = odd [factor out a 2 and you get 2 times an integer, which is an even number, plus one, which makes an odd number]


Now, I’ll try to tackle geometric angles. The two angles on the straight line will always come to 180 degrees. So angle A plus angle B equals 180. Equally, Angle B plus angle C equals 180. Since this is true we can say angle B plus angle C equals angles B plus A. When you subtract angle B from both sides you get angle A equals angle C. Therefore, vertical angles are congruent:
line E = 180º
line F = 180º
angle A + angle B = 180º
angle B + angle C = 180º

angle A + angle B = angleB + angleC
- angle B - angle B
angle A = angle C


Statistics. I don’t think we place too much value on statistics, but I do think we can trust them too much – if that is a distinction I can make. Statistics allow researchers, the public, etc. to quickly estimate current preferences, feelings, opinions, and trends of a population. I don't think they should be taken as definitive findings, but statistics provide a strong first step in beginning to understand a topic or focus research. Of course, there are a lot of problems that make statistics fallible. There will always be outliers in the data - unaccounted extremes on either end of the spectrum. Margins of error and varying confidence levels reveal that statistics can be wrong or misleading. Researchers must avoid attributing causation to correlation. Statistics can't account for the human nature of a topic - the social and psychological side of things. The nature of percentages usually means there is a chance - however small it may be - that things can go the "other way." Statistics are far from perfect, but I think they have value when used carefully.