02.14.06

As far away and a s muffled all my senses are right now, I'll recall and retell the lat understandings of my previous days for they are quite important to my upbringing.

1. I have just discovered toad, through teaching Jennifer Garcia, how to simplify trig. Expressions that math is nothing but a game of pattern recognition. If a(b+c) = ab + bc then those two side of the ='s sign are a pattern for renaming as are the letters inside of them. All a pattern which can be placed on any combination such as: sec²x –secx and used to rename it. Then the father renaming of the letters can be used to expand them and once again, a third renaming can lead through that abstract pattern to an expanded version of the concrete expression w/ secx's.

My insight is that math is a world where you transform old relations into new ones through patterns you know or discover(those know patterns too are created from previous patterns you knew or had discovered)

2. Of the utmost importance is how I view the things I learn. They must be interesting in some form or fashion. It might be that:

1. I think to myself "in the future if someone practically asked me how to solve this problem, or I asked myself this problem, by creating its relation of the analysis of other data, how would I approach a solution to it",

I think of the concepts presented as those in Saturday Morning Physics, not dull and constricted to the book, but available for discussion, with an opportunity for me to voice my ideas with confidence and support from others, while reviewing and thinking over their opinions, and not meddling with details such as computational numbers. It is important to view problems in an abstract sense and figure out what information you need through the variable, not be stuck in a situation where you can only solve a particular type of problem with particular givens. You must know what givens you need to reach a solution you want, and that is only achieved through an abstract view of the material without the constrictions of the numerical computations.