A whirlwind week of algebra - Pre-Calc Week 1

I finished my first week of pre-calculus by UCIrvine through Coursera. It was harder than I expected due to the sheer magnitude of the workload. Although it was algebra, exponent rules, radical, rules, polynomial operations and inequalities, the fact that it was 30 videos and quizzes made it labor intensive. However, in the end I grit my teeth and got throughout them.

 

As I mentioned in a past post, the way mathematical expressions needed to be input into the quizzes was giving me trouble. Yet, thanks to economies of experience, the more exercises I did the better I got, and the faster I was able to do them.

 

I felt and odd satisfaction when I finished my last quiz on the due date. I knew the first-week homework would not be part of the final grade so I could have very well skipped the exercises and done nothing, but I felt compelled to do it. To be fair, I re-learned (I wonder if that term is trademarked) many concepts that had been dormant since high school.

For example, the arithmetic commutative, associative and distributive properties are basic knowledge almost since elementary school. However, most of the questions I have when solving a problem have to do with these properties. And the fresher I have them in my mind the easier the problem becomes.

 

Other concepts I re-learned this week:

• Roots can be expressed as exponential fractions and be subject to exponent rules.
• When you divide or multiply both sides on an inequality by a negative number you need to flip the inequality symbol that joins them.
• Factoring polynomials can help you understand the relationship they have with other polynomials.
• The "two trains leave the station" type of problems have to do with time, distance and rate...not (necessarily) geography, thank heavens!

I find it thrilling to work with all this math again. As an adult, I have a different perspective on all of this. You see, for many mathematically inclined adults working doing algebra exercises from junior high would be a waste of their time. For them this math is just too simple to be worthwhile and they see no point. The way I see it, before this math became the stuff of junior high, very smart and serious adults were discovering and working with it. What we now find simple, was a breakthrough for scholars in other times. Therefore I am following the path these great minds paved...how's that for self delusion.

 

Let me know your thoughts on this in the comments.