Is anyone here experienced in algebra two?

[paloftoon]

I'd have to say Geometry is actually more abstract than algebra because of the visuals. I guess Algebra could be looked at as more abstract because the idea of a letter or variable means that any number or a set of numbers could substitute a letter/variable that represents a certain kind of mathematical relationship/pattern that always occurs.

 

[paloftoon]

I was very, very angry with my highschool math. 2x+3 is not an answer, that is a step before the final answer, and I HATED how incomplete it was. Trig was evil, I felt that if it could not be solved directly through pencil and paper then it was a waste of time. So I didn't get along with calculating by most sin, cosin, and tangent. Now, I love it. Gimme a few functions, I'll plug and play all day long. It's just something I grew in to. I even made peace with trigonometry, and gladly accepted sec, csc, and cot. But I am a lot more abstract and grey area than those days, I was still very black and white and rather strict about things.

Greek and I are still in tense terms. That sigma...

2x+3 as an answer implies that the answer you're looking for is a pattern rather than a specific number. Sometimes in life, we need to understand patterns so that we can get specific answers in life to multiple things in a timely fashion. Computers need an understanding of these general patterns themselves to run. Specific numbers by themselves would not be conducive if even feasible. The pattern you solve for could have restrictions depending on the situation. If you're not given a word problem for this, then it helps you understand the patterns to solving for that kind of answer. By starting students off with word problems instead of algebraic problems purely, 99.9999% of people would get more confused because there are the layers of learning the math linguistics on top of the algebra itself.

You don't have to enjoy learning a topic, but you do need to show respect to those who have to work with you.

 

[paloftoon]

Can you explain Natural Log to me? I mean, I understand how its used, but I don't understand what it actually means or how it is found. Am I making any sense? Probably not. Maybe you will.

Natural log makes a beautiful slow curve on a graph and generally computes growth. As for what it means, I dunno. It came after the lesson on the square root of negative one, and I'm still trying to figure how the heck that works.

With math, don't expect to understand how everything is found until you start learning and understanding patterns in more advanced math such as with calculus, linear algebra, and differential equations. And if you focus on where those are derived one, then those would be with more advanced math courses. The understanding is layered. If we had to figure out math based on the way the famous nerds figured many of these principles out decades or centuries ago, not a lot of progress would be made from us!

With y = ln x, it is the opposite of y = e^x. Both curves have patterns that happen in life, or that can be used as a basis for what happens or what may happen in life. Just like how 0 is a starting number for addition and subtraction to get the same number, and how 1 is a starting number for multiplying or dividing to get the same number, y = e^x and y = ln x basically do the same thing, but in much more complex ways that are not important for you to understand to a "T".

y = e^x could represent a general, slowly increasing trend up to a certain point. After that certain point, no matter how much time passes by, if all other factors are constant (ceteris paribus), this pattern of y = e^x would hold true. Not all things in life follow a straight line pattern, so that's why we learn about more complex functions that represent curves. If you sell more items in a company you run, it doesn't necessarily mean you make more money. There are other factors to consider such as how long people have to work, and/or how long a machine can run properly to produce your product, or what happens to products that are produced properly. Those external factors can be based off of y = e^x or y = ln x. These kind of patterns follow through in economic, statistical, medical, and engineering research basically. Most applications with more complex math patterns like these will be one of those things. If you really want to understand something to a "T" beyond the explanation of that these patterns can be used for economics, statistics, etc., then you need to learn and understand a lot more math in addition to what you are currently learning and have learned before!!