HALP me learn pre-calculus~

[Ksandra]

OK, now that I got my California certification for English, I am trying to expand it to lower-level math. The way it works in California, once you get your certificate you can expand to different subject areas by passing certain state tests (cset) for that subject. Math works a little funny though.

There are three subtests:

1. Algebra, Number Theory

2. Geometry, Probability, Statistics

3. Calculus, History of Mathematics.


Now, for me to teach middle school mathematics (what I'd want to do), I'd have to pass the first two tests. test 2 is supposed to be really easy, and test one is supposed to be insanely hard. I am going to try and pass test 1 first, because if I can't do that, there's no point in doing 2.

ANYWAY, even though it's algebra it's pretty much pre-calc levels. I did extremely well in school for all my math courses but that was over ten years ago now, and I never took pre-calc. I have been going over the khanacademy.org website to basically relearn everything from scratch, but while I'm doing the foundation, what I am studying on there isn't really going to be on the test.

tl;dr I'm going to start asking questions on where I can find good sites that break down some of the stuff written in a study guide I bought. The guide is supposed to be good in the sense of pointing out what you need to learn, but it assumes you already know what all the terms n' such mean. Some of which I can't find explained in the khan academy site.

I'll probably ask a few bit by bit then study the shit out of it before moving onward.



Here we go:

First bullet is-

a. Know why the real and complex numbers are each a field, and that particular rings are not fields (e.g., intergers, polynomial rings, matrix rings).

book goes into a list of fields and rings. The only difference I see is this:

field

-every non-zero element has a multiplicative inverse in F

- + and X are commutative

ring

- + are commutative

why is this?

It then lists common rings that aren't fields as: integers, the set of square matrices of a given size, the set of polynomials with coefficients in another ring, natural numbers, and quadratic polynomials.

What is it about each of these that causes them to be a ring and not a field?


You do not have to answer each of these, and if you have a website that breaks down the differences in these two applications I would appreciate it as the site may help with further questions.

Most of the questions on the test seem to be about the why and how, not actual computation, which is why I think khan isn't going to help too much with this stuff. I feel a bit overwhelmed, but I know I can teach basic algebra/geometry, so it's worth having to learn the theories behind it all.

[quannum]

https://www.khanacademy.org/math/trigonometry

https://www.khanacademy.org/math/tri...omplex_precalc

[Abandon]

I would assist, but it appears that I am on thin ice.

[Abandon]

That being said, I'll light the Sath signal

[BerenTebogo]

Do you even math?

[Ksandra]

https://www.khanacademy.org/math/trigonometry

https://www.khanacademy.org/math/tri...omplex_precalc

none of the videos seem to focus strictly on rings vs. fields and the theories behind why something is a field and not a ring, and the formation of the term field and rings. If you know a specific video that addresses this, feel free to link it.

khan is great for learning how to apply terms, but I have to learn how these terms came about.

[SDSD]

http://en.wikipedia.org/wiki/Field_(...aic_structures

The answer to your first bullet point can be figured out from here and some of the rules you just noted.

For example the ring of integers. Why is this not a field? Integers = {...-2,-1,0,1,2,...}. Take the inverse of any integer n; 1/n. 1/n doesn't belong to the ring of integers, so then the set of all integers can't be a field.

It'll take some legwork but you can figure it out for most of the rings noted. Polynomials with coefficients in another ring and quadratic polynomials can be tough if you don't have some introductory logic training.

[Ksandra]

ty SDSD, looking over the stuff now. And ya for sure it's a bit over my head, but hopefully I can at least get there enough I can pass the test. Part of the test is multiple choice, but another part is short answer, which is what I am the most nervous about.

[SDSD]

http://home.comcast.net/~dgarlock/Index.htm

A helpful place to start, especially the Chapter 1 introduction to basic notation and logic. I'd guess you'll need to do learn a little undergraduate level algebra to be fully ready for this exam if they've already introduced you to rings/fields.

also this: http://www.math.brown.edu/~jhs/frint.html

[Mizango]

I would assist, but it appears that I am on thin ice.

Same not sure I could do this properly without punctuation

Do you even math?

<3

[Ksandra]

http://home.comcast.net/~dgarlock/Index.htm

A helpful place to start, especially the Chapter 1 introduction to basic notation and logic. I'd guess you'll need to do learn a little undergraduate level algebra to be fully ready for this exam if they've already introduced you to rings/fields.

also this: http://www.math.brown.edu/~jhs/frint.html

thanks! I think this will help a lot.

dumb question (they probably all will be). I keep seeing this symbol: ∈ I'm unfamiliar with it or just forgotten about it. What does it represent?

[Abandon]

to be honest, you're talking about stuff i NEVER saw in middle school math; where is all this shit coming from?

[Ksandra]

to be honest, you're talking about stuff i NEVER saw in middle school math; where is all this shit coming from?

It seems to focus more on the theory behind everything, which tbh, is understandable because as a teacher you should know the whys and hows. But the big thing is because "technically" if I passed those two tests I could teach high school algebra and geometry. It's just that I wouldn't do it because a. I like teaching middle school compared to high school b. I'm well aware of my own abilities and feel I wouldn't be able to handle teaching advanced algebra/geometry.

I do wish they separated it to high school vs. middle school or something, but if wishes were wings, cream soda would be flying on a bike.

I just gotta try to fake it as best I can to pass the test.

tbh, I am probably not even ready to be learning this stuff, but I feel I've spent too much time trying to relearn the other stuff, and I really had wanted to get this done before the next school year.

[SDSD]

Here are some basic symbols you'll see over and over

∈ means "inside the" or "exists in".
∃ means "there exists a" or "there are"
∀ means "for all" or "for any"

So for example if I wrote ∀ x and y ∈ {the set of real numbers} ∃ some number m ∈ {the set of real numbers} where m=x+y, you would translate that to for any x and y existing in the set of real numbers, there exists a number m in the set of real numbers where m is the sum of x and y. This is just a basic example. You wouldn't necessarily write it out so explicitly or in this form.

http://en.wikipedia.org/wiki/List_of...atical_symbols

This should cover about anything you're likely to see.

[Ksandra]

I love you

[Mizango]

Find a book store and pick up "A Slice Of Pie" by Liz Strachan. Shit costs about 2 bucks used, maybe less at used book stores. My Calc. professor suggested that book to us the first day of class when I took it and that shit was a god send. I dont have an issue with Math, but I still thoroughly enjoy that book. My daughter read it this past summer, so its shouldnt be too terribly difficult for a mod to pick up.

[Abandon]

oh christ, the underhanded jab there was perfect

[Nirokun!]

Thank you for reminding me what it was like to be in school again and allowing me to realize I'm finished with that, have my degree and RN license, and can move on with my life. <3

[Ksandra]

Thank you for reminding me what it was like to be in school again and allowing me to realize I'm finished with that, have my degree and RN license, and can move on with my life. <3

haha, I love learning, but usually prefer to take a class rather than be on my own.

[Mertron]

+ means you put the thingies together