I decided to restart my college classes. I’m starting off with just one class soon, called “Math for Business Analysis”. I figured I’d share about it here. I could maybe get some feedback on some stuff but I’m not too expectant and getting a crazy amount of help for the math. Its more so to share what I’m learning, maybe get some help, and to share some stuff in real time about a college class online.
The math covered:
From Section 6.1 Functions of Several Variables
A real-value function of f of x, y, z, … is a rule for manufacturing a new
number, written f(x, y, z …), from the values of a sequence of independent
variables (x, y, z, …) .
A real-value function is a rule. It’s a rule for coming up with/outputting a number. You follow the rules and you get a number. The output is based on the values of independent variables.
The graph of the function f
of two variables
consists of all points of the form
(x, y, f(x, y)) .
The graph of a function that has two variables consists of points coming from both variables and their output.
Hmm. Is the graph of a function that has one variable this then: (x, f(x)). I think I’ve seen it like that before. So graphs of a function consist of the points going into the function and the output.
In 3d space, there are 3
mutually perpendicular axes:
• x-axis (extend to the front)
• y-axis (extend to the right)
• z-axis (extend upwards)
Huh. That seems so odd to me. I’ve never exactly dealt with space before, but just going off of how an xy coordinate plane looks y just felt like the part that extends above.
So x-axis is in front and behind me
y-axis is to my right nad left
and z-axis is above and below
In 3d space,
there are 3 coordinate planes:
• xy-plane where z = 0
• xz-plane where y = 0
• yz-axis where x = 0
So a plane is when the graph looks flat? I guess? Also what does the coordinate have to do with anything here.
From Plane (mathematics) - Wikipedia :
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely.
Ok. So I get what the plane here being referred to is. What’s the coordinate? From Gemini:
The term “coordinate plane” refers to a Cartesian plane, which is a two-dimensional plane defined by two perpendicular number lines called axes. It’s called a coordinate plane because it allows us to locate points by using coordinates, which are pairs of numbers that specify the point’s position relative to the axes. The plane is named in honor of René Descartes, who developed the system.
Hmm. It seems Gemini highlights the part it thinks I’m looking for. Neat.
Ok. That makes sense . So coordinate planes are planes that have coordinates. When you have three dimensional place you can form three different coordinate planes.
If we hold a variable constant,
the graph of the set of points is a plane.
Hmm. So the coordinate planes are when the variable being held constant is 0. At least thats what it seems like so far. Why is that? Hmm seeing this:
My thought process is that you could do a coordinate plane from there. Its just when doing coordinates I guess you assume its 0 otherwise you would list that third coordinate even if its a constant.
The graph of a function f of
two variables is the set of
points (x, y, f(x, y)) in three
dimensional space where we
restrict the values of (x, y) to
lie in the domain of f.
I forgot what a domain is. Let’s see. From Domain of a function - Wikipedia :
In mathematics, the domain of a function is the set of inputs accepted by the function.
Ok.
This course sounds like it would have algebra and more as prerequisites. But you recently said you wanted to work on a prealgebra book. So I’m a bit confused; if you think you know algebra well enough to build beyond it, why work on prealgebra?
Hmm. Let’s see. To start off with, I didn’t know what math this class covered. I did know it was built on calculus (I already completed a calculus class before).
Did I not share before that I did math up to Calculus? I feel like I have. Maybe I’m misremembering, but I think it was in call before starting tutoring where you asked a lot of questions.
The reason I want to work on the pre-algebra book is because I don’t think I know the math that well. Or put differently, from Cycle Between Learning Critical Fallibilism and Its Prerequisites :
E.g. the way people think about arithmetic, algebra or grammar is good enough to pass school tests but not good enough to build up to advanced philosophy. Improving those basic skills to atypically high quality standards is relevant to CF even though it’s many layers separated from CF.
I think I know the math well enough to do this math for school, but not well enough for CF. This is the only math course for my degree that I can tell. Well that and Calc 1 I guess which I already took. So I’m not too worried getting far in math classes I don’t understand well. Plus, skimming through the material I think the Professor is definitely teaching in a way that I can get the answers he wants on a test but not really teaching it for high quality understanding/learning. So I think I should be fine.
Oh yeah I guess the other thing to your question: I’m not trying to necessarily build up my math skills. I recently changed my major to Business (Law) (the parentheses is in the name of the degree). I’ve heard Business is an easy major. So I figured an easy major with a focus in something I’m really interested in will make getting this degree easier. I’m only really pursuing this degree for law school after all. So my goal with this class is just to finish a pre-requisite.
So I watched two of the lecture videos so far and one I’m realizing is that the lectures are just reading off the slides word for word. I wonder what the point is? Maybe for people who don’t like reading? Also, it didn’t help me with material but I have had better success at understanding stuff from listening as opposed to reading,
Maybe one reason the lectures aren’t too helpful is that it covers math I’m already familiar with? Or, in other words, I’m comfortable reading the material on my first try due to familiarity.
From Section 6.2 Partial Derivatives:
The nth partial derivative of f
with respect to x is the
derivative of f with respect to x
when all other variables are
treated as a constant.
and
The nth partial derivative of f
with respect to y is the
derivative of f with respect to y
when all other variables are
treated as a constant.
Huh. So I thought treating all the other variables was a shortcut. Or, put differently, I thought multivariable derivatives would involve some complicated method to find the derivative in relationship to two variables and the partial derivative stuff is a simple thing we’re doing for this class, but after googling it seems pretty standard.
Hmm. So I went through the problems and they seem pretty easy. Idk what the point is of doing partial derivatives (but truth be told I don’t even understand what a derivative really is, yet I was one of the best math students in high school definitely could be a big fish in a small pond situation but just wanted to share that point) but the hard part just seems to be keeping track of when a variable is treated as a constant and when its being treated as a variable.
Students expect lectures. Lectures are generally advertised as part of courses. Teachers are told by their bosses to give lectures. I imagine poor lectures get a lot fewer complaints than no lectures.
