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CookieSalesman

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**TL;DR Summary:**linear algebra confusing & hard; how to study right?

I plan to return to linear because that was one of the classes that you couldn't just try to shamble your way through somewhat. multivar calculus theorems still make some sense visually. Linear algebra exams were like trying to imagine the 5th dimension and I felt like the homework wasn't even remotely similar to exam content and had no idea how to prepare. I would look at the homework and go 'yeah that makes sense, I can probably get a B+' and then the exam question 1 would be written in hieroglyphics. This did wonders for my morale.

I'm trying to go over the basics, starting from calculus 1 (eventually will reach linear alg) But I'm at the dot product and cross product and this stuff makes no sense already. This time I want to understand everything deeply and have no questions.

Well, I understand the justification for calculus itself but not the dot product. Why the heck are you turning vectors into numbers? It seems like an arbitrary operation. And the cross product is just that but worse. The cross product has equivalences, too, where you can calculated the cross different ways. I mean, I've got my own equation too! We just chop off the right column of each matrix. How about that? Why isn't that operation mentioned in the textbook?

This is deeply weird, because this is basically just reminding me of high school spray and pray physics where you just threw numbers into equations as long you have one number for each variable right? - and just memorized the equations. How is this d.p and cxp in the textbook different at all?? You just gave me two operations (presumably written on the stone tablet handed to Moses) and just instructed me to use them. Right? Arguably, it's the exact same stuff, isn't it?

But what's frustrating is that the textbook (rogowski, adams, franz) doesn't explain where this stuff is coming from. Here I am trying to figure this stuff out seriously and these equations for d.p and cxp just spontaneously appear in the world? What?

~~~

Well, the above problem is actually not the focus - it's just an example of the problem.

I feel like I don't want to revisit math in the convoluted collegiate context again.

Let me give two examples: It would be less frustrating if I understood where things like the dot product came from. Otherwise, everything is just algebraic manipulation of equations that chose to spontaneously appear in the world. Why does the dot product even have the right to exist? Well, the textbook sure doesn't know!

And furthermore second example, I only recently asked myself, how the hell is it that I can just take the log of both sides of an equation? Squaring an equation - makes sense to me. But applying a logarithm? I can't really explain it but that feels like a wholly different operation. But yet we just 'do it'. No one explains this! It's not even an educator problem, the textbook won't even tell you!

Am I just reading the wrong textbooks? How to study this convoluted and cancerous discipline that presumes to haunt my existence?

**[Mentor Note: Post has been edited to remove extensive profanity]**

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