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How do you ace honor physics and trigonometry, yet struggle to understand algebra? High school physics and trig are basically just coming up with the correct al
by genter 3y ago
How do you ace honor physics and trigonometry, yet struggle to understand algebra? High school physics and trig are basically just coming up with the correct algebraic equation, and then solving it. (Or just turn the crank, my physics teacher always said.) I can understand not knowing calculus for simple physics, since you can just approximate it with the slope of the curve or area under the curve, but that still takes algebra. Trigonometry is just using the various theorems and identities, but even using the Pythagorean theorem takes a little algebra to isolate the variable you want.
I admit math is very easy for me, but it blows my mind that people don't understand algebra at least.
- SenAnder 3y agoMaybe they've since reduced the quantity and difficulty of the math part of physics education.
- latency-guy2 3y agoThen its no longer a physics education, its just fun tidbits.
- imtringued 3y agoI am always surprised when I hear how americans students learn "Algebra" in highschool. It makes me think that German schools are way behind. I mean algebra is about mathematical structures like Fields, Rings, Groups or even "Algebras" (https://en.m.wikipedia.org/wiki/Algebra_over_a_field https://en.m.wikipedia.org/wiki/Algebra_over_a_field).
- serialNumber 3y agoAre German schools behind? In North America, learning algebra means we learn to solve for x/y : solving quadratic equations is pretty much the ceiling for "algebra" and even that isn't taught until grade 8, usually grade 9.
- pxc 3y agoIn American schools we what we call 'algebra' is just doing basic symbolic computation, like solving very simple equations. The kind of algebra you're describing was called 'abstract algebra' at my university, and was an advanced pair of courses for math majors. The first semester covered group theory and the second semester covered ring theory.
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- Frannyies 3y agoIm really not sure how though. I'm from German too. We use algebra as the generic term for math more or less. I wouldn't have assumed algebra would only mean fields and rings. The Wikipedia article algebra also links to algebra over a field.
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- turboponyy 3y agoPersonally, I've always found algebra the most difficult - it's just symbol soup with no apparent concepts to latch onto. Perhaps it's just the way it's usually presented, but I don't "get it" at all. It's still by far the most daunting part of math for me, even after taking 5 math courses in university.
- genter 3y agoIt's interesting. I love math, and it's always been super easy for me. Yet ask me to play an instrument or paint a painting, and I'd have an easier time flying to Mars.
- FooBarBizBazz 3y agoFor me, algebra made a lot more sense after doing proofs in geometry class, and really pedantically showing what was going on. Before that, it was all "moving symbols around", which was slightly mystical, and more an exercise in doing what you're told than in figuring things out. The key insight, which maybe people think is too obvious to say out loud, but which does need to be said out loud, is that if two quantities are the same, then they remain the same if you do the same thing to both of them. For example, if x = y, then also x - 3 = y - 3. So the entire game of algebra is to choose things to do identically to both sides of an equation. Anything about "moving" symbols is a shorthand for this process. For example, if you know "x = y + 3", then, yes, you do also know that "x - 3 = y", and someone may speak of "moving the three", but fundamentally what you're actually doing is not "moving" anything, but rather subtracting three from both the quantity on the left, and from the quantity on the right. You picked an operation to perform on both quantities, to get another true statement. The exercise that finally made this make sense, was to painstakingly walk through simple proofs, in tiny tiny steps, starting from small numbers of self-evident postulates. This is in the tradition of Euclid's Elements, which has a totally different vibe from most math education. It was important to do this so slowly and pedantically that you would be embarrassed to do it -- you would worry people would think you are stupid -- if the correct norms had not been established. You need to establish the norm that leaping ahead and skipping steps is not a sign of intelligence but is instead sloppiness, ugliness, something missing, a flaw in the argument you're constructing.