Is linear algebra more useful than calculus? Should we teach that to HS students instead of calculus? Of course, if possible, we should teach both, but if you had to pick, which would you pick?
Calculus. But really that's a dumb question, you need both for science.
>>7712289
They are both useful but I personally like more linear algebra because I find calculus to be boring.
But the introductory topics in calculus are way way easier to grasp than the introductory topics in linear algebra. HS kids are already killing themselves because of calculus so I think we should leave them like that.
>>7712289
Both are unnecessary. Absolutely everything is solvable by cross multiplication alone.
>>7712296
sociology needs neither
>>7712304
>I find calculus boring
Doesn't everyone? Pretty much the least interesting area in math.
Here in Germany I learned both in high school.
Linear Algebra is probably more important.
>>7712306
That's why he said science.
>>7712289
These days linear algebra is more applicable. Data science and software engineering is more prevalent than mechanical engineering or other fields that use diffeq.
>>7712289
I dunno.
Honestly they're both very improtant but I guess it really depends on what you're going to do. If you're working with programming and circuits I guess it's pretty important to learn linear.
If you're working as a mech engineer I'd figure calculus would be pretty useful.
>>7712320
Engineering Statics is applied linear algebra and vector geometry
>>7712289
Calculus is still far more useful for the theoretical side, specifically physics. Since that is the building block of many different sciences, it should be taught so people know why they use the formulas they use.
Are nouns more important than verbs ?
>>7712289
I think Calculus is nice because it has so many applications -- it's also a fair weed out in my opinion. Students that want to move on to applied science or engineering will sac-up and get through the whole of it/understand it enough to apply to their fields, and kids who want to study math at the university level usually end up finishing the bulk of Calc in high school anyway and moving right into diff. EQ or lin. algebra quickly.
Even high school kids that have no fucking clue how to understand mathematics or science will end up using some basic Calculus concept in their finance classes, business, etc.
I had friends from home ship off to college all over the country to pursue non-STEM degrees. The amount of times they would complain about "business Calc" was nauseating.
They are both essential.
Image to solve a simple physics problem, you find the direction of magnetic field with your linear algebra/geometry skills but you can't solve the integral to find magnetic field value along the space of interest.
It's like knowing only a part of alphabet :)
>>7712392
Good example. For physical applications, I like to think of math like a set of tools. You can only get so far borrowing someone's screw-driver before you have to buy your own.
they should teach proofs and discrete maths in high school desu
>>7712289
linear algebra the course is fucking worthless. the topics discussed could be self taught inside of a week. its just another course so universities can turn 120 hour stem degrees into 160 hour stem degrees
Calculus.
Linear algebra should be taught at school or learned at home.
Linear algebra is in general a lot less used but it is too easy to not be on the required list.
Quite honestly,you need a bit of both to understand differential equations, and a ton of professions use diff eq - physicists, engineers, mathematicians, academic economists and finance guys, etc. Unless you're a cs major who will only utilize matrix algebra and a bit of vector space knowledge, any work that uses math beyond simple operators will need both. You can't really throw either out.
>>7712928
Linear algebra can be learned on the spot and used instantly afterwards.
Calculus needs more elaborate approach, so its value as a subject is much greater.
>>7712936
Well I don't know. I've had two courses in linear algebra and I literally strolled through it only having to look a couple of times at some of the more descriptive information. Though maybe it was because I started with it back in school.
Calculus 1 was the same as I just was going through what I did extra in the school math.
But Calculus 2 was the thing. Probably the only subject I've had, besides maybe machine learning, that I would definitely not pass without seriously studying it as a fully-featured subject.
>>7712946
Calc 2 is hard, not conceptually, but practically. It's literally a class where you're supposed to become great at integrating. Its kinda brutal imo.
>>7712327
>what is a grassmannian
>what is a (co)tangent space (and one-forms)
>what is a tensor
>what is a lie algebra
>what is a hilbert space
>what is a field
>what are dirac inner products
I'm no physicist, but from over here it looks like algebra has all but replaced calculus wherever possible.
i use algebra more often. calculus is like a bag of tricks you can use at any level of mathematics
ITT: highschoolers & people who took "linear algebra for scientists" who prolly only did finite dimension real vector spaces up through finding bases, eigenspaces, and decomposition
>>7712928
>unless you're a cs major
solving a problem with a computer is often a sort of calculus, and i think this is why algebra is more useful to know than calculus.
tbqh i see calculus as the highest, or most precise, or maybe i don't have a good way to describe it, level of computation at any level of math
>>7714163
u have gr8 insight :^)
I took both linear algebra and Calculus AB/BC in high school, and I feel like linear algebra was more beneficial for me to take during those years because it helped me to think of math in more than just one way, but I would not suggest switching calculus out for linear algebra. Calculus is utilized too often in college level science class for it to be taken out of the high school curriculum.
I also took a math logic course in high school, which greatly improved my understanding and grasping of more advanced mathematical topics.
I feel like most school shouldn't replace current mathematics courses, but should instead offer more diverse intro courses. I mean you get to 12th grade, and if you like English topics, most schools let you pick from remedial English, AP Literature, British literature, creative writing, and even theater is related. But if you like math in 12th grade, given that you've taken the most advanced courses you could, most schools have just Calc BC, if they even go that far with math.
>>7714172
in preemptive response to your sarcasm I already posted a bunch of applications of linear algebra in a science that is not even my own in >>7714157,
not to mention I think generally it is much more applicable in programming, data sciences, and algebra overall is more useful for developing reasoning
>>7714185
agreed. so i let the undergrads do their thing.
>>7713392
>calcII
>brutal
it was literally just not being a retard and memorizing a bunch of substitutions and patterns.
>>7712289
This is a very interesting suggestion that I'd never really given any thought to. I guess teaching linear to high schoolers would be much more valuable if the school curriculum is STEM oriented. I took 3 years of comp sci in high school and learning linear would have been much more valuable than learning calculus. I certainly don't see any reason to not implement an optional AP course for linear. However, those who are less STEM oriented are likely better off in calc courses. Calc theoretically has more real life applicability to a certain degree.
