[liammclennan]

It's not just the books it is the whole method of teaching. I remember learning the steps to calculate an eigenvector without a single comment on why one would ever want to do that. I think it is done so that the educator can claim "this course teaches all of calculus and linear algebra and quantum mechanics". To actually explain things properly would require more modest course goals.

[vasco]

I think I only learned linear algebra about 3 or 4 years after I graduated. I learned how to do the computations during the course but the teacher was so bad I had no idea what anything was for. Could've been an IQ test course for all it mattered. Here transpose this matrix now. Ok.

[klysm]

Pretty common with lin alg and diffeq unfortunately. Many schools teach it as a toolbox instead of for understanding.

[ozim]

I still would argue that method of teaching is perfectly fine.

You cannot simply explain to someone complex stuff - best way is to let people grind through to build their own understanding.

Parent poster wrote that "it’s useful for determining the similarity of two vectors" - now I would ask why do I need to determine similarity of two vectors as it does not mean much to me - if I would be grinding through math problems I would most likely find out why, but there is no way I could understand and retain it when someone would just tell me.

[z3phyr]

> Ask why do I need to determine similarity of two vectors

Simple:

Start with

a) Suppose you are making a video game..

b) Suppose you are determining ballistic trajectory of your missile system based on model rockets

c) Suppose you are running a fighter robot group..

Or any of the stuff children are supposed to *actually* do and then take these classes with determination to do the actual creative things that they wanna do all life.

There is an aspect of jest in the above comment, but it also contains some likely truth. Children love doing stuff, and these are the things that may enable them.

[jampekka]

I think more intuitive/holistic ways of teaching would be a lot better. But it's hard to do, especially in dead tree format.

To get someone understand something holistically, as in link to their previous knowledge base, requires knowledge of what their knowledge base is. Traditionally this has been done with structuring the teaching with prerequisites etc and hoping it works.

I struggle with this quite a bit when I teach students with heterogeneous background. To be effective, one has to first probe what the students already knows to be able to relate the new stuff to that, and this requires interaction. Hypertext is/would be helpful for self-learning, but it's sadly very underutilized. LLMs may be better. But probably even those can't at least in the current form replace interactive human teaching as they don't really form/retain a model of what the user knows.

[vasco]

> You cannot simply explain to someone complex stuff

This is absolutely not true. Many times I've experienced the moment of something complex "clicking" after hearing or reading an appropriate explanation for a phenomenon - finally seeing the right visual or appropriate example or comparison. I find it hard to believe you've never experienced this other than through grinding problem sets.

[The_Colonel]

You're making a false dichotomy. Learning is a combination of guidance and own hard work.

Maybe you prefer to figure out everything yourself, but you have just one lifetime, and having access to guidance while grinding will allow you to learn things faster (and thus more).

[hobs]

And you'd be dead wrong by all methods of pedagogy that we find useful! People learn best with stories and meaning, its why the ancients were able to reproduce stories of almost inhuman length via memory.

Grinding through to build your own understanding when someone can just give you useful meaning and context to connect to your other parts of learning is a core teaching skill, and anyone avoiding that because its "too hard" is doing a deep disservice to their students.

[codingrightnow]

Knowing why and when to use math is equally as important as knowing it. One of the reasons I lost my love for learning it was this missing information.

[aerhardt]

I was taught linear algebra and multivariate calculus as a business major. They could hardly justify why they were teaching it in that context - they were weeder courses - but I always wished they had at least tried to give us a hint of applications. Nothing, it was all algebra for the sake of algebra. Atrocious.

[klysm]

I think the concepts of linear systems and multivaribale calculus are important for just understanding systems in general. Even without applying them all the time you can think about dynamics with them

[ozim]

I still would argue that weeder courses are fine. If you start as a major whatever the field is - you should be interested in the field enough to plow through.

Otherwise at the end you get people dissatisfied they cannot get job but they have a degree.