# Calculus And Linear Algebra As The Minimum
There is a sense that an educated person should know Latin and
Greek. I think the same thing should be said for calculus and linear
algebra.
Because similar to Latin and Greek, studying these subjects is more
like studying worldviews than just studying technical knowledge.
It's also similar to studying evolutionary biology.
By saying "calculus" and "linear algebra", I don't mean differentiation
& integration rules and matrix calculations. I mean studying analysis
& algebra via an easy way. Like these:
## Calculus
* What does "differentiation = linear approximation" mean?
* Calculus of variations i.e. optimization (this is criminally
dismissed)
* What does "integration = measuring the holes of a space" mean?
* What is de Rham cohomology? (OK, this might be too much)
* What does "integration = measure" mean? (This too)
&c.
## Linear Algebra
* What does "matrix = linear map" mean?
* Sturm-Liouville theory (I consider this linear algebra)
* Why properties that do not depend on the choice of basis are
important?
* What does "V ~= V**" mean?
* Classical groups & Erlangen program (This might be a bit much)
&c.
I intended that the top is a must and things go hardcore after.
But you can definitely study all of them while studying calculus &
linear algebra.
I think an educated person should know at least one (the top) of
each subject. Even a high school student can study the top ones if
someone ever tries to teach. Those are not that hard and would
change worldviews, but people usually do not study them.