>>13236107If you're doing math at work on a regular basis you probably don't have a math undergrad. in my professional experience, actually doing math/math research professionally is reserved for Phds.
>>13236117The reason Differential Equation instruction is so fucked is because they approach it from the practical side. They want to "create intuition by posing a real problem" and then "solving it". Because of the "practical approach", they leave a lot of blank holes and unproven theorems in 2nd year DE courses. At least that's how I was taught. Here's an example:
Fourier series derived by getting a solution to the heat equation. I did not understand that first time around. The heat equation is not intuitive to someone who never took or was interested in physics.
The proper way to teach fourier series imo is to come from the linear algebra perspective. You prove that and are orthogonal for distinct , you prove that it spans , and you have a basis for . Then you can do a linear combinations ... This makes much more sense to me than any practical "derivation" and intuition building.
