[orbitingpluto]

Nothing so quickly emphasizes that a bag of tricks can turn into actual math more than a linear algebra course. In a math degree you can literally take the same course twice. At a first year level you will learn to perform all these tricks with matrices and get a hint of inner product spaces. In 2nd or 3rd year you'll do the reverse and justify why matrix algebra works in the first place.

But the harder a subject, the longer it feels like learning a bag of tricks. The first partial differential equations course feels like you are working on only 3 problems for 4 months.

edit: I had a prof whose first DE course was at the graduate level. At the oral exam he was asked to give an example of a differential equation and all he could do was point to phi on the blackboard.

[Lawtonfogle]

I'm thankful that my calculus courses were extremely heavy in showing how the tricks actually worked. It wasn't on the level of grad school analysis, but the professor pulled no punches and we went extremely in depth.

Years later when I was learning multi-variable calculus, I found most of it easy because, even having forgotten most of the tricks within those years, the method behind the madness was still there.

[sp332]

Illustrated: http://www.wastedtalent.ca/node/716