I’ve taught a variety of math classes, and statistics has been the hardest to teach. The thing I find most challenging is coming up with homework problems. Most exercises are either blatantly artificial or extremely tedious. It’s hard to find moderately realistic problems that don’t take too long to work out.
The course I’ve found easiest to teach has been differential equations. The course has a flat structure: there’s a list of techniques to cover, all roughly the same level of difficulty. There are no deep analytic or philosophical issues to skirt around as there are in statistics. And it’s not hard to come up with practical applications that can be worked out fairly easily.
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