>>11537671it's one of the first classes that requires hefty formalism and some nontrivial intuition.
It's really good for teaching, since most introductory analytic theory isn't super hard - if you read baby Rudin, you can fly through the reading for each chapter in a small amount of time. However, the flipside is that analysis problems often test a command of both rigor and creative problem solving. Sure, it takes only 5 minutes to see a metric space and the easiest examples, but working through things like the Hausdorff metric, showing a weird metric is complete, etc., are all problems that prepare you for thinking for yourself.
