I spent most of the day on Monday designing the course standards for my real analysis class in the fall. I ended up with a rough draft and went home.
Later that night, I got this mysteriously clairvoyant tweet from Joss Ives: “writing learning goals is a task well-suited to collaboration.” He is right, of course, but I was astounded that—seemingly out of nowhere—he decided to tell me exactly what I needed to hear at exactly the time when I needed to hear it. He was some sort of JIT Jedi mentor.
(What actually happened was this: Joss was tweeted last week that he was writing learning goals, I replied, and he was just replying back. I like the Jedi version better, though).
Anyway, here is the first draft of the standards. I welcome feedback in the comments (what big ideas are missing, which of these aren’t so important, etc):
Core Topics: repeatedly demonstrate
Apply the Completeness Axiom
Determine convergence/divergence of sequences
Determine if a function is differentiable at a point
Apply the Mean Value Theorem to solve problems.
Use sequences when working with functions to show divergence
Determine if functions are continuous
Determine if functions are uniformly continuous
Determine if a function is integrable
Supporting Topics: demonstrate at least once
Determine limits of sequences
Determine limits of functions
Determine convergence/divergence of series
Know three equivalences for compactness on R (compact, closed bounded, finite subcover)
Determine if a sequence of functions converges pointwise; if so, determine the limit
Determine if a sequence of functions converges uniformly; if so, determine the limit
Apply Abel’s Theorem
Determine radii of convergence for power series
Apply the Fundamental Theorem of Calculus