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

\end{tabular}

**Supporting Topics: demonstrate at least once**

Determine limits of sequences

Determine limits of functions

Determine convergence/divergence of series

Apply Bolzano-Weierstrass

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

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Tags: 343, Analysis, Real Analysis, SBF, SBG, Standards

This entry was posted on June 29, 2011 at 6:26 pm and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed.
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June 30, 2011 at 3:38 am |

If someone did one of the core topics well, would they necessarily have done some of the supporting topics? Or maybe vice versa? Not being fully versed on some of these, I’m not sure if supporting means tangential (do only once because you don’t care about them as much) or not-cool-enough-to-be-core-but-still-important-skills where they might be able to be folded into the core ones.

June 30, 2011 at 4:12 pm |

Hi Andy,

My intent was that the Supporting Topics are less important than the Core Topics. This is why the students need to demonstrate them less frequently.

Their semester grade would be determined by the number of topics (and frequency, for Core Topics) that they demonstrate. I think that I should write another post on that—you can expect one within the week. Bret

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