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I am going to teach a flipped real analysis class next term, using Abbott's book. Does anyone know of resources for such a class? I have found the article:

"Flipping the Analysis Classroom" by Christine Ann Shannon

but would welcome student-friendly notes or videos, exercises, etc.

For context: I teach at research 1 public university in the USA. Students taking this course have passed an intro to proof class.

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  • $\begingroup$ I have used Abbott's book to teach a real analysis course, and I'm wondering about this, as well. (In fact, I learned real analysis from the 1st edition of this text and am now teaching from the 2nd edition.) I have beamer slide presentations for the topics I covered in class and would be willing to share them, although they're a far cry from a full set of resources for a flipped classroom. $\endgroup$
    – Brendan W. Sullivan
    Nov 20, 2018 at 21:51
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    $\begingroup$ If you're interested in an Inquiry Based Learning approach, the book Closer and Closer: Introducing Real Analysis by Carol Schumacher does a good job. $\endgroup$
    – Jason Siefken
    Dec 12, 2018 at 3:06
  • $\begingroup$ @user2016529 I would accept this as an answer $\endgroup$
    – David Steinberg
    Feb 28, 2019 at 18:11
  • $\begingroup$ update: I two quarters of intro Real Analysis from Abbott, and was pleased with the results (though there's lots of room for improvement). I will post resources somewhere if anyone is interested. $\endgroup$
    – David Steinberg
    Jan 31, 2020 at 18:39
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    $\begingroup$ @BrendanW.Sullivan I am also in this boat. Would you mind sharing your slides? $\endgroup$
    – Nights
    May 7, 2020 at 1:48

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I've found that a lot of success for introductory advanced math hinges on getting students to feel comfortable talking about their math ideas and actually having a discussion wherein they can start to develop an awareness of how to precisely express what they do and don't know.For example, in an RA course I once took, we were put into study groups and had a (twice) weekly GoogleDoc discussion of the problem set.

So maybe one thing to do would be to model some problem set discussions early on in the semester with a Fishbowl discussion strategy (maybe use some of the stronger students or call in a couple of grad students). Then, monitor how the groups are doing on their independent GoogleDocs and pull out exemplary segments to analyze in detail in class.

As for other resources, I've found the early portions of Frank Morgan's "Real Analysis" have a simple conversational tone that's pretty good for developing baseline intuition about how unexpectedly weird the Real Numbers can be once you delve into their structure past what's necessary for basic arithmetic.

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