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Advice for summer geometry course content

  • Thread starter sparkster
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I'm teaching a junior level geometry course this summer (I'm a math grad student). The title of the course is simply "Topics in Geometry" with no other description in the catalog. I've asked the DUS and he says the content is pretty much left to the individual teacher. But I'm having trouble deciding what to cover.

My text choices are Henle's Modern Geometries or Kay's Geometries, and I'll probably use Greenburg's book as a reference. I've talked to the prof's and grad students who have taught the course in the past couple of years and no one has really done it the same way. The techniques varied from a strict axiomatic approach starting with neutral geometry and working up to hyperbolic and elliptic geometry, to teaching it historically, to a very broad survey course covering things like the complex plane, basic knot theory, and origami, among others.

The class is both an elective for math majors and required from future secondary math teachers.

Any advice from experienced teachers?
 

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