Fresh(wo)men's course on Foundations
In two months I’ll be teaching ‘Logic and Set Theory’ for the first time, a first year, first semester course on Foundations. And no (though I considered it for a nanosecond) I will not trow HoTT at them…
There are few thing I like more than composing a new course. In the Belgian (university) system, a teacher is completely free to decide the content of his/her course. Clearly, there are the expectations of colleagues on what the course should (minimally) contain.
For this first semester, first year course I know I have to tell them about sets, maps, relations, truth tables, quantifiers, real numbers, and, perhaps, something about the axiom of choice and Zorn’s lemma. Btw.the guy in the picture is Anders Zorn.
Earlier this week I began LaTeXing the notes, starting with the naive view on sets and their operations (intersection, union, subsets, power sets, products,…) and maps (images, inverse images, injective, surjective, bijective,…) but got quickly bored, as would be the students I guess.
The plan now will be to end this first 2 hour block with something a bit more fun: the notion of cardinality, proving that Q can be enumerated, Cantor’s diagonal argument that R cannot and, as a possible application of power sets, that here will always be a still higher cardinality.
I chuckled while typing the final line of that first session: “Nobody knows whether c=aleph1, that’s called the continuum hypothesis”… Hope this will blow their minds out, the first week of math-school.
The present plan of the other lessons can found on my new bloghttp://noncommutative.org/freshwomens-course-on-foundations/
All suggestions are welcome!
(Added august 3): Oops added a photograph of the wrong Zorn, Anders the artist, not Max the mathematician....