Thinking about how to teach logic

July 11th 2023
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I'm starting my full-time teaching load in a
little under three months and while I was full of
confidence and vigor before now a lot of the
self-doubt is creeping in.

I'm teaching multiple sections of the intro to
computer science class, CS 160, and CS 250 the
intro to math/logic for CS. I'm also supposed to
work on revising CS 205, the intro to C and
assembly programming class so I can start teaching
it the following term. That one is the one I'm
weakest on in terms of practical experience but, I
mean, I still know this stuff I just need to
practice specifically x86-64 programming instead
of risc ISAs used in teaching compilers classes
such as MIPS. I'm rusty on C but not incompetent
at it, if you get what I mean.

So part of my first focus this past week and this
week is the intro logic class, since that's my
bread and butter. I mostly like how the other
faculty member teaches it except that I disagree
with the book's presentation of showing a lot of
ways to prove things about natural numbers and
integers without teaching induction. I guess it
makes sense from the perspective that integers are
immediately a little harder to deal with in terms
of induction principle, a little messier, but
integers are also the most familiar to students
relative to the structural purity of the natural
numbers. Peano arithmetic and all that is really
unnatural the first time you see it.

Mostly I just think I want to try and introduce
Lean and The Natural Numbers Game at some point
fairly early in the class in order to give just a
hint of how proof systems work. Lean isn't my fav
proof system but it is one that I think has a lot
of support behind it and lets you do a lot of math
in a convenient way.

I don't know. I just don't want to heck over
students by shoving in my favorite topic into the
class, I just think it's the kind of thing that
could potentially be really fun and interesting
and teach you a lot about the applications of
logic to computer science and math. As it stands,
I think the course is extremely abstract and
doesn't have a lot of obvious uses unless you're
already sold on being a mathematician.