Section 4.19 Session 18: Review of Test 2
Happy New Year!
I worked Test 2 out on paper first, but I simply couldn’t resist the looking at the review. I think I’m going to keep that separate for now, but have an idea of what I want to do with it. Stay tuned.
I am, however, going to do a self-reflection on Test 2 in a problem block below. I always told my students how it’s an important part of the learning process, so it’s only fair I practice it myself.
Problem 4.19.1. Test 2, Problem (1).
...fixed point...
Solution.
I think my solution is "close enough" to Danilo’s, but I did leave out the parentheses where I thought they were obvious. A picky professor might ding me on that I suppose.
To include or not to include? It’s hard to write math not knowing who the target audience is sometimes. Assuming the associative property implies that the parentheses don’t matter, but putting the explicit parentheses in makes the substitution a little clearer.
Problem 4.19.2. Test 2, Problem (3).
Find an example...
Solution.
I think I made the same "mistake" as Katie did here and should have explicitly tested every point. Calling out that everyone’s diagram looked the same was a nice touch too.
The natural sequence of diagrams here was very interesting, and reminds me of some of the diagram sequences I drew in Session 16 — only backwards.
Problem 4.19.3. Test 2, Problem (2).
Find all maps...
Solution.
On the bright side, I found the correct number of of maps and I know at 3 out of my 4 maps are correct. Had I not spent a whole month on Session 15, I probably wouldn’t have found the fourth, so it’s nice to have some validation that I’m on the right track.
Had this been an actual test, I probably would have tripped up on this one and run out of time. I worked through a page and a half before I realized I had confused "irreflexive graphs" with "reflexive graphs". Furthermore, my approach of proving that \(s' f_A = f_D s\) and \(t' f_A = f_D t\) through "giant tables" isn’t a very test-friendly strategy.
