Histogram of scores:
Score Value Number of Scores Doing* -------------------------------------------------- 91-100 3 very well (A/A+) 81-90 3 well (B+/A-) 71-80 5 fine (B) 61-70 8 OK (C+/B-) 51-60 3 marginal (C) below 50 8 failing* Obviously, there is plenty of room for interpretation here; I am only suggesting a first-order approximation!
A few observations:
1. Several of you managed to write transformations going in the wrong
direction -- this should not happen at the end of the class.
2. Many of you still have problems proving that a transformation preserves
"no" instances -- in fact, a lot of you attempted to prove the "no -> no"
implication instead of using the contrapositive, as I mentioned time and over
again in class, with the predictable result that those proofs are weak or,
indeed, wrong.
3. Vagueness remains a major problem: many of you defined your transformations
in words, giving rise to a lot of possible interpretationsw. Use labels,
variables, functions, formulas, etc., to define your transformation as
formally and accurately as possible.
Final semester grades: ranged from F to A+ as follows:
A+: 3 A: 3 all As: 7 A-: 1 B+: 3 B: 3 all Bs: 10 B-: 4 C+: 2 C: 3 all Cs: 5 F: 5 I: 4