Histogram of scores:
Score Value Number of Scores Doing* -------------------------------------------------- 110-125 5 very well (A+) 100-109 5 well (A) 90-99 6 well enough (A/B) 80-89 3 acceptably (B) 70-79 2 borderline (B/C) 60-69 5 not too good (C) 40-59 4 poorly (F) below 40 5 very poorly (F)* Obviously, there is plenty of room for interpretation here; I am only suggesting a first-order approximation!
I thought Problem 5 was a dead giveaway -- as usual, alas, several
studens proved me wrong. In fact, a number of you did far worse
on the last two problems than on the first three. That is understandable
for Problem 4, surely the trickiest on the test, but not on Problem 5,
surely the easiest on the test. Fatigue?
A few observations:
1. Too many of you with low grades have real problems
with simple Boolean algebra, such as how to negate a logical proposition
using deMorgan's laws.
2. Many of the same people confused "countable" (a concept connected
to the cardinality -- size -- of a set, but independent of any algorithm)
and (recursively) enumerable (a concept that is purely algorithmic).
All of the sets we have studied --whether finite, infinite recursive,
infinite nonrecursive r.e., or infinite non-r.e. -- are subsets of N
and thus countable... Sure, a set must be countable to be enumerable,
but that's all one can say.
3. Vagueness remains a major problem; English is good for conveying a concept,
but not for formalizing a definition.
4. Your best resource during the take-home test is me. The vast majority
of students who sent me questions (or came to my office with said questions)
did fine on the test. They might well have done fine in any case, but
I think most were helped significantly.