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To: 6042-lecturers@theory.lcs.MIT.EDU
cc: adbirka@MIT.EDU, twang@MIT.EDU
Subject: Re: quiz 2 is ready for proofreading.
In-Reply-To: Your message of "Tue, 12 Nov 2002 13:43:49 EST."
             <E18Bg0r-00032D-00@munster.ai.mit.edu> 
Date: Tue, 12 Nov 2002 22:43:49 -0500
From: Georgi P Peev <georgepf@MIT.EDU>
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hello,

i have proofread quiz2. here are my comments:

problem 1 is not very clear about how that 100M is to be used for scholarships.
namely, it is not apparent that the money can (will) be gone at the end of the
year 2102. also, nowhere does the problem state that the current year is 2002
and that students should think about the period 2002-2102.
i don't find the solution particularly clear either. i fail to understand the
first sentence:
'Paying $4M/year starting in d years for (2102-2002)-(d-1) costs...'
next, there is a small mistake in the derivation of the closed-form formula
that follows that sentence. there is a r^(30+d) that should be r^(100-d). the
last r^99 should be r^100, which changes the arithmetics that follow. there is
also a small typo in line 3 of those arithmetics (easily visible). the result
is miscalculated and should be d~=8.87 (for r^99), and d~=8.92 (for r^100).
one more thing i don't like is the fact that 4M is used for 4 million dollars.
for consistency it is better to either keep both units ($4M), or neither.
and one last thing - the problem assumes that students have calculators. did
we tell them to bring calculators?

problem 2:
part a) does not explicitely say that the students should count 7-letter
sequences, as opposed to any-length sequences. i suggest changing the wording
to 'how many different rearrangements of these seven letters are there?'.
the solution for part c) should probably mention that we are using the
inclusion-exclusion principle, and that is the reason to add back the 3!.

in problem 3 there is not enough space for students to write the value of c
(more space is needed between the 'If yes, c=' and the 'n0=').

problem 4:
part b) asks to translate 4 italicized sentences into probability notations.
i strongly suggest we copy those sentences so that it is clearer which
sentences the problem is talking about. besides, in part a) there is also an
italicized sentence ('increase, decrease or stay the same'), which the
students are not asked to try to translate into probability notation.

problem 5 seems a bit tricky and a lot of students will get into very messy
arguments, which will consume their time and will be impossible to grade.
i suggest we remove problem 5 from the quiz.
also, part a) of that problem is incorrect. namely, it is supposed to say
'any multiset/collection of at least n sequences', since a set can only
contain one element once and the solution actually makes the assumption
that the set can contain one element k times, in which case that element
counts k times.

each of the subparts in problem 6 is said to be worth 0 points, the whole
problem being worth 1 point. clearly a mistake. also, the solutions say
that there are subparts k) and l), but these have apparently been removed
from the problem. i have checked that the removed subparts were the last
two, since the answers for the rest are correct.

--george