Here are my comments on the quiz and assignment

Quiz
1 a) b)
This was not done well. Students didn't realize that these cases imply
that M=_M_.

2
a) Definition was done fairly well. Some common mistakes include not
mentioning LMS, and ending with a_j.

b) Some students got the inequlities backward. Others forgot to
initialize.

c) This was done well by those who did a) b) correctly. Some got confused
with the range of the loops.

Assignment

2 a) b)
Some students claimed that it is always possible to exchange edges
between ST T1 and T2 to get new ST T1' and T2'. This does not follow from
the Exchange lemma. Others define their induction hypothesis incorrectly.
Most of them say something like 'promising and unique'. But these terms
are not properly defined. They showed that the MST by Kruskal's algorithm
is unique in the sense that Kruskal cannot produce any other. But they
still have to show that the MST is unique in G. The best way is to show
that Kruskal extends to any MST (as in the official solution) and
therefore by transitivity of equality, the MST is unique in G. 

c) Everybody (well almost) got it.

3
a) Mistakes include not saying consecutive numbers differing by 1, and
ends with a_j.

b) Some students got the inequalities backwards. Others used equality
instead of inequality. Others got the max range wrong. Some forgot to
initialize.

c) This was done well, even when the first two parts were incorrect.