Here are some comments on the first homework assignment.

In section 1.1 I graded problem 10.
-Almost everyone did well on this problem.
-The average score was 4.44 / 5.
-No common mistakes come to mind.

In section 1.2 I graded problem 10.
-I wanted to grade at least one problem from each section, but
this one took a while to grade.
-Out of the 25 students who turned in this homework:

13 attempted to do the whole problem.
4  attempted to do part of the problem
8  didn’t attempt the problem or did very little.

-This explains why the average score was 7.76 / 15.

Only two people were able to correctly compute the
multiplicative inverse of (a + bi). Most of the students
answered by saying (a + bi)(a + bi)^(-1) = 1, therefore
the inverse exists and is unique.

Some students also seem to think that 0 is the
identity under addition and 1 is the multplicative
identity for the complex numbers. Strictly speaking
this isn’t right. I didn’t take any points off for this.

Many students didn’t realize that if you define ‘x’ and ‘+’
for the complex numbers wisely, that the proofs of the
field axioms become much easier. And you don’t have
to assume commutativity of imaginary numbers when
proving that complex numbers are commutative. I was pretty
lenient on this. Because if you don't get the first step right
in defining ‘x’ and ‘+’ it is very hard to have completely
legal proofs. Only about five people started the problem
by defining ‘x’ and ‘+’ for the complex numbers right.


In section 1.3 I graded problem 16.
-Almost everyone did well on this problem.
-The average score was 4.2 / 5.
-No common mistakes come to mind.


Rundown of scores & analysis
-The average score was 16.4 / 25.

I wrote a lot of comments on the papers. I figure it's best to let
students know at the beginning what your expectations are. If a
student's handwriting was hard to read I told him/her about it. I
didn't necessarily take off points though. In two or three cases I
did take off one or a half a point if I thought the student was
performing well below minimum standards.