Partial HW3 solutions

Here you go. I haven't typed up number 7 yet, and number 8 is incomplete. The rest are there, probably in more detail than you would like ...

If you didn't get every part of every problem, don't panic. They were very hard problems, and for the most part chosen to illustrate a certain point. If you mostly understand how these problems work out, but didn't quite get every last detail, I'll be happy with that (and partial credit will be generous).

For example, some of the problems (e.g., 5, 6, 8) have a relatively straightforward part followed by a much harder part. If you got the first part reasonably well, you will be fine on the exam, and I'd say you know what you are doing. The harder parts were mainly there to see what you could do, and make you think about things a little more. Again, if you didn't quite get everything, but found yourself thinking carefully about what the problem means, then mission accomplished.

Exam-wise, you can expect stripped-down versions of the easier parts of these problems. I can't stress enough: if you feel like you know what you are doing on the HW problems, but don't quite get them all the way worked out, you have no reason to panic.

On the other hand, panic should set in, a little, if you are not doing the homework (or at least reading the solutions after the fact).