Hansen is... interesting. Little bit disorganized. Little bit crazy. Whole lotta fun. Definitely worth taking this class if you: A) Know how to write proofs really well (and I mean really well) B) Have covered the applications of the material before and want a strong theoretical foundation C) Love math (like, really really love it) If you fall into category C without being in either A/B, no worries! So long as you're talented, willing to put the work in (and/or give 0 shits about your GPA)then take the class! Hansen has an excellent teaching personality, maintaining his student's interest in lecture topics most would find dry. Watch out for quips - they come out of the blue but are absolutely hilarious. He's helpful in office hours, although he does expect you to not be useless as a math student and have done relevant background research in whatever it is you're asking about. Basically gives everyone a pass on the homework (as long as your avg grade is decent) but balances that by not curving the midterm or final - so study! I personally came into the class with very little relevant background - it ended up kicking my ass (and my GPA went up in flames), but also helped enormously in developing my study habits and my understanding of mathematics.
If you are a (prospective) math major, or just a lover of math, you NEED to take a class with robert friedman. if not, run far, far away! as a fellow number geek, robert friedman rocks my mathematical world. his lectures are engaging and interesting...he goes at a very fast pace, but thoroughly covers the material. he is a fair grader and his exams are straightforward and almost predicatable. if you put a lot of effort into completing and really understanding the homework, you should easily do well on the exams/in the course, since generally the homework is much more difficult than the exams. highly knowledgeable and somewhat quirky, friedman is an excellent prof. although, i would advise any one who is not a math major/who has no interest in mathematics to avoid friedman at all costs.
Maybe it was just for this class, but really not that hard a prof. Talks to himself though---not engaged in the class at all. He randomly recalls a Vietnamese song or poem and sings it to the class and translates it. Despite only 4 people showing up to class regularly he would start exactly on time even if only one person was there. If people slept in class he pretended not to notice. Kind of a space cadet. I don't really recommend him, though he seems to have a good rep.