I took both 32a and 32b with Jared over a year ago. (I would have submitted a review earlier, but he wasn't listed in bruinwalk last year.) I can't compare him to other professors since I have not taken any other math classes at UCLA, but from my previous experience with math taechers (only high school math teachers) that he teaches well and his tests aren't too difficult.

His teaching style is very much out of the book, but he explains the notation well. Certainly, the book is enough to get you through the class, but if you don't like reading the book word for word and deciphering the notation that is used by those versed in math, you can go to lecture and get the same information provided in the book with similarly simple examples. Of course, the simple examples aren't very much like the tests and homework problems, but that's the way math classes are. If the most difficult problems were explained, then there would be very little challenge in a test, and the curve would work against everybody instead of only against those who are very very bad at reasoning through math problesm.

His tests in 32a were much easier than the homework with problems covering only basic concepts, and his tests in 32b were more in line with other university level tests consisting of problems that force you to think hard about exceptional situations that you may not have encountered frequently in the homework or previous classes. I would provide examples, but it's been a year and I have already forgotten most of multivariable calculus.

(Obviously, if you cannot understand the math book very well, you probably will not get as much out of his teaching. I would recommend asking questions in class if something is confusing you. If you don't understand the basics, don't worry about feeling stupid if he laughs a little at your simple questions. You're only stupid if you think you're stupid. Or if others think you're stupid. You don't need to be too self-conscious.)

I assume the reason for the jump in difficulty between quarters is that he was still new to teaching when he taught 32a (it was his first time teaching here) and he was unsure about the ability of students here. After he ascertained the general ability of students here (meaning he realized that we can all understand the basics) he started making challenging tests to create more of the bell curve in test scores that are the norm for competitive classes.

While some of the life science majors that reviewed him think he was hard, he really isn't too hard. They are just not as good at math, which is okay because they are life science majors. I am a life science major too, and I did fine in a class of engineers, physics, and math students that are all probably much more accustomed to working with integrals.

If you have yet to take math and you're a life science major, I would recommend taking 32a over 3c if you are actually interested in math. If you just want a good grade and are competent in math, then you can take 3c and have less of a challenge competing with less math-oriented people. After 3c or 32a, I recommend taking 32b even though it's not required. Understanding how to solve slightly more complex integrals might be beneficial when taking physics B.