Gieseker was not a bad professor, but not a great one either. The material was taught in a semi-straightforward (if boring) way. The midterm and final mirrored the homework material and the stuff we learned in class well (no surprises). My TA was incredible and basically made the class easy (Duncan). He is accessible, there was a grading mistake on one of my tests and he quickly corrected it. There's a little confusion on whether your homework counts towards the final grade, during my class, it didn't, but it was still helpful for the tests. If you have to take Math 61, your experience will be fine with this guy
Winter 2019 - Professor Gieseker is enthusiastic to teach, though his lecture is kind of disorganized. His field is algebraic geometry so he tended to introduce a lot of algebraic geometry ideas in class, which makes the lecture even harder to follow. His exam is fair enough and the curve is generous as well. Overall, not bad but not the best.
Winter 2021 - This is a weird class. I think the difficulty spike from 110AH to 110BH is pretty hefty. It was relatively easy to get an A (because we had a take home final and take home midterm) but I was confused for about 90% of the quarter. Our TA Khang was really nice. Although I wasn't the biggest fan, he did help us a lot. If you had DAG before, you probably know what to expect. If you haven't, go read some reviews on 115AH and 110AH cuz its probably all the same. Nice man but awful lectures that get side tracked.
Spring 2021 - If you're taking this class, you probably had DAG for 110AH/BH. Otherwise, read some of his 110AH/BH, 115AH reviews as the general style is applicable. I've had this mans for four quarters now at UCLA and he continues to be one of my poorer lecturers but one of the nicest professors I've had. The class is simply "here is 50 problems - get 40 of them right and here's the A". I found field theory/galois theory to be tedious and very unmotivating (though some of problems are pretty cool). He will give you "recommended due dates" but at about week 9 and 10, will say the rest of the problems are due. At that point, only about 25 were assigned. I think I spent about 3 all nighters trying to catch up on material and do some of these problems. I will also note I was part of the not as smart people in the class as you can tell by the grading distribution. I wanted to drop this class not because of DAG but because of the difficulty of the grading which leads me to our TA Tim. He's pretty nice. I have very mixed opinions on him. On one hand, he has a bit of a condescending attitude which made me feel the dumbest person and his grading made this course a lot more stressful than 110AH/BH. On the other hand, if you ask for help, he will be there and support you. I think because of the Covid/online environment, I personally got burnt out and found it harder to ask for help because it seemed like everyone already knew what was going on besides me. However, all in all, if you want to go into pure math for grad school or really want to learn about Field/Galois Theory, take this course. You will learn a lot. If you have any other ambitions, I suggest avoiding it. There's a lot more other things you could be doing with your time.