While the class is definitely doable if you have the time and the will to really learn the material, Professor Balmer is definitely not a professor I would recommend for Math 115A. His lectures were meh (definitely not the most engaging things in the universe and his delivery of the material was definitely awkward at points), and the homework was really time consuming if you actually do it (it's only marked for completion, and you don't have to do all of it).

Exams in the class were pretty awful as many of the reviews below suggest. To put things into perspective, the first midterm had an average of 50%, the second midterm had an average of 30%, and the final had an average of 47%. The class culture is pretty depressing as a result of these scores and Balmer's poor read on student understanding really shows in this respect.

If you get stuck with Balmer, here's some advice:
(1) He's not joking when he tells you to read the book. The book is 10x better at explaining the concepts than he is and if you read the assigned material beforehand, lecture will become somewhat useful for you.
(2) Do not waste your time studying with mechanical proofs because Balmer makes you complete more elaborate tasks on the exams. For example, you are much more likely to provide an example of some obscure linear transformation rather than verifying a linear transformation is indeed a linear transformation.
(3) Don't be hard on yourself after exams. No one really does well. Take a shot of vodka and let life go on. (Top score on one of the midterms was a 60%)

While I definitely survived this class with a higher grade than I would've ever dreamed of, I don't think I'll be putting myself through another Balmer class ever again to keep my sanity haha...

Professor Balmer uses his own lecture notes. You start out with fundamentals of category theory, such as the Yoneda lemma and adjoint functors, and move on to group theory and ring theory. For group theory and ring theory, you will be covering similar material from Math 110AB, except for the facts that (1) you will use the language of category theory often so you'll wrap your head around familar concepts but in different language, and that (2) the pace of the course is three times faster. Professor Balmer's tests are hard - the average grade for the midterm was less than 50% and the average for final was around 60~70% - but he curves.
As category theory is covered in a very short amount of time, you may find the first two weeks of Math 210A, which is all about category theory, challenging. However, know that you will and can get through it, and that everyone else in your class is also struggling to learn category theory in such a short amount of time - so I would not be discouraged. I would definitely reach out to your peers to study together.
Whether or not it's Professor Balmer who is teaching Math 210A, I would not take this course if you don't have familiarity with all or most of what's covered in Math 110AB; you'll be crushed if you are taking this as your first abstract algebra course. Again, it's expected that you already know the Math 110AB material.
I would make sure that I am being courteous and respectful when I am engaging with Professor Balmer; he is very much approachable once you know that he appreciates courteousness. He is a very funny person, I laughed several times during his lectures. There is no attendance but his lectures go so fast. His lecture notes can be terse at times, so I would not hesitate to confer different books on abstract algebra as supplements if his lecture notes confuse you.
I would like to thank Professor Balmer for his teaching this course.

Balmer is a great professor. Explains stuff in lots of detail, but works very fast. If you want to learn linear algebra take it from him. This class is pretty tough though thats for sure.

Note for 115AH while I did not receive the best of grades, that was on me..while there are no practice tests the exams are pretty straightforward, some questions from homework/lecture/notes. The homework is graded on completion, but go to office hours to talk over the critiques on the homework.
He has 3 office hours right before class, and was very helpful/clear during them. He teaches clearly, and does not go to quick. Best of all he does not force his students to get a textbook, instead using his collection of notes for the whole quarter(which have the theroems, and excercises).

The grade distribution is as follows:20% homework, 20% two midterms, 40% final, or 60% final if have a poor midterm.
I would definitely take the class again with him.

He is a pretty clear Lecturer, and his tests are not hard. But I did not understand why he cared about brackets and those details so much!
I missed two points during the whole quarter because of not writing the brackets and not indicating which one is Q and R for QR factorization. Because of this I missed A+ by 0.3%!!!! He is a harsh grader, he made 94% to be A and 98% to be A+. Just be careful about those brackets when you take him he is a fun of brackets!

I was kinda afraid of Balmer at first, but liked him by the end. He has an awesome french accent. I got c's on both of the midterms but got an A- in the class cause of the final. His class is very straightforward which I really liked. The same with his tests. I would definitely take him again. Just keep in mind for tests that he does not give partial credit.

Avoid Balmer if you can. I essentially taught myself the entire class. He goes over the really easy concepts in lecture and then leaves the students to figure out the hard stuff that shows up on the tests. I also had trouble understanding his accent. And I agree with the others in that he will not be flexible about anything - I had a close relative pass away unexpectedly 3 days before the midterm and he made me take it the same day as everyone else. I got a B- in this class, but I got an A in 32 B, a class which I believe to be much harder than 33 A. If you do not want to put at least 14 hours a week into this class, this professor is definitely worth avoiding.

Professor Balmer was pretty awesome as a professor. He explains well and he was sometimes funny. However, the choice of textbook for Math 33A is just atrocious. The textbook just fails at everything in explaining linear algebra, and that's why many people in any Math 33A class would have trouble in the class. I got by just because I had a better linear algebra book, which was by Anton.

For his tests, they were extremely straightforward and they're not that difficult. In fact, Balmer was going easy on us because he didn't put any proofs until the final, but the final had one or two easy proof problems. If you want to do well in the class, consult a different linear algebra even if it has to be a math 115a book and do the problems in the atrocious math 33a textbook. Also, if you're a math major, listen to his advices since they will most likely help you through your upper div classes.

Professor Balmer is unbelievably smart and extremely approachable. However, his exams are brutal. There is no partial credit and you can get marked down on the most menial of mistakes. I do like Balmer as a person and admire his ability to understand the most complex topics of mathematics, but if you're looking for a manageable (not even easy) class, walk the other way.

What the previous person said before me is true, you need to be extremely, extremely careful on not making any computational mistakes or you will get it wrong. His midterms are only out of 13 points so there is some to no partial credit. when you miss by one number you are screwed so be very careful!!! The tests are easy but you need to be careful with your numbers, thats what gets you!