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...

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.

Intending to take his class next quarter

I took the honors version of this class. The class was definitely tough, but Balmer is a good professor that can communicate the material very well. However, I still think Elman is a better professor in term of lectures. Both are very demanding. Balmer gave a very generous curve which more than 1/3 of class got an A and more than 2/3 got a B. Recommended and good preparation for other upper-divs.

Balmer was a tough professor, but I'm only a math minor so take this with a grain of salt. The exams were really difficult, as the previous poster said, but he was always inviting people to his office hours so it's not like he didn't want to help. Sometimes the homework was misguided, especially when there were sections that had multiple problems within a problem. I think the homework would have been better had there been less problems selected more carefully, even if it were graded for correctness rather than completion. He's super smart though if that's any consolation.

If you're as terrified of taking M115A as I was, this review is for you. I probably couldn't have been any less prepared for this class - I had taken lower division linear algebra at my community college years ago and our work was entirely computational. As such I didn't remember any of the computations and had literally no experience doing proofs going into this class.

Professor Balmer definitely expects you to have some familiarity with proofs - he uses all the standard notation that you should familiarize yourself with. As for his lectures, I did not find them to be even remotely helpful. It was 50 minutes of him racing across the board and I found it impossible to keep up with him. I was usually lost within the first few minutes and spent the remainder of class in silent agony.

Here is the good news - this class does become easier as the quarter progresses. And by easier I mean there are actual computations you can do! Yay! Not only that, but the proofs are a bit easier to understand - similar to proving trigonometric identities, in my opinion. As for the midterms, the median for the 1st midterm was 52%, the 2nd was 44%, and the final was 58%. If you get scores within the average you should at least be in the B range - lower than average will be in the C range.

My advice if you are struggling with this class is to visit him during his office hours as often as possible. He was a bit ornery during his first office hours session but he quickly warmed up to us afterwards. Good luck!

Balmer does a great job at making his students understand linear algebra. His lectures are clear, he makes a good joke from time to time, he assigns an appropriate amount of homework, and his exams do a good job at testing your depth of knowledge. He is a tough grader, but getting a 0/5 on a problem can be better for learning than a 3/5 because it forces you to reflect on what concept you might not be grasping. Not a generous curve (I was top 15% of the class for the final which was worth 60-75%, and top 33% for both midterms which are worth 15% each if final is with 60%, and got a B+), but you'll be well prepared for other upper division math after this class.

Balmer is really funny and smart. He is a low key, amusing Frenchman with a talent for simplifying complex ideas. He is very available and helpful during office hours, and leads good lectures. This is a very difficult course, there is no denying. But if you are going to have to take it, take it with him.

There are 2 midterms and 1 final, like any usual math class. Hw is 10% and you only need to turn in 8 to get full credit. even though you don't finish all of the problems. If you do better on the final than one of the midterms, grade is the higher midterm is 15% and final for 75%. If else, it's 15 for each midterm and 60 for the final. The professor himself is super duper smart, you can tell from his CV (available at UCLA math department). However, the thing about professor Balmer is he thinks we know everything. He tells us to read the material beforehand from day 1, but I don't have that kind of time towards the end of the quarter. After you read the book, you will see he is a really good professor because he explains those tough stuff. But if you do not read the material beforehand, you have almost no idea what he is talking about during the whole lecture. (That's me pretty much the whole quarter.) The mean and median for the three exams did not go over 50 out of 100. The 2 midterms have the full credit of 25 and the final is 49. There is 5 true or false questions for midterms and 10 for final. The feeling you get from seeing the problems at first sight is you don't know how to use what you know to solve them. During dis sessions, we usually do hw problems. However, the TA never tell us why he did what he did. He always writes down a claim and prove that claim afterwards when we don't even know how he came up with that claim. :/ And sometimes he will make a mistake and spend some time finding out where or leave a problem unsolved because he does not know how, either. Good thing that he only teaches 2 undergrad classes, 33A and 115A.