Royer goes really slow in the first half or so of the class which means that when it comes to the more complex topics, he goes by super fast. The class is easy up to the second midterm but the the final is a completely different animal. Take an easier professor if possible, otherwise he isn't too bad, it's just the speed that becomes a problem and the nature of the final is weird, it has more abstract type questions than the midterms.

33A with Royer is laughably easy up until midway between the two midterms, when the learning curve suddenly takes a sharp upward incline. He goes very slowly at the beginning to make sure the class understands the fundamentals, but do NOT take that as an opportunity to slack off. If you don't have the beginning half of the material down front and back, the second half of the quarter will be very difficult to wrap your head around. Computationally, the class isn't difficult, but there are many abstract concepts in the latter half of the quarter that can really bite you in the butt if you don't make sure you have all the prerequisite knowledge down pat. As a lecturer, Royer is very clear and goes slowly. He also implements a "clicker" system (no points given for them) in order to gauge how well the class is mastering the material, and clearly cares for student learning. Both midterms are generally straightforward, but the final will destroy you, as the difficulty level is much higher than the other midterms. Overall, a good class. Would recommend taking.

Aaron is the most wholesome person I ever met. His lectures are pretty good (sometimes boring but I mean it’s math), and I learned what I needed for the homework in lecture. Tests are fairly easy and very straightforward, the final was a little more challenging but he curved it. He seems like a nice guy and it’s obvious that he’s trying his best and just wants us to succeed. Would definitely take again.

I took Royer during the Fall of my sophomore year. Based on the information from my friends, this class was the easiest of the available teachers. I think that the class was pretty chill, and having a bit of background on matrices from Khan Academy was helpful. We covered most of the chapters of the textbook, starting from vector addition and reduced row echelon form and ended with complex eigenvectors.
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Pros:
*The midterms were pretty easy for math midterms; they even include multiple choice, which means that you can sort of guess
*The lectures were pretty engaging and were well paced
*Quizzes are taken directly from homework problems, and you can have them out during the quiz.
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Cons:
*Royer himself won't be enough to understand the material
*Due to a time crunch, he skipped out on lecturing an entire chapter and told us to read it
*He might be slow/boring for some people (I found it good though)

Take 33A with someone else

Midterms were okay. That final though...

He seemed enthusiastic about the material and teaching, but his lectures were dense and hard to absorb if you were seeing the concepts for the first time.

I honestly thought this guy sucks. He is extremely mediocore and is not suited to teach introductory courses. Linear Algebra is challenging to a lot of people since it is very different and is the first class where it is better to teach by proof rather than example. However, that doesn't necessarily mean it is a difficult subject, especially at this introductory level. The logic is extremely crisp and I found the material to be extremely simple once you make sense of it, especially in the beginning of the class which is SUPPOSED to get you used to matrix algebra first before you start to do cool stuff with it.

However, this guy just seems to not understand the background from where his students are coming from, since it was literally impossible to communicate with him. He tends to speak proofs out to you when you ask him a question rather than write anything down on the board. He doesn't seem to be able to not communicate without using heavy math jargon and his lectures were impossible to follow. He apparently admitted to me that he wants his lectures to make his students very confused until they look through the material and then it becomes clear...like what? Why not just be very explicit and clear in lecture instead so I don't have to waste so much time re-reading the textbook over and over again?

Also the fucking textbook. It doesn't help that the textbook is god awful. 33A needs to rely on a new textbook. Otto Bretscher (apparently a hardcore communist, look him up on facebook) decides to make the book as convoluted as the teacher tries to. Introductory linear algebra does not need to be so horribly confusing.

I honestly thought the entire class was following him 100% and I was the only one struggling super hard, but then the averages on the 2nd midterm and the final were abysmal, so go figure. He curves, but holy shit his final exam was rough. Only a small fraction of students truly understood the material to be able to survive the tough ass final. They probably had the appropriate study strategies or had exposure to linear algebra before.

If you want to do well in 33A make sure to do all the true false questions in the back of each chapter to truly check to see if you know the material. Also 3Blue1Brown saved my fucking ass. Even though I got a B+ I still feel very comfortable with linear algebra and capable of doing it for physics courses.