I remember in a library on campus a couple quarters ago (back when that was legal), and I heard in passing a comment made between friends:

“Imagine having an entire building for teaching math, but no one there can actually teach it.”

And I can understand that feeling. The reputation of a subject that is seen by many as very difficult and tedious and hard to understand (which it indeed is quite often) makes it easy to end up hating on math teachers and professors a lot for making already hard courses a nightmare.

What’s worse is that sometimes teachers are so incredibly smart that they actually have a hard time teaching explaining some concepts at a basic level, especially important for say a class about Real Analysis where many undergraduate students are becoming familiar with its difficult details for the very first time.

But I’m here to say in this review that Professor Eriksson-Bique has completely broken these molds, and I can’t believe I got so lucky to have the opportunity to join his class, even in this online quarter. He has not only demonstrated that he cares about us and our learning, but he has also shown some of the best adaptability to an online environment that I’ve seen so far (Not to mention, he’s pretty funny and easy to talk to/ask questions, but that’s just a nice cherry on top).

One of the key differences immediately apparent that makes this professor stand above the rest I’ve seen so far is that he seems to be the most aware that’s he’s not just writing some notes on a page for us to read; he’s actually aware of the cognitive processes going on, what’s important to highlight, what is an important trick that we’ll see later, overarching ideas that help us as students put the pieces together. In particular, when he writes proofs, one small but really helpful detail is that during the proof writing, he writes off to the side little notes like “1. Choosing delta” or “3. Estimation” so that we get a good sense of how the proof should flow, and highlighting the importance of what needs to be said/invoked before we can move on.

Another great example that helped at least me is that for this part 2 of Real Analysis, we start talking about a general concept of uniformity, both for continuous functions and for sequences of functions. While textbooks and I bet many professors would simply give definitions and go right on to applications and problems, Professor Eriksson-Bique took at least a bit of time to really explore how these ideas differed from previous concepts like regular continuity and pointwise convergence. In particular, he highlighted the importance of the order of the quantifiers, and took some time to explore how this key difference could change the answer to certain questions you could ask about certain sequences or functions.

As for office hours, I have mostly positive feelings. Especially in an online quarter where it was harder to connect with everyone face to face, I believe that Professor Eriksson-Bique made a great decision to make some practice problems to discuss in groups, added a much needed element of being able to bounce ideas off of each other and even have a bit of fun sometimes. The more important piece of feedback I have for these though is that sometimes, he would assign a problem that was a bit too hard to think about on the spot there. He gave good room to throw out ideas, but at the end of the day, he was just showing us a solution (which we often did not entirely understand in the moment), which is not really what office hours were supposed to be about. In fact, I think I would suggest that instead of just asking for “any homework questions” (which in my experience, being asked that out of the blue doesn’t really elicit many responses, even if people have some), he could make a more clear split between office hours that were devoted to homework help/actual questions and purposefully not have as much discussion of new problems in those hours, and these discussion office hours. The problem boils down to the fact that sometimes, these proofs or problems take time to digest, more than can be done often in a discussion style office hour, so having this split could give time to come more prepared with homework/general questions.

Finally, I think no review would be complete without mentioning this: I know there is a strong stereotype especially nowadays of math professors being a bunch of old dudes stuck in their own heads, unaccommodating, dismissive, and unsympathetic of students who are concerned with the state of our country and are in truly tough spots. However, Professor Eriksson-Bique once again breaks this mold by showing true compassion for us as the students who have to learn in this condition. Quoting a post he made to Campuswire:
“Many of us, myself included, are minorities of various types, and may face fear for their safety. Even those of us who are not, can sympathize and know that the constant threats of violence and injustices serve only to limit us all. The healing is all of our responsibility, and each of us can think how their position allows for improving diversity, fairness and equality. I myself am committed to these in the courses that I teach, and am deeply mindful how there are still many impediments in our colleges to diversity and roadblocks to access.”

How many math professors say things like this unprompted, and not just something like “oh, well, sucks for you guys. Finals as planned.” in response to requests for accommodation? What a guy! I really respect Sylvester as a person.

I don’t really say this kind of thing too often, but I am really thankful for Professor Eriksson-Bique for making Real Analysis fun for the first time for me! Please do take a class with him if you get the opportunity to.

(Ok, well Professor has just said he will not be returning to UCLA, so I suppose much of this might not be useful, but no use deleting my thoughts. Maybe I’ll leave this just as a shining example that good math teachers do exist!)