As a disclaimer, I am writing this before I take the final and receive a grade for the class to be as non-biased as I can be. First time writing a review here, so I'll try to update what grade I got.

Greene is an incredibly funny and down to earth guy who is great to talk to. In office hours, he really takes the time trying to explain certain concepts and ensuring you understand everything. His homework sets are challenging, but fair and the week of time is enough to be able to completely solve them.

However, there are some flaws with his class in my eyes. At least for me, and some of my other classmates, Greene's lectures can be a bit difficult to follow and his hand writing is a bit messy. Greene will often go onto tangents about material not related to class or sometimes not baby you through a process/proof because it is simply natural to him. The guy has been doing math longer than I've been born, so it's expected some of the stuff he's teaching is just second nature to him. For someone who has never taken analysis though, this can be challenging to fully understand what he is saying. I also personally don't mind him going on tangents, but others do.

Greene's hand writing also makes it hard to sometimes read what he is teaching, his notes, or the homework assignments. A few times the homework assignments have had typos, but Greene always makes sure to correct them via email.

For me and many others, Greene's notes are a god send. His notes are concise and have a nice flow to them making it easy to learn the material through them. However, it still runs into the issue of messy hand writing. So from time to time you'll be squinting your eyes.

Greene also uses a separate email from his myucla email to send out various things because his myucla email doesn't work. This is fine and all, but many times his emails would go to my spam folder randomly. MAKE SURE TO BE IN A CONSTANT HABIT of checking your spam folder if you take a class with him, so you don't miss out on his emails. His emails usually have notes, homework, and study guides attached to them.

Greene's myucla is also a bit disorganized, but not terrible. Greene labels all his notes and such via the date he gave the lecture or published them. This is fine, but makes it difficult to exactly find the topic you want to review or take a look at. Our class ourselves had to make our own drive with the notes labelled for ease of access.

The midterms are killer for Greene. The questions themselves aren't too hard, but with only 50 minutes to do them and some of the proofs being quite long. Most often run out of time. The average was around a 35% on the first midterm and a 50% on the second midterm. Unsure how he's gonna grade the distribution at the end of the class, but that's how it was for the midterms. To have success on the midterms, I highly advise you go back through each note set and make sure you can do the important proofs by memory. I also recommend doing this for previous homework. The name of the game here is speed and most of Greene's midterms problems come from his lecture notes and homework assignments. I always felt Greene's midterms were fair, but really tested if you could discern what the question was asking in time.

On a separate topic, our TA was Nicholas. The TA strike is still ongoing, so we did not have him for all of the quarter. Nicholas is an INCREDIBLY hard grader as a TA and does most of the homework and midterm grading. He's extremely good at making sure your arguments are rigorous, but not so great for your homework or midterm scores. The class is graded on some distribution, not discerned how it is, but it can be a bit unmotivating for some. Nicholas graded the 1st midterm, while Greene did the 2nd and the averages definitely shows the rigor in grading between the two (although part of it is also due to people knowing more of what to expect for the 2nd midterm). Overall, Nicholas is a great TA who does a great job explaining stuff in detail and making sure you can prove stuff rigorously. He is an incredibly harsh grader as a result, but a nice guy. Certainly a good TA to have, but just be prepared to have a great amount of attention to detail.

Overall, I think Greene's 131AH class has been incredibly enjoyable. You can tell he really cares about his students and is passionate about the material. I do think following the class only from his lecture can be difficult at times. Consulting outside sources and referencing his notes HEAVILY will be your key to success.

Greene is a fucking legend. No question. The man does not have to be here but he blesses us with his infinite jest, wisdom, and grace. Be warned: This class is not for the weak-hearted. Greene will make you work harder than you ever have in a class. But if you are crazy enough to do so, you will ascend to newfound mathematical heights the likes of which you cannot possibly conceive. So tread carefully, and know that the journey will not be easy, but quite worth it.

131AH with Greene is extremely hard to follow. Lectures are unclear and interspersed with irrelevant tangents and I was never sure which of the three assigned textbooks we were working out of. He also seems to assume a lot of prior knowledge, which adds to the difficulty of an already difficult topic. However, the curve is extremely aggressive - my C was from a 50% raw score - so if you want honors credit and don't mind a world of pain, go for it. Just beware that the topics covered do not align with the topics on the department's website or with 131A, so going from 131AH to 131B is going to leave gaps in your knowledge, namely differentiation, integration, and FTC.

TL;DR: This course tells you what mathematics is really about.

The Math 131AH/131BH/132H series is typically worthwhile if you follow Prof. Greene throughout the year. Successfully completing this course introduces you the language of modern mathematics through topology and analysis. I suggest to prepare to study 30h+ for midterms/finals. Lecture notes are extremely important since rarely anyone can follow his lecture style (at least not me).

Finally, believe in yourself. If you do your best, you are gonna ace this.