Maybe I'm the stupid one in the class as everyone in the class gets like As on their tests. Not the best lecturer, but also not the worse. The test are extremely long and definitely not 3 hours for the finals. The class is not curved so keep that in mind (45% midterm, 25% hw, 35% finals). I just pnp the class cuz I know I will not learn anything from the class. Take it with another professor if you can.

The worst class I have ever taken at UCLA, watching any of the lectures after week 3 is a waste of time. You'd be better off spending that time rereading the textbook and watching khan academy videos. The professor is hard to understand and barely explains the main concepts we need to cover. Although he doesn't give a lot of work, this means there is almost no structure to help you learn the material.

The whole class is a straight reiteration of the textbook. The teaching approach in general is just not really teaching. After the midterm I completely lost what we were doing. I am still not sure I internalized anything fundamental about distributions. And that is unfortunate 'cause I really need to understand the material well for my future CS class. Be sure to check the weights of the exams. In our midterm (there's one midterm and final) each point corresponded to 1% of the final grade. And of course this class is not an exception to the mockery that is the math department during pandemic: exams are twice as long and at least twice as hard as they would have been in person. The people who do not cheat are punished the most, so...

GENERAL WARNING: Though not listed as a prerequisite, make sure to take Math 131A or equivalent before taking this course, as there are proofs that involve the limits of sequences and series as well as exchanging limits and unions/intersections, summation/integration, etc. I believe these rigorous aspects are a part of the course regardless of the instructor, so having knowledge of relevant topics is really necessary.
Another general comment: Stochastic processes are, based on my limited knowledge of math, a very deep subject. Having taken honors math upper divs and some grad courses (in applied math, though), I could feel that some aspects were deliberately left out in the textbook and/or lectures as they involve more advanced knowledge in e.g. real analysis (more precisely, measure theory as I would guess). That being said, the course contents are still pretty well presented in both the textbook and Dr. Nguyen's lectures.
Textbook: Written by Prof. Rick Durrett at Duke University and completely free (available on his personal website). A very well-structured book with more than enough examples, which is good for understanding, but at the same time, it is a good idea to take notes in class and/or make notes of the important results, as they tend to scatter all along the way in the textbook.
Grading: 25% HW + 5% Discussion Attendance + 25% Midterm + 45% Final. Towards the end of the quarter, another grading scheme was added: 25% HW + 5% Discussion Attendance + 10% Midterm + 60% Final. The syllabus says that the class is not curved in either way, but I speculate that we got curved up a bit.
Lecture: In person, but lectures were recorded, at first with Zoom installed in the classroom but the quality was very bad, so he switched to his phone after a week or two. The lectures are very clear and at a reasonable pace, though I find them a bit slow sometimes. He went through important proofs and examples step by step, which is very helpful. The only caveat is that one concept or two showed up in HWs that he did not cover in class, so once in a while you need to read the textbook on your own.
Homework: Combination of textbook problems and self-written ones. I think they are well picked/written, as they either serve as good practice of using formulas covered in class, or ask you to prove important results (with reasonable difficulty) that appear later in the course or on the exams. Some problems took plenty of time to think about, but it is very rewarding once you figured out the key point. There were nine sets of five problems in the first eight, but the last homework due on the final day of instructions had nine problems, which was actually a bit too many.
OH: Dr. Nguyen is very happy to answer questions and read your work on the HW and help you write better solutions/proofs during office hours.
Exams: 1 midterm + 1 final. Both exams were in person and a bit pressing on time, with the final more so. The distributions of scores turned out to be okay. Having a good understanding of the lectures and homework problems is essential, especially considering that there is not much time to be at a loss or fix mistakes.
Overall Dr. Nguyen is a very great instructor for this course. Due to its challenging nature, our lecture ended up having just short of 20 students, but Dr. Nguyen is very willing to help and I felt I learned a lot in his class.

ugh i am taking this class right now and it is just a mess lmao. no one goes to lecture and he never gives any feedback. most of us got a B on the midterm, but ... thats 45% of our grade so nearly impossible to get an A in the class unless we ace the final. he doesnt provide solutions for anything, and they take forever to grade hw, and even when they do they don't really explain how we were wrong just says "its wrong." workload is doable, but their grading is so harsh without explanation its frustrating :/ i had swee hong for math 170e and id recommend him

Grade Composition: 45% Midterm + 25% HWK (Assigned weekly from Week 2 to Week 10; 9 in total) + 30% Final

The Professor was very willing to help during his Office Hours. He did give clues to challenging homework problems.

The distribution of easy, medium, and hard questions on the exams was around 50%, 30%, and 20%.

The only thing I disliked about this class might be that my TA could hardly speak English. I simply skipped discussions and hardly took advantage of any resources from her.

Fair Professor and pretty tough class for me, so definitely requiring some hard work.

His lectures are clear as he explicitly writes out every step for solving a problem.

Sometimes he skips proofs and/or explanations and tells us to refer to his notes posted on CCLE. His notes are hand-written but readable and pretty detailed.

Homework is doable. He goes over some HW problems during his office hour, which is helpful.

Midterm and Final can be challenging, but they are open book, open notes, open R, open calculator, etc., and he gives extra credit problems on the final.

He replies to your emails promptly and answers your questions with detailed explanations.

I was lucky to have a super nice TA who reviews concepts and goes over homework problems in discussion sections, which also helps.

LECTURES: Lectures are very clear and helpful because everything is explained in a step-by-step manner, and Professor Nguyen always tries his best to explain the details and in-between steps in the proofs or solutions. He also assigns around 10 in-class exercises in total--those are extremely important and helpful, so make sure you go home and try!

HOMEWORK: Only 5-6 problems per homework, but typically every one of them is challenging and time-consuming. Nevertheless, doing his homework is quite helpful in getting familiar with the material.

OFFICE HOUR: Probably the best thing about Professor Nguyen's MATH 171 is his office hours. He is always patient, helpful, and approachable during his office hours. He will give useful hints to homework problems and his exercises, and he will also help you write better solutions.

EXAMS: He gives difficult exams, but perhaps the exams will be hard regardless of which Prof you take MATH 171 with since this class is a proof-based class. Due to COVID, we had a 24-hour midterm and final, which are both very challenging. However, if you put honest efforts into this class throughout the quarter, you will be fine!

OVERALL: I will highly recommend taking this class with Professor Nguyen.

He is great! The finals is a bit tricky but he made the midterm very straightforward! I think everything is fair :)