I don't know what the professor did to make people write positive reviews - most of the student in this class agreed that he is literally the worst professor in the math department. His lecture was extremely unclear, and sometimes when he forgot how to prove a theorem, he just told the class to figure out on our own, saying that it would appear on an exam. His exams weren't hard, but with his teaching, half of the class did not do well. Other reviews said that he was pretty helpful, which wasn't true at all, and he did not care about his students' learning at all. My TA and the workload were the only good things about this class, and all other aspects were just pure crap. Avoid taking this class with this professor at all cost, and if you have any doubts about what was said in this review, just ask others who took this class with him. I suspect that people who wrote the lengthy positive reviews either wanted to trick others into suffering through this class like they did, or the professor made them do it - his 170E reviews are much more accurate than the ones on this page.

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.

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.