Honestly, best online notes available I've had yet for a math course. You can take these notes and understand the material in a rather short amount of time because of how well-written they are. Homeworks are difficult, but going into tests after them makes the tests feel easy by comparison. He also has a VERY generous grading scheme for individual tests. Overall, this class was a good experience and very welcomed given my experience with past math professors.

He is a considerate and nice professor who consistently went out of his way to help students. He's super understanding; he would push back homework due dates during busy weeks and hosted a lot of extra online office hours during the COVID19 craziness. His lectures are clear. His homeworks are pretty proof-heavy and difficult to complete unless you go to office hours, but his exams are reasonable and easy if you study the homework solutions and his lecture notes.

The homework is ungodly difficult sometimes but the exams are MUCH easier. He also writes and posts his own lecture notes, which is really convenient and lays out all you need to know for the exams. Not a bad class by any stretch

I love this professor. Allen is one of the best professors I've had at UCLA, especially in the math department. I'm taking his 33B class in the spring because I love how much he cares about his students.

He writes his own problem sets as homework, as well as his own lecture notes (always shared with you on CCLE!). You do not need the textbook at all, although he does tell you what parts would act as a nice supplement.

His homeworks are pretty hard and graded on accuracy, but you are able to collaborate with others (and submit your own homework) so it's not *that* bad. Although honestly yes the homeworks are hard and time-consuming. I probably spent about 8 hours on each homework (due weekly). The last 3 homeworks he let us submit with up to 2 other collaborators on Gradescope so we didn't have to write so much individually. Homework was around 30% of the grade so it was important to do well on them, but he dropped the lowest score. I think I overall got an average of around 92% on the homework (or around there).

His midterms are honestly pretty fair and involved a fair amount of memorization of theorems. He would ask you to recite them for 5/10 to 15 points on any given problem. Then the second part of the question would ask you to do a proof involving them. There were also some computation-based stuff later in the course, but they were worth like 10/60 points on the midterm. Proofs were more important. He also tended to do between 16-20/60 points of the midterms as T/F questions, with 0 points for a wrong answer, 1 point for a blank answer, and 2 points for a correct answer. So around 8-10 T/F questions on each exam. These are tricky and often mess up for edge cases (such as, when x = 0 or x = some very specific value) so it's often worth it to leave a lot of them blank.

The final was online because it's winter 2020 and so the proofs were harder and there was no theorem reciting. The T/F was easier though because it was an open-Google test so there was a lot of ways to check whether they were true or not. The rest of the exam was all proofs and a few computations.

Overall I liked Allen's teaching style because he is very clear on everything and you essentially can just copy his notes word for word as he writes them on the board and gain a good understanding of the course. I didn't pay that much attention most of the time but I still felt like I understood things fairly well. Also if you miss lecture, his own lecture notes are available like a week in advance and he tells you what each lecture goes over so it's easy to catch back up. He is very nice and answers questions as best he can, and he says "um" a lot because he has kinda nervous energy but I don't think it's to the point that it's annoying. It gets a lot better when he's actually going over math stuff and not like answering questions or going over like announcements about the course, as well.

I'd encourage anyone to take his class regardless of whatever course he is teaching because he is just a really good professor. Even if you don't like his teaching style you can just read his notes instead, which are very clear and I used them as a reference a lot for homework/studying. I'm so glad he was available for two of my 7 math courses I have to take.

Like everyone else has said. The homeworks are impossible. You need help in office hours. He writes his own questions so you can't google the answers either. However, Gehret offers every week a study session where he and sometimes a TA will come in and help anybody who needs it with the homework. His exams are much more reasonable the homework assignments where the proofs are actually doable if you understand the stuff covered from lecture. Gehret was pretty decent at teaching the course, but it is definitely challenging if it is your first proof class. Although, I ended up liking it a lot. Then, there is Ben Spitz. literally the best TA ever. He truly cares about his students. Often times he would stay for an extra hour during his office hours because students still had questions. He was unbelievable at explaining material to students. In addition, he held review sessions where he created his own review packets and baked desserts for us! If you can take a class where Ben is TAing, you really need to take advantage of this gem!

Professor Gehret was not only a great professor, but also an even nicer person. This was the third time I took his class with all three of them being equally enjoyable. His assignments were not as hard as some people claimed as I personally enjoyed solving the problems a lot. Those problems are structured to train the students to think thoroughly about a concept and apply the theorems in a critical manner. His tests were easy with emphasis on basic concepts, so there wouldn't be any issue if students just simply read his notes. Overall, this class is a good preparation for upper-division courses, and taking this class with Professor Gehret would be enjoyable for people who like math.

Allen is a very kind guy. He delivers very clear lectures and has well written lecture notes for you to reference after class. Homework is hard but tests are easy. He cares his students a lot. Definitely recommend!

This class was a huge challenge for me. I came in with a lot of experience with computational math (i.e. solving and finding answers) and almost no experience with proofs. This is a VERY proof-heavy class, and you don't really get a run-through on how to do a formal proof in this class unless it's induction or I guess proof by cases. With that said, here is my review:

The professor is a very nice person. He is really considerate of his students, and he shows this by going above and beyond outside of class to help us. Every Thursday, he reserved the Student Math Center so he and some TA's could help students with homework and the class material. That is the main reason I passed the class. The lectures themselves are very fast-paced, and I told myself that I would just write down what he wrote down and try to understand it later. Definitely go to the lectures, even though he posts all of his lecture notes online (also really helpful). Also, try to sit in the front so you can see.

As stated before, this is a VERY proof-heavy class. Literally 90% proofs in some form. If you're not comfortable with doing proofs, this class will make you get comfortable with them real quick. For me, it was a whole new type of math, and I had so much difficulty in switching my mindset from calculus-based computations to proofs and whatever discrete math is, but I'm glad I had Professor Gehret, because he was so helpful in that case.

The TA's also really helped during section. The one I had taught in a way I didn't like at all, so I went to another's, and it was a huge improvement. Definitely know which TA is the best TA early in the quarter and go to their sections sooner rather than later.

The workload may not seem like much, as it was at most 10 questions per week, but boy does it take LONG. Some questions are extremely tough and took me the entire week to figure out, but that forced me to become familiar with the theorems and the definitions, which you really need to be familiar with for the exams. The exams call for definitions, proofs, computations (thank god), and true/false. Know the definitions verbatim, and good luck on the true/false bc you're gonna need it. The exams were waaaaaaay easier than the homework, but the homework is graded more leniently than the exams.

Overall, this was by no means an easy or chill class. If you want to pass or get a high grade, you have to out in a ton of extra effort and go to discussion, office hours, and, especially, the Student Math Center he reserves. Also, group chats help a lot. Course material aside, I would say that Gehret is a truly phenomenal professor, and I am glad to have had him. If you don't have to take this course but want to, please don't take it because it's exhausting. If you have to take it, definitely take it with Gehret, he's a great prof.

PROS:
- The lecture notes online are godly. The notes are clear and well organized. I know a lot of people who don't go to lectures because they can read the lecture notes and get the same result.
- You don't need the textbook at all, given you have lecture notes.
- The professor is good at explaining concepts and proofs.
- Exams are reasonable. Roughly 1/2 definitions (memorize what the words mean or what properties something has), 1/4 proofs, and 1/4 true-false. The proofs are not bad and are easier than the homework.
- The professor is reasonable with deadlines. He extends weekly homework deadlines occasionally.
- The curves are generous. The midterm averages are low but the curve is around two grade-levels up.
- You get a lot of help. Other than his office hours and the TA's discussion/office hours, there is also a weekly meeting where you can discuss homework in the SMC.

CONS:
- Extremely hard homework. You get homework weekly (10 total) with the lowest one dropped. You go over basic proof examples in class, but the homework proofs are usually on a whole other level. Homework is due on Sundays and I will spend the entire Saturday doing the homework. There are usually 8-10 questions, with 2-3 being pretty easy and 2-3 taking hours each to figure out.
- No curve for the final
- I've heard that Prof. Gehret makes this class more proof-based than it should. It is occasionally unclear as to what exactly is a "correct proof" as it might be hard to know what are the exact steps to reach the correct proof (other than induction, which is easy). Sometimes I wonder why some proof is correct when it is long-winded and hard to follow when another proof that seemed to make more sense is wrong.

OVERALL: Take this class if you are ok with hard homework sets. You have many resources provided for you though. Prof. Gehret also seemed like a really nice and approachable guy.

Allen's math 61 class was overall not a terrible class, he was a pretty good professor and was very willing to help students in his office hours and after class. He uses his own lecture notes throughout the quarter, which his in-class lectures basically reiterate. They are helpful to go over and study for the midterms and final as you don't have to stare at a 500-page long textbook but instead focus on about 20-30 pages of notes. The only problem I had with Gehret was the insanely difficult homework that he gave. Some weeks I would look at the problems and not even know what the fuck some of them were saying or asking. It almost seemed like he expected us to have some upper-division math experience that obviously no one has since its a lower div math course. And btw, 61 is not a solely computational course like the 30 series, so be prepared to become comfortable with proofs. Another problem I had with Allen was that he never really gave an introduction to proof writing which made the first 4 weeks super stressful and tough for me, as I had never experienced this type of bath. When I looked at his very first homework, which consisted of about 90% proofs, my heart sank a little and I knew this was gonna be a super tough class. So like I said, the homework sucks ass but the midterms are what saves kids. They're usually restating definitions, some simple computations, and some not so bad proofs that are in the lecture notes. The true/false parts of his exams though can easily fuck you over if you're not careful. He penalizes guessing, so basically you get 2 points for the right answer, 1 point for not answering at all, and 0 points for a wrong answer. This is really annoying and generous at the same time because if you don't know it then at least you get something from nothing but if you fuck up then it can destroy your whole test grade. Overall just be careful on this section since you will likely be playing mind games with yourself about your answer. Allen was super generous with school being canceled and all and introduced a new grading scheme that made it very reasonable for students to get at least a B or B+. He was probably the nicest professor when it came to dealing with the whole situation. I would definitely recommend Allen as a math professor, just gear up for some hard ass math homework and be prepared to be best friends with your TA and the tutors at the SMC.