The workload is high. Each week there are two assignments assigned, each containing 8 questions with multiple sub problems. The instructor uses his own lecture notes as the textbook, in which the proofs are somehow razzle-dazzle. Considering dropping the course.

Take a class with Allen Gehret. He looks out for his students and always willing to help. He had like 3-4 office hours throughout the week which was awesome. His lectures were a bit slow in my opinion which I would rather have than too fast. He was very thorough with his explanations and made the material easy to understand. His homework is not too difficult and was the perfect blend of math+programming. He had about 15 homework problems but as long as you did 7 correctly you received full credit. He had quizzes which were extremely easy and median for almost every quiz was a 100%. Plus, he drops a quiz and homework which was a plus. The midterm and finals were easier than the homework and had about a 92% average. He grades on a standard [93,100]: A, [90, 93) A-, [87,90) B+, etc. scale. The TA was alright. His lectures were okay but still good and his worksheets were as hard as the homework if not harder. Long story short, I would definitely take another class with Allen

I love professor Gehret. His lectures are super organized and clear. I would definitely recommend taking 115A with Gehret if this is your first proof class. His homework can be sometimes challenging but it covers every topic he talked in class. And my TA Jaehoon Lee is so far the best math TA I've had. They both put a lot of efforts into teaching and they care about how well their students are doing in the class. Most people did not like 115A that much, but Professor Gehret made it great. His tests are fair too.

I took this class online due to COVID-19. The professor's lectures were easy to follow! He always explained any concepts from Linear Algebra we needed in class which was useful. Grading consists of weekly quizzes and homework which take up a lot of time but are very helpful for studying for midterms and the final. Midterms and the final were fair and were pretty similar to the hw. Overall, the class was a lot of work but the concepts themselves seemed easy! We also didn't need a textbook since he would post all the lecture notes on CCLE.

Professor Gehret is an amazing professor overall. He's clear in his lectures and is sure to elaborate on any unclear topics. Great explanations for material. Suggest going to class every day because you don't wanna miss his teaching.
Professor Gehret also has to be the most passionate and helpful teacher. I went to his office hours regularly and it helped tremendously. Homeworks are sort of difficult, but you can always go to office hours to get some hints of any questions on homework. So, please make the most of these resources.
He is very honest, fair, and loves what he does and shows it through his teaching. It is not an easy class, but he offers a welcoming learning environment however because he gives it so much effort he expects the same.

Professor Gehret is a great lecturer and he genuinely cares about his students. The homework problems are hard but totally doable as long as you think through the problems and not give up. The first few assignments were significantly harder than the rest so don't get intimidated and drop the class. (around 10 people dropped before week four, while the rest of the quarter worked out just fine for the remaining classmates) Furthermore, his exams are way easier than the homework problems, so reading the notes he posted on CCLE at the beginning of the quarter would suffice. Overall, I would highly recommend taking his class if you want to know what Analysis is all about.

Allen is a nice guy, but he operates under a high, possibly unconscious, assumption that students somehow know material from 115A other upper division math courses. It's clear that this is his first time teaching Math 61. The homeworks are unnecessarily time-consuming, cryptic, and difficult. Allen paces the material quite quickly and doesn't spend a lot of time on how techniques to writing proofs. He often stutters in lecture and doesn't have much stage presence which is extremely problematic considering how early he teaches (his 9AM lectures are terrible).

Ben Spitz, one of this class's TAs, is a saving grace. He is an extremely kind and knowledgeable instructor who always tries to help out during review sessions and office hours. Anyway, be careful taking this class. Although midterms were easy, the content will often times leave you scratching your head in pure bewilderment and many hours will be spent self-studying the material.

Homework is extremely difficult to the point of being nigh impossible sometimes without going to office hours/looking up answers/attending the hours he's reserved for his students at the student math center. Tests are very very different. They test on memorization of definitions of theorems and lemmas for half of them and there's not too many proofs on the test. The true or false sections are killer though. I enjoy this hard homework and easier test format. Additionally, I've heard that Gehret made this class to be more rigorous and based more around number theory. I often spend anywhere from 5 to 15 hours a week on the homework, but YMMV. As a math major I feel like this class, though hard, has prepared me better for proofs.

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.

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.