MATH 131A
Analysis
Description: Lecture, three hours; discussion, one hour. Requisites: courses 32B, 33B. Recommended: course 115A. Rigorous introduction to foundations of real analysis; real numbers, point set topology in Euclidean space, functions, continuity. P/NP or letter grading.
Units: 4.0
Units: 4.0
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Most Helpful Review
Spring 2023 - I really loved 131A with Professor Wu! He is an amazing professor, during lecture he used many colored chalks and helped build intuition for the harder concepts. He also always provided midterm/final reviews and during office hours he was very approachable and helpful. Although the class is one of the hardest math courses, this class really helped me build strong foundations in proof writing and core concepts I still use. It was overall a very rewarding class, so if you have the option to take 131A with Wu, I highly recommend. You will learn a lot and are in good hands :)
Spring 2023 - I really loved 131A with Professor Wu! He is an amazing professor, during lecture he used many colored chalks and helped build intuition for the harder concepts. He also always provided midterm/final reviews and during office hours he was very approachable and helpful. Although the class is one of the hardest math courses, this class really helped me build strong foundations in proof writing and core concepts I still use. It was overall a very rewarding class, so if you have the option to take 131A with Wu, I highly recommend. You will learn a lot and are in good hands :)
Most Helpful Review
Fall 2025 - I hated this class so much. I am not a proof person, so I knew this was going to be difficult. I would say he is pretty clear in lecture and teaches decently. However, sometimes he decides to change his mind and do the proof a different way (just for funzies), but then he gets it wrong. He posts the entire course lecture notes from the beginning, and those were helpful. There is only one midterm, which I've never seen before in a math class. The midterm was 4 questions. He provided a practice midterm, and two of the questions from the practice were the exact same questions on the actual midterm. The other questions were provide an example of a certain thing and restate a certain proof of a theorem from lecture. Median was 16/24. He shortened the final to 6 questions because he didn't have another proctor. For the final, he provided 37 practice problems with each unit. Based on the midterm, you would think that he would pull at least some questions from the practice to put on the actual final. Like out of those THIRTY SEVEN PROBLEMS, you would think so. However, he put only one similar problem from the practice on the final. The rest were basically all proofs for theorems he went over in lecture. So don't even do the practice problems or redo homework when studying, just go over how to prove the theorems again and stuff in lecture. So I studied a week for hours and hours for that final, doing all these practice problems and briefly going over lecture, and I got 45%. Like it was fair because it was all from lecture, but I studied the wrong things. The median was 19.5/34. You can bring a 3x5 notecard for the final. Homework was assigned weekly, and only 3 problems were graded on correctness. 2 homeworks were dropped. Midterm would be dropped if it increased your overall grade after the final. If you were at a boundary between grades, he said he would take into consideration how much effort you showed in class in terms of answering questions, office hours, etc. Grading scheme: 30% Homework, 30% Midterm, 40% Final. From previous years, the grade distribution looks HORRIBLE. He bases the distribution on the median and how you do in comparison to this. Grade cutoffs: A+ 94-100, A 84-94, A- 79-84, B+ 73-79, B 67-73, B- 62-67, C+ 60-62, C 55-60, C- 53-55 but this changes from quarter to quarter. Although I received an A in MATH 115A, this did not follow in MATH 131A. I didn't think there was a significant gap in difficulty from these two classes but maybe that's just because I hate proofs. In short, study by redoing lecture proofs and don't do the final practice problems.
Fall 2025 - I hated this class so much. I am not a proof person, so I knew this was going to be difficult. I would say he is pretty clear in lecture and teaches decently. However, sometimes he decides to change his mind and do the proof a different way (just for funzies), but then he gets it wrong. He posts the entire course lecture notes from the beginning, and those were helpful. There is only one midterm, which I've never seen before in a math class. The midterm was 4 questions. He provided a practice midterm, and two of the questions from the practice were the exact same questions on the actual midterm. The other questions were provide an example of a certain thing and restate a certain proof of a theorem from lecture. Median was 16/24. He shortened the final to 6 questions because he didn't have another proctor. For the final, he provided 37 practice problems with each unit. Based on the midterm, you would think that he would pull at least some questions from the practice to put on the actual final. Like out of those THIRTY SEVEN PROBLEMS, you would think so. However, he put only one similar problem from the practice on the final. The rest were basically all proofs for theorems he went over in lecture. So don't even do the practice problems or redo homework when studying, just go over how to prove the theorems again and stuff in lecture. So I studied a week for hours and hours for that final, doing all these practice problems and briefly going over lecture, and I got 45%. Like it was fair because it was all from lecture, but I studied the wrong things. The median was 19.5/34. You can bring a 3x5 notecard for the final. Homework was assigned weekly, and only 3 problems were graded on correctness. 2 homeworks were dropped. Midterm would be dropped if it increased your overall grade after the final. If you were at a boundary between grades, he said he would take into consideration how much effort you showed in class in terms of answering questions, office hours, etc. Grading scheme: 30% Homework, 30% Midterm, 40% Final. From previous years, the grade distribution looks HORRIBLE. He bases the distribution on the median and how you do in comparison to this. Grade cutoffs: A+ 94-100, A 84-94, A- 79-84, B+ 73-79, B 67-73, B- 62-67, C+ 60-62, C 55-60, C- 53-55 but this changes from quarter to quarter. Although I received an A in MATH 115A, this did not follow in MATH 131A. I didn't think there was a significant gap in difficulty from these two classes but maybe that's just because I hate proofs. In short, study by redoing lecture proofs and don't do the final practice problems.
Most Helpful Review
Winter 2024 - Great professor and someone you should take for a class like this. While homeworks could be a bit tricky, he offers to solve them in office hours. Notes do go by the book, but he usually provides alternative proofs to various theorems which helps with understanding. Exams were fair and he never tried to trick you. They were based off of in class examples and homework problems. I wish he were teaching 131B because he did a great teaching this course.
Winter 2024 - Great professor and someone you should take for a class like this. While homeworks could be a bit tricky, he offers to solve them in office hours. Notes do go by the book, but he usually provides alternative proofs to various theorems which helps with understanding. Exams were fair and he never tried to trick you. They were based off of in class examples and homework problems. I wish he were teaching 131B because he did a great teaching this course.
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Spring 2025 - Professor Zhao is a great professor and I'd highly recommend taking 131A with him if you get the chance. This is a very difficult class, but Professor Zhao taught it very effectively and was helpful outside of class as well. He's incredibly smart and his lectures can be very fast-paced, to the point where I stopped trying to keep up with his notes a couple of weeks in and just started taking photos of the board to copy down later so I could follow along better. That said, he is a very clear lecturer and at times is very funny too. He also makes sure to take time for questions if people are confused. The topics in this class are largely the same as the topics in introductory pre-calc and calc classes: sequences, limits, derivatives, functions, integrals, and key theorems related to each topic. However, instead of simply giving you a definition and asking you to solve computational problems, this class focuses largely on the theory behind each definition and on learning rigorous proofs of all the theorems. On the exams, you are asked to give proofs of various statements using the theorems and definitions from class. This is what makes the class so challenging, especially if you have limited experience in math upper-divs, and the exam scores reflected that. The average for the midterm was around 50%, and although he didn't release the average for the final, my guess is that it was similar. Both the midterm grade and the class grade as a whole was curved up heavily, so don't panic if you feel like you bombed a test (I barely answered 2 of the 5 questions on the midterm and got an A). The best thing you can do to prepare is go over all of the practice problems Professor Zhao recommends from the book and make sure you know the solutions thoroughly, because multiple questions on the exams were from the book. Aside from the exams, the homework was manageable enough and you should be able to get 100% on everything if you give a decent effort and turn it in on time. Overall I ended up really enjoying this class because of the way it gets into the "why" of everything you've learned in calculus, and I feel like I walked away with a much deeper understanding of most of the math I'd learned up until this class. Professor Zhao was a big part of that and I'd certainly recommend him to anyone who needs to take this class, with the understanding that it will be challenging for most people.
Spring 2025 - Professor Zhao is a great professor and I'd highly recommend taking 131A with him if you get the chance. This is a very difficult class, but Professor Zhao taught it very effectively and was helpful outside of class as well. He's incredibly smart and his lectures can be very fast-paced, to the point where I stopped trying to keep up with his notes a couple of weeks in and just started taking photos of the board to copy down later so I could follow along better. That said, he is a very clear lecturer and at times is very funny too. He also makes sure to take time for questions if people are confused. The topics in this class are largely the same as the topics in introductory pre-calc and calc classes: sequences, limits, derivatives, functions, integrals, and key theorems related to each topic. However, instead of simply giving you a definition and asking you to solve computational problems, this class focuses largely on the theory behind each definition and on learning rigorous proofs of all the theorems. On the exams, you are asked to give proofs of various statements using the theorems and definitions from class. This is what makes the class so challenging, especially if you have limited experience in math upper-divs, and the exam scores reflected that. The average for the midterm was around 50%, and although he didn't release the average for the final, my guess is that it was similar. Both the midterm grade and the class grade as a whole was curved up heavily, so don't panic if you feel like you bombed a test (I barely answered 2 of the 5 questions on the midterm and got an A). The best thing you can do to prepare is go over all of the practice problems Professor Zhao recommends from the book and make sure you know the solutions thoroughly, because multiple questions on the exams were from the book. Aside from the exams, the homework was manageable enough and you should be able to get 100% on everything if you give a decent effort and turn it in on time. Overall I ended up really enjoying this class because of the way it gets into the "why" of everything you've learned in calculus, and I feel like I walked away with a much deeper understanding of most of the math I'd learned up until this class. Professor Zhao was a big part of that and I'd certainly recommend him to anyone who needs to take this class, with the understanding that it will be challenging for most people.
Most Helpful Review
Spring 2017 - Took him for 131A. Avoid this professor at all costs. The midterms and final are doable. However, the material itself is already very difficult and this professor did a horrendous job of teaching it. All of the lectures were him mumbling incoherently, and it is extremely hard to understand him through his accent, making it basically impossible to learn from lecture. In addition, after writing something down on the board, he will often erase it immediately rather than erasing something he wrote earlier. Out of the ~40 people who were in this class from the beginning, only 9 people, including myself, were showing up consistently during the last few weeks. That's not a typo. Several of them dropped out, as evidenced by the grading distribution of the final showing a paltry student count of 22. The averages for the midterms were around 50-55%, and presumably the only reason the average for the final was higher was because of the lower student count. The only reason why I managed to pull a reasonable grade in this class was because of the TA's much more helpful discussions, though unfortunately one discussion a week doesn't make up for 3 whole days of inefficient lecturing. If you're a self-learner, you may do well in this class. But otherwise, choose a more well-known, competent lecturer instead of this guy. He is the absolute worst lecturer I have had at UCLA and doesn't deserve to be teaching at all.
Spring 2017 - Took him for 131A. Avoid this professor at all costs. The midterms and final are doable. However, the material itself is already very difficult and this professor did a horrendous job of teaching it. All of the lectures were him mumbling incoherently, and it is extremely hard to understand him through his accent, making it basically impossible to learn from lecture. In addition, after writing something down on the board, he will often erase it immediately rather than erasing something he wrote earlier. Out of the ~40 people who were in this class from the beginning, only 9 people, including myself, were showing up consistently during the last few weeks. That's not a typo. Several of them dropped out, as evidenced by the grading distribution of the final showing a paltry student count of 22. The averages for the midterms were around 50-55%, and presumably the only reason the average for the final was higher was because of the lower student count. The only reason why I managed to pull a reasonable grade in this class was because of the TA's much more helpful discussions, though unfortunately one discussion a week doesn't make up for 3 whole days of inefficient lecturing. If you're a self-learner, you may do well in this class. But otherwise, choose a more well-known, competent lecturer instead of this guy. He is the absolute worst lecturer I have had at UCLA and doesn't deserve to be teaching at all.
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