MATH 210A
Algebra
Description: Requisites: courses 110A, 110B, 110C. Students with credit for courses 110B and/or 110C cannot receive MA degree credit for courses 210B and/or 210C. Group theory, including theorems of Sylow and Jordan/Holder/Schreier; rings and ideals, factorization theory in integral domains, modules over principal ideal rings, Galois theory of fields, multilinear algebra, structure of algebras.
Units: 4.0
Units: 4.0
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Most Helpful Review
Fall 2023 - Professor Balmer uses his own lecture notes. You start out with fundamentals of category theory, such as the Yoneda lemma and adjoint functors, and move on to group theory and ring theory. For group theory and ring theory, you will be covering similar material from Math 110AB, except for the facts that (1) you will use the language of category theory often so you'll wrap your head around familar concepts but in different language, and that (2) the pace of the course is three times faster. Professor Balmer's tests are hard - the average grade for the midterm was less than 50% and the average for final was around 60~70% - but he curves. As category theory is covered in a very short amount of time, you may find the first two weeks of Math 210A, which is all about category theory, challenging. However, know that you will and can get through it, and that everyone else in your class is also struggling to learn category theory in such a short amount of time - so I would not be discouraged. I would definitely reach out to your peers to study together. Whether or not it's Professor Balmer who is teaching Math 210A, I would not take this course if you don't have familiarity with all or most of what's covered in Math 110AB; you'll be crushed if you are taking this as your first abstract algebra course. Again, it's expected that you already know the Math 110AB material. I would make sure that I am being courteous and respectful when I am engaging with Professor Balmer; he is very much approachable once you know that he appreciates courteousness. He is a very funny person, I laughed several times during his lectures. There is no attendance but his lectures go so fast. His lecture notes can be terse at times, so I would not hesitate to confer different books on abstract algebra as supplements if his lecture notes confuse you. I would like to thank Professor Balmer for his teaching this course.
Fall 2023 - Professor Balmer uses his own lecture notes. You start out with fundamentals of category theory, such as the Yoneda lemma and adjoint functors, and move on to group theory and ring theory. For group theory and ring theory, you will be covering similar material from Math 110AB, except for the facts that (1) you will use the language of category theory often so you'll wrap your head around familar concepts but in different language, and that (2) the pace of the course is three times faster. Professor Balmer's tests are hard - the average grade for the midterm was less than 50% and the average for final was around 60~70% - but he curves. As category theory is covered in a very short amount of time, you may find the first two weeks of Math 210A, which is all about category theory, challenging. However, know that you will and can get through it, and that everyone else in your class is also struggling to learn category theory in such a short amount of time - so I would not be discouraged. I would definitely reach out to your peers to study together. Whether or not it's Professor Balmer who is teaching Math 210A, I would not take this course if you don't have familiarity with all or most of what's covered in Math 110AB; you'll be crushed if you are taking this as your first abstract algebra course. Again, it's expected that you already know the Math 110AB material. I would make sure that I am being courteous and respectful when I am engaging with Professor Balmer; he is very much approachable once you know that he appreciates courteousness. He is a very funny person, I laughed several times during his lectures. There is no attendance but his lectures go so fast. His lecture notes can be terse at times, so I would not hesitate to confer different books on abstract algebra as supplements if his lecture notes confuse you. I would like to thank Professor Balmer for his teaching this course.
Most Helpful Review
Fall 2022 - I took this class as an undergraduate in my sophomore year. It was pretty fast paced but still possible to take as one's first algebra class. The primary difference between this and 110A is that the undergraduate class only covers group theory while Merkurjev spends the second half of the quarter on category theory. Lectures were the best I've had at UCLA in terms of clarity. However, Merkurjev doesn't interact much with students so it's on you to pay attention and take notes. He has a handout that he uploads at the beginning of the quarter and lectures closely follow the handout. The content got a little bit too abstract for me towards the end but take that with a grain of salt as this was only my second ever rigorous/proof-based math class here. HWs took me about 5 hours a week to complete and were graded very leniently. Tests are similar to HWs. They're not incredibly hard but the professor grades them very strictly. If your argument is not perfectly clear, you'll most likely get a 0 in that question. However, since it's a grad class, the curve is pretty lenient. Tests are open notes and open book (you're also allowed to carry laptops/tablets but you can't use the internet) which helps quite a bit if you practice for the tests by solving exercises from textbooks. Discussion sections mostly focused on solving past algebra qualifying exams which I didn't love. Overall, it's a challenging class but worth it if you're willing to put in extra effort.
Fall 2022 - I took this class as an undergraduate in my sophomore year. It was pretty fast paced but still possible to take as one's first algebra class. The primary difference between this and 110A is that the undergraduate class only covers group theory while Merkurjev spends the second half of the quarter on category theory. Lectures were the best I've had at UCLA in terms of clarity. However, Merkurjev doesn't interact much with students so it's on you to pay attention and take notes. He has a handout that he uploads at the beginning of the quarter and lectures closely follow the handout. The content got a little bit too abstract for me towards the end but take that with a grain of salt as this was only my second ever rigorous/proof-based math class here. HWs took me about 5 hours a week to complete and were graded very leniently. Tests are similar to HWs. They're not incredibly hard but the professor grades them very strictly. If your argument is not perfectly clear, you'll most likely get a 0 in that question. However, since it's a grad class, the curve is pretty lenient. Tests are open notes and open book (you're also allowed to carry laptops/tablets but you can't use the internet) which helps quite a bit if you practice for the tests by solving exercises from textbooks. Discussion sections mostly focused on solving past algebra qualifying exams which I didn't love. Overall, it's a challenging class but worth it if you're willing to put in extra effort.
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