Prof Gieseker lives up to his fame as a mathematician, but also to his fame as someone who is too smart to teach.

Lectures were not too engaging. Professor made a few errors in writing, and his writing was not too legible. However, professor is a nice person. He sometimes told jokes in class and liked to address students' questions in office hours. Speaking of the office hours, in addition to two hours on Wednesday and Friday, there was another workshop on Monday as chance to ask questions. The TA was also knowledgeable and his office hour on Tuesday was helpful too. Maybe not all your questions will get answered well, but at least you might have a better idea how to approach them. Plus, the environment was usually cozy.

The textbook was Hoffman/Kunze, which I personally found to be nice and helpful. Homework assignments, which were assigned a little more than weekly (we had 7 in total, the last one wasn't collected), were generally fine. A few double star problems were bound to be graded, and detailed, absolutely correct proofs were required, as that's what this class is for. There were also many problems from the textbook and sometimes certain extra problems made by professor. You probably would not hand in most of them, but doing them would be important for the midterms and final. As for the exams, professor released many past exams as practice for us and in fact some of this year's exam problems were very similar to past ones. The second midterm was probably a bit different though, since it was made take-home due to COVID concerns, and it let us explore the new topic of Jordan forms. But as long as you try to do the homework well and keep practicing, the exams would turn out to be fair. There were extra credit problems for one midterm and final, and they were worth about 10%. Attempting them would definitely help your grade, they were usually not too hard. Still, watch out for possible harsh grading: as said, a rigorous proof is much valued in this class, so even a small mistake (like not citing being a basis to assume linear independence) would result in many points being deducted.

Overall, this is an honors class, so much effort should be expected. But with practice, I think you can learn things and manage the material well. Don't overlook homework! It only counted for 10% (the final was a whopping 50%, or even 60% depending on the grading scheme), but it is key to your success on the exams!

if you have a serious interest in math then go for Gieseker

Gieseker is a really nice prof, you just need to come to the office hours more

Gieseker is a really nice prof, you just need to come to the office hours more

Lectures aren't too captivating. He makes a few errors with notation so watch out for that. But Gieseker is a very nice guy, with an odd sense of humor. He gives sort of cryptic hints when you're confused with homework, but they're actually helpful once you decipher what he said. He has loads of practice midterms/finals, and his exams have the same exact type of problems as the practices provided. The curve is decent. I had a raw average of 85 and got an A. Lots of time has to be spent reading Hoffman and Kunze (you can find it for free on Google) to understand the lingo of the course and to do well on hw and exams. Your TA will be your best friend in this course. !!If you are ever looking for an amazing TA Bjoern Bringmann is your guy!! All in all, I'd say don't take the terrible reviews too seriously. This class was a great learning experience for me, and I really liked Gieseker. I would take his class again.

His lectures were very unmotivating and I stopped going after the first midterm. Your TA will often carry your through the class. I also recommend Axler's Linear Algebra Done Right to supplement. My poor grade was because of an unfortunate grading scheme change at the end of week 10. He usually offers a 10% HW 90% Final grading scheme and I had lots of personal issues I had to attend to after the first midterm and until the end of week 9 so I could not put much focus on the course and was banking on it. However, because of Covid-19, he changed the grading scheme. I cannot blame him for that but it still was unfortunate. He gives past midterms and finals and a lot of his questions are repeats or similar in style and would highly recommend studying those first. The textbook questions are definitely harder than the midterm

The textbook is Hoffman/Kunze, and I didn't like it very much. I ended up downloading a PDF of Axler and reading it instead, and I found the proofs in Axler much more clear. However, the exercises in Hoffman/Kunze are more challenging. Usually a few textbook problems would be selected as graded homework problems each week, with a bunch more optional problems that we were encouraged to do.

As for exams, I just did all (well, as much as I needed to) of the previous exams that Prof. Gieseker gave us and I was fine. He taught this course like 7 or 8 times and he gave us both midterms and the final for all of them. A lot of problems are recycled.

His teaching can be hard to follow. I don't exactly know why though.

See the other review from Fall 2019 for class structure (HW, exams, grading schemes). I mostly agree with everything else. Just a few things to add...

The amount and difficulty of the homework varied from week to week. Sometimes, I'd be staying up late for hours the night before the homework was due (we turned them in every Thursday in discussion) just trying to pound out the double star problems or even start to understand what I was reading. My quarter we had a class group chat where everyone tried to help each other, which was pretty nice. And the homework grader literally only graded the "double star" problems (~2 to 4 a week), and you didn't *have* to do the extra non-double star problems if you didn't want to or didn't have time to. They were each 15 points, but the grader only gave you the full 15 if your proof was rigorous. If it wasn't, you might have gotten partial credit, but you could resubmit the same problem later in the quarter as many times as you want, only losing a point each time (I resubmitted one problem and got bumped to 14/15).

However, it's highly recommended that you actually try the proofs on the homework by yourself (before referring to Slader or a classmate), and I tend to agree; otherwise, if you don't understand what you're doing, you'll be pretty screwed come exam time.

As the other reviewer said, Gieseker was pretty unengaging during lecture, and I pretty much stopped going after the first midterm. Instead, I self-studied the assigned textbook sections for each week's homework and went to discussion, where the TA Laurent was a literal savior. From the few times I did go to lecture, it seemed that he taught from the textbook, or his own notes from the textbook, and oftentimes the class would get lost because he'd forget to say something or use something he hadn't taught yet.

For midterms and the final, he posted a link on the class website that linked to previous class websites, where you could find practice midterms and finals. Definitely practice the hell out of them before each exam, as not only do you have to have the right approach down to each type of problem, but some problems Gieseker recycled from previous exams. The midterms were both time crunches, as we only had the 50-minute lecture period to do the 5 questions (and extra credit). The final was nearly as bad, though Gieseker gave us an extra 15 minutes at the end that was really useful for me (I was stuck on Problem 12, the last one, for like half an hour before it clicked with ~10 minutes left).

I do feel like Gieseker has the best intentions, though he's not the greatest lecturer anymore (if he ever was). He's very clear in what he posts on the class website as to what will be covered on every exam. Also, one time I emailed him about a grading issue and he responded and fixed it within minutes. Finally, the curve on the class is real thicc, so don't be discouraged if you don't think you're doing too well -- as you can see, he curves the class to 50% A's!

Homework: weekly homework sets consist of questions from the book (some computational and some proofs) and a few ones added by Prof. Gieseker (proofs), but only the double star questions (2-3 proofs designated by him) will be graded

Exam: Midterms are 5 proofs (20 pts each) with a bonus question (10 pts. The name is misleading because it is not optional/extra credit and contributes to your total score) Final is 11 proofs and 2 bonus questions (all count to score). Prof. Gieseker gives exams from the past to practice, though I find the difficulty differs across years.

Grading scale: 10%HW+20%(MT1+MT2)+50%F or 10%HW + 90%F

Lecture/OH: Lecture is not engaging. Prof. Gieseker's voice is low and difficult to hear at times; his notes on the board are often indiscernible or have mistakes. His lectures lack clarity, since he will start writing on the board without explicitly saying what the proofs are for, eventually concluding with “so this is ….“ before moving onto the next topic immediately. There is no doubt that Prof. Gieseker is a very nice person and he is willing to stay after his designated office hour times to answer students’ question. He is friendly and approachable though sometimes he goes on tangents. While it is nice of him to ask the students what their majors are and talk about future courses that they should take, Prof. Gieseker would then go find different books or open related websites, instead of focusing on the questions that the students have.

Teaching Assistant: Laurent Vera is the best math TA I have ever seen. The man is very knowledgeable and can answer any question the students throw at him. He spent some time covering content that is not in the course but the thorough and clear explanation made them enjoyable/relatively easy to learn. Besides, I believe those content will be useful for any pure math students continuing to 115B

Personal note: It was definitely my fault that I did not study the final well enough (plus the nerve really made me forget some basic stuff I’ve seen before), which led to a dismal final performance and B for the final score. However, I did find the class quite taxing because of the professor and think I would have learned better/had more confidence if the teaching style is clearer. Professor Gieseker is knowledgeable and respected in his field but his age hinders his ability to teach well