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As a first-year, I decided to take Math 115AH with Professor Merkurjev. I came out of the class with a C unfortunately, but that was at the expense of thinking the class would teach me how to write proofs and that I can transition well into proof writing. However, it took me about 4 weeks until I got the hang of it according to my homework score. So, I would recommend anyone who is planning to take this class to have a strong foundation in proof writing (as in take the honors version of 32 series and 33 series). Despite the C, I still learn a lot from the class and I improve from knowing nothing to knowing how to write, and writing proofs is an essential skill if you're thinking of going to graduate school that is mathematically intensive.
Overall, I enjoyed having him as a professor since he is straightforward with his theorems and proofs. However, he does seem difficult to approach since he tends to leave immediately after class and he does not talk much during office hours unless you are able to start off with an interesting conversation with him. Regardless, he is helpful during office hour and he does reply quickly to emails.
Regarding the homework, some are straightforward, some might take time to think about. Still, his homework should somehow prepare you for his exams. For me, I guess it didn't and even I did a bunch of book problems to supplement the homework to help improve my proof writing skills. I guess I'm not very skillful at writing proofs under pressure.
Regarding his exams, Professor Merkurjev does not give any partial credit unless your proof is going in the right direction. Otherwise, it's full points or zero points. Furthermore, the midterms are 5 questions each given 50 minutes. So, good luck writing proofs on demand. And also know how to do some of the computational aspects of linear algebra. That surprised my class for the second midterm and as a result, we generally did horrible.
So, I would recommend taking honors linear algebra with him, but only for people who has a good foundation in proof writing.
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