I’m an average undergrad math guy who graduated in 2022.
I want to give students who want to study topology my opinion. I dropped topology twice because I cannot construct proofs properly. At first, I took a topology class because professor of the class is a recipient of clay research awards. After taking first mid-term, I decided to drop the class because I could not get what problems ask. I heard that the median score was 34 from my roomie who was also a math major (He majored in CS as a second major). For second time, I took the class with a different professor. I failed second test and weekly problem sets, so I dropped the class because it was my last semester. I still remember that one of questions was about Urysohn lemma and I had to provide alternative proof of that. Well, I got an A on my complex analysis class and introduction to analysis class before I took the topology class (I took abstract algebra and topics in number theory class later). I was quite confident with writing and reading proofs, but I realized that I don‘t want to study topology (but I have to take topology again in order to apply grad school from a different college.)
That being said, I recommend you to study a lot of math before taking topology. If you are very good at constructing proofs(constructing mean writing and reading proofs), then ignore my comment. At least, you have to study set theory and intro analysis before taking it. Prof. Munkres states that there is no prerequisite for studying his legendary book, but it is for MIT pure math(or CS or physics dual major) undergraduates, not you.
I want to give students who want to study topology my opinion. I dropped topology twice because I cannot construct proofs properly. At first, I took a topology class because professor of the class is a recipient of clay research awards. After taking first mid-term, I decided to drop the class because I could not get what problems ask. I heard that the median score was 34 from my roomie who was also a math major (He majored in CS as a second major). For second time, I took the class with a different professor. I failed second test and weekly problem sets, so I dropped the class because it was my last semester. I still remember that one of questions was about Urysohn lemma and I had to provide alternative proof of that. Well, I got an A on my complex analysis class and introduction to analysis class before I took the topology class (I took abstract algebra and topics in number theory class later). I was quite confident with writing and reading proofs, but I realized that I don‘t want to study topology (but I have to take topology again in order to apply grad school from a different college.)
That being said, I recommend you to study a lot of math before taking topology. If you are very good at constructing proofs(constructing mean writing and reading proofs), then ignore my comment. At least, you have to study set theory and intro analysis before taking it. Prof. Munkres states that there is no prerequisite for studying his legendary book, but it is for MIT pure math(or CS or physics dual major) undergraduates, not you.
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