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ahsanxr
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So I'm planning to delve into both of these subjects in some depth during the summer to prepare for undergrad analysis (using rudin) and a graduate differential topology class. My question is which one should I start out with and pay more attention to. I obviously need to study a lot of topology if I am to comprehend that diff top class but I've heard conflicting views on which should be studied first, for example,
Micromass says:
whereas Monocles says:
So what are your opinions on this?
As for texts, I am looking at Munkres for Topology and Pugh for Analysis.
Micromass says:
Personally, I would take analysis before you take topology. Make sure you know about metric spaces before topology (metric spaces are usually studied in analysis, but not always).
whereas Monocles says:
I took my first analysis class this past fall semester, and I actually studied topology first. Analysis is a pre-req for topology at my school, but I had some free time over the summer and really wanted to start with graduate level topology this fall, so I studied undergrad topology on my own from Munkres and consulted one of the professors who had taught it recently to check some of the work I did and answer questions. I also didn't have much math background before this - just 2 proof based classes before this (linear algebra and abstract algebra).
I found it challenging and very fun. It probably helped that I already had a strong interest in topology, in the sense that I had been learning about how manifolds are used in physics before then. I didn't find the lack of motivation from not having taken analysis too much of roadblock - and it did help motivate analysis when I took it this fall! It also made analysis really easy. At my school, analysis is thought to be quite hellish, but the majority of the problem solving techniques you require you'll have picked up from topology, making analysis a walk in the park.
So what are your opinions on this?
As for texts, I am looking at Munkres for Topology and Pugh for Analysis.