- #1
Chaostamer
- 104
- 0
Hey everybody. I'm a Pure Math major and I'm trying to finalize my schedule for next semester. Originally I was enrolled in a second ODEs course (focusing predominantly on systems of linear ODEs, existence and uniqueness theory, and qualitative solutions), but after a rough semester with PDEs, I need a break from the more "applied" classes. The issue has become finding a class from my rather limited set of options to take its place.
I'm most interested in taking Topology, but I have a few concerns about doing so. Among them is my background. Among my math classes, I've taken an introductory, proof-based course in discrete mathematics and a first course in linear algebra that put a fair bit of emphasis on theory. This semester, I also took courses in Combinatorics and Theory of Computation that focused largely on proofs. The point is, I definitely have some proof experience, and in those classes, I did pretty well.
However, I haven't taken any courses in analysis or abstract algebra (and won't be able to until the Fall semester). I was told that both of those classes make topology a good bit easier to understand. Plus, since Topology is very rigorous, do you think I have the background to handle the material and appreciate it? I don't want to take it if I'm going to be lost the entire semester or if I lack the perspective to appreciate the subject.
Also, how much will it benefit me to take Topology before analysis. I know the two go hand-in-hand quite often and I was hoping that, should I take Topology, it would provide more motivation for my year of analysis. Also, if I do take it, it would provide me with more practice with rigorous proofs. Is the benefit worth it?
Okay, so I got a bit long-winded here trying to sort out my thoughts, but I'd like to hear your perspective on the matter. For reference, these are the other math classes I'm taking next semester:
Linear Algebra II
Graph Theory
Statistical Theory II (advanced probability theory and introductory mathematical statistics)
Thanks in advance for your help.
I'm most interested in taking Topology, but I have a few concerns about doing so. Among them is my background. Among my math classes, I've taken an introductory, proof-based course in discrete mathematics and a first course in linear algebra that put a fair bit of emphasis on theory. This semester, I also took courses in Combinatorics and Theory of Computation that focused largely on proofs. The point is, I definitely have some proof experience, and in those classes, I did pretty well.
However, I haven't taken any courses in analysis or abstract algebra (and won't be able to until the Fall semester). I was told that both of those classes make topology a good bit easier to understand. Plus, since Topology is very rigorous, do you think I have the background to handle the material and appreciate it? I don't want to take it if I'm going to be lost the entire semester or if I lack the perspective to appreciate the subject.
Also, how much will it benefit me to take Topology before analysis. I know the two go hand-in-hand quite often and I was hoping that, should I take Topology, it would provide more motivation for my year of analysis. Also, if I do take it, it would provide me with more practice with rigorous proofs. Is the benefit worth it?
Okay, so I got a bit long-winded here trying to sort out my thoughts, but I'd like to hear your perspective on the matter. For reference, these are the other math classes I'm taking next semester:
Linear Algebra II
Graph Theory
Statistical Theory II (advanced probability theory and introductory mathematical statistics)
Thanks in advance for your help.