Topology or logic or other start point?

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Discussion Overview

The discussion revolves around the preparation for advanced mathematics courses, specifically topology and mathematical logic. Participants explore the order in which to approach these subjects and seek advice on improving proof-writing skills, which is identified as a challenge.

Discussion Character

  • Exploratory, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant expresses uncertainty about whether to take topology or mathematical logic first, seeking advice on which would be more beneficial for their preparation.
  • Another participant suggests that having a foundational course in proofs is crucial for success in upper division courses, implying that this background may influence the order of study.
  • A participant notes their experience with a limited introductory course and mentions the recent introduction of a dedicated proof course at their school, indicating a gap in their prior education.
  • One participant shares their personal success with proofs in topology, attributing it to intuition developed from studying related subjects and suggests that proof books may not be sufficient on their own.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the order of studying topology and mathematical logic, with differing opinions on the importance of foundational proof courses and the role of intuition in understanding proofs.

Contextual Notes

There is an acknowledgment of varying educational backgrounds and the impact of course availability on participants' preparation strategies. The discussion reflects individual experiences with proof-writing and the challenges faced in advanced mathematics.

Who May Find This Useful

Students preparing for advanced mathematics courses, particularly those struggling with proof-writing and seeking advice on course sequencing and study resources.

trap101
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So i just recently had to drop two math courses, topology, math logic, because my math maturity wasn't up to the level needed to excel in them. I intend on taking them again, but not without first more preparation which leads to my question. Which order would i benefit more from in preparing for the courses? Topology first and then math logic? Or math logic first and then topology?

The reason is that proofs tend to be my major weakness and it is coming to haunt me in these more advanced courses. Anyother suggestions would also be appreciated

Thanks
 
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Have you taken an intro to proof course? The rest of your upper division courses will rely on that foundational course (unless you are focusing on numerical applied math.)
 
The most my school offered when i took the courses was "concepts in abstract math" so there was no direct intro to proofs course, of course the school has now realized their mistake and created the course, but it is a first year course and i don't think i am eligible for it anymore considering i am in 3rd year. So it appears i will have to self prepare. Suggestions of any good proof books?
 
I don't see any particular advantage to doing one or the other first. My own success with proofs, especially in something like topology, I attribute to reading Visual Complex Analysis and studying subjects like electricity and magnetism that boosted my intuition. In a subject like topology, my thought process was usually a matter of translating my intuition into a logical proof. Proof books may help, too, but they may not be the whole story.
 

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