Topology or logic or other start point?

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SUMMARY

The discussion centers on the preparation for advanced mathematics courses, specifically topology and mathematical logic. The participant expresses a need to improve their proof-writing skills before retaking these courses. Recommendations include taking an introductory proof course, which is now offered at their institution, and utilizing resources such as "Visual Complex Analysis" to enhance intuition in topology. The consensus is that the order of taking topology or logic does not significantly impact success, but foundational understanding is crucial.

PREREQUISITES
  • Understanding of mathematical proofs
  • Familiarity with topology concepts
  • Knowledge of mathematical logic fundamentals
  • Experience with abstract mathematics
NEXT STEPS
  • Research introductory proof techniques and resources
  • Study "Visual Complex Analysis" for intuitive understanding of topology
  • Explore foundational courses in abstract mathematics
  • Practice proof-writing exercises to strengthen skills
USEFUL FOR

Mathematics students, particularly those in undergraduate programs, who are preparing for advanced courses in topology and mathematical logic, as well as anyone looking to improve their proof-writing abilities.

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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