Topology or logic or other start point?

[trap101]

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

 

[TheKracken]

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.)

 

[trap101]

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?

 

[homeomorphic]

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.

 

[Matrix0]

for reaching out and sharing your experience. It's great to hear that you are determined to improve and excel in these challenging math courses. I can definitely understand the importance of having a strong foundation in both topology and math logic.

In terms of which course to take first, it ultimately depends on your personal learning style and strengths. However, I would recommend starting with math logic before moving on to topology. Math logic provides the fundamental tools and techniques for constructing and analyzing mathematical proofs, which are essential for success in topology. By strengthening your skills in math logic first, you will be better equipped to tackle the more abstract concepts and rigorous proofs in topology.

In addition to taking the courses in a specific order, I would also suggest seeking extra help and resources outside of class. This could include working with a tutor, joining a study group, or utilizing online resources such as practice problems and video tutorials. It's also important to practice regularly and consistently, as building a strong foundation in math requires continuous effort and dedication.

Overall, I believe that with determination, hard work, and the right approach, you can excel in both topology and math logic. Good luck in your studies!