It might be possible to find such ordering for specific textbooks, but this doesn’t make much sense on the level of topics. It helps to know a bit of each topic to get more out of any other topic, so it’s best to study most of these in parallel. That said, it’s natural to treat topology as one of the entry-level topics, together with abstract algebra and analysis. And separate study of set theory and logic mostly becomes relevant only at a more advanced level.
Thanks for your insights Vladimir. I agree that Abstract Algebra, Topology and Real Analysis don’t require much in terms of prerequisites, but I think without sufficient mathematical maturity, these subjects will be rough going. I should’ve made clear that by “Sets and Logic” I didn’t mean a full fledged course on Advanced Set Theory and Logic, but rather simple familiarity with the axiomatic method through books like Naive Set Theory by Halmos and Book of Proof by Hammack.
It might be possible to find such ordering for specific textbooks, but this doesn’t make much sense on the level of topics. It helps to know a bit of each topic to get more out of any other topic, so it’s best to study most of these in parallel. That said, it’s natural to treat topology as one of the entry-level topics, together with abstract algebra and analysis. And separate study of set theory and logic mostly becomes relevant only at a more advanced level.
Thanks for your insights Vladimir. I agree that Abstract Algebra, Topology and Real Analysis don’t require much in terms of prerequisites, but I think without sufficient mathematical maturity, these subjects will be rough going. I should’ve made clear that by “Sets and Logic” I didn’t mean a full fledged course on Advanced Set Theory and Logic, but rather simple familiarity with the axiomatic method through books like Naive Set Theory by Halmos and Book of Proof by Hammack.