It could be useful to (already) know many things, but another question is how to efficiently get to learn them, starting from what background. Once you are at graduate level, a lot more becomes accessible, so the first step is to get there.
My sequence meant to suggest a way of reaching that level by self-study, and getting a good grasp of basic tools of logic in the process. It’s probably not the best way, but if you suggest improvements, they ought to be improvements in achieving this particular goal, not just things associated with elements of the original plan, such as “more math books”. Other goal could be worthwhile too, but it would be better to state the different intention before proceeding.
My sequence meant to suggest a way of reaching that level by self-study, and get a good grasp of basic tools of logic in the process. [...] Other goal could be worthwhile too, but it would be better to state the different intention before proceeding.
Ah, I see. You could make that more clear in the post fairly easily.
It might be helpful to suggest two paths of self-study, targeting those below and at graduate-level respectively. I’m not sure if that would be best done in a separate post or not.
if you suggest improvements, they ought to be improvements in achieving this particular goal
A suggested order might be useful. I’d at least recommend reading about algebra and topology before category theory, so that one builds up fundamental examples of category-theoretic objects.
I’d at least recommend reading about algebra and topology before category theory, so that one builds up fundamental examples of category-theoretic objects.
I essentially followed this rule. “Conceptual mathematics” is elementary, “Sets for mathematics” deals mainly with set theory from category-theoretic perspective. The more general treatment of category theory is given in Awodey’s book, which comes after Munkres that presents general and algebraic topology. Mac Lane’s algebra comes before “Sets for mathematics” as well.
It could be useful to (already) know many things, but another question is how to efficiently get to learn them, starting from what background. Once you are at graduate level, a lot more becomes accessible, so the first step is to get there.
My sequence meant to suggest a way of reaching that level by self-study, and getting a good grasp of basic tools of logic in the process. It’s probably not the best way, but if you suggest improvements, they ought to be improvements in achieving this particular goal, not just things associated with elements of the original plan, such as “more math books”. Other goal could be worthwhile too, but it would be better to state the different intention before proceeding.
Ah, I see. You could make that more clear in the post fairly easily.
It might be helpful to suggest two paths of self-study, targeting those below and at graduate-level respectively. I’m not sure if that would be best done in a separate post or not.
A suggested order might be useful. I’d at least recommend reading about algebra and topology before category theory, so that one builds up fundamental examples of category-theoretic objects.
The books are suggested in order as given.
I essentially followed this rule. “Conceptual mathematics” is elementary, “Sets for mathematics” deals mainly with set theory from category-theoretic perspective. The more general treatment of category theory is given in Awodey’s book, which comes after Munkres that presents general and algebraic topology. Mac Lane’s algebra comes before “Sets for mathematics” as well.