The advice I gave is not exclusive to working through the typical undergraduate books.
I was questioning why the OP wants to self-study an undergrad math curriculum to begin with.
It's probably not to become a pure mathematician. So I suggested, instead of creating a massive goal of getting through a collection of books just for the sake of being a completionist, to have a concrete personal goal. Otherwise, people can throw books "you have to read" at you until the cows come home. Especially since this person is talking about applied math.