What resources exist detailing which mathematics to learn in what order?
One could acquire a university syllabus for a degree in mathematics and use textbooks and or MIT Opencoursware to learn with.
What resources exist that explain the utility of different mathematical concentrations for the purpose of directing studies?
I am having trouble understanding this question. By the words “mathematical concentrations”, could one substitute the term “mathematical subfields”? If so, then I would say the best resource could be more experienced people with similar instrumental goals to one’s self.
I listen to a weekly podcast called skeptoid. It’s a very concise, information packed show focusing on pseudoscience and rationality. I’ve listened to episodes on the validity of IQ testing all the way to an entire episode on Zeno’s paradoxes.
It may be light-hearted and entertaining, but it’s still a very informative and educational podcast.