I think the problem is that students don't know these fields exist unless they took an especially strong liking to the standard school math curriculum. Going in

I think the problem is that students don't know these fields exist unless they took an especially strong liking to the standard school math curriculum. Going into college I couldn't have told you what most of the fields mentioned were about even broadly. Truly I had no idea what math was, because we barely talked about proofs through high school. The only reason I swung back around to learning some of it is because my upper level college CS classes introduced me to ideas that then made me want to revisit my math curriculum. There ought to be some way to encourage late high school/early college students to "survey" the field without necessarily taking full courses in these topics. This could also give some earlier understanding in how the different fields relate - for example you could present a toy graph theory problem within linear algebra as a matrix problem, later presenting the same problem in graph theory section and walk through it using graph representation. I think high school courses struggle with memorability precisely because most units are taught basically in a vacuum. Regardless though, the point of the survey course wouldn't be to remember details so much as to find topics of interest for further study/be generally aware of their existence in case a relevant problem comes up in the future.