Is 'at the same time' an option? I mean, by junior year, math majors should be taking at least two math classes per semester, right?
When I was an undergraduate at Penn State, these two courses were the only 300 level math courses, both designed to be taken first semester junior year. The introduction to abstract algebra used "Numbers, Groups, and Codes", ...
Despite the names of these fields, as a student I found real analysis more
abstract than abstract algebra: real analysis was less real and more abstract to me than abstract algebra. I don't think I can justify this, but let me give two examples:
in abstract algebra: The order of a subgroup $H$ of a finite group
$G$ divides the order of $...
The apparent conflict between points of view expressed in the OP is illusory. There is no real conflict. The mathematics education researcher quoted in the OP is arguing that students find the definition difficult to appreciate and master. The mathematicians quoted in the OP are arguing that, once mastered, it provides clarity.
I have questions about the ...