I wonder sometimes if when
It seems that these questions are asked of people that they aren't always end up with answers skewed towards tier-1 research university admissions processes. That's not to say it isn't valuable knowledge, but for someone who is very enthusiastic about math, but for one reason or another had trouble with some classes, might like to know a tier-2 research university would expect (I am describing myself here, I am not merely hypothesizing). I'm honestly not sure, I will be applying in the fall to schools in both categories.
I here people talk about graduate courses being a plus universities and I know people who have gotten into grad school without graduate courses under their belt. Similarly many who have gotten into graduate school that never took the Putnam exam.
I also somewhat wonder whether Applied Math programs look at applicants in different ways than Pure Math programs (though especially the distinction is not always made, and sometimes what is essentially an applied study of pure math program will not even have "math" in the title, or a program that rather than applied... could potentially satisfy an anyone comment on applied math person in their wants)or tier-2 research universities?