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first: am i correct in assuming that most applied mathematicians these days program? if so what is the point of these "computational science" programs? it seems like applied math lite or applied math + all the stuff you should've learned on your own with less time to do applied math.

second: can i get into an applied math program having not taken pdes/self studied pdes? more so than "can i", is it normal enough?

third: would an applied math phd prepare me for industry?

fourth: would it be sufficient to have one research project under my belt/published? I'm working on an computational physics problem right now that I'm enjoying but i don't think i'll have time to complete another one before i graduate. sufficient for top tier schools? i think not...

fifth: physics/pure math is kind of out of the question simply because i feel like if i didn't make it in academia with those specializations i couldn't sell those degrees. of course if i did do physics it would be computational but again that seems to me like it gives me the same skills as an applied math program just a different context to develop them in.

sixth: what can i do to improve my chances of getting into schools that i want to go to? start an email/letter exchange with professors there? go see them? for the record i'd like to go to school in new york, ny.

finally: there's a program in new york called teach for america which pays for a master's in math education from columbia, bard, or nyu but conscripts you to teach high school math for 4 years and gives you a 90k stipend over the 5 years.. though i don't want to be a high school math teacher it's a fall back plan, allows me to move to new york comfortably, and gets me a graduate degree. after completing the 5 years i would go back and get a real phd. will one graduate degree in a semi-related field make me a better candidate for another graduate degree, maybe better my chances at a top tier school? I'm also hoping i might be able to squeeze some audits of real math classes during that year I'm earning the master's in education though that might not be feasible. note I'm not worried about going back to school during early-middle age so no worries there. again this is a fall black plan and will only be seriously considered if you guys think one grad degree will better my chances of getting into a really good school.

if you've gotten all the way down here i appreciate your time.