I have been reading through the great posts and admire so many of you for replying to questions of the Newbies!
My son is a recent U of AZ college grad with a BS in Math/Physics minor.
May I ask why
you are reading all this material and asking questions, and not your 22 year old son?
He wanted to go into an Officers program after college but his GPA is 2.96. So he is looking at military options for some hands-on experience. He likes the Nuke Program and did well on their preliminary screen. He saw the curriculum covered in Nuclear Power School he was disappointed in that he has taken most of those course in college. Recruiters encouraged him that he would do well because of it. I am wondering - would the Nuke Program be a waste of his BS degree? Would he be with a bunch of 18 year olds? Plus six years is a long time commitment. He'd like to get a Masters at some point.
2.96 might be non-qualifying for nuke officer, but there are other officer programs where your son meets qualifications, provided that he does exceptionally well on the ASTB and has extra-curriculars/community involvement. Specifically, your son should inquire about SWO/EDO options.
Your son will not use his BS in Math as an enlisted nuke. He won't even use it as a sub or SWO nuke. Officer students get a 3 week crash course in about 66% of calc-1/2, then it's onto classes like fluid flow, electrical engineering, heat transfer, but all of these are specifically focused to principles in Navy nuclear reactors. If it doesn't specifically apply to a Navy nuclear reactor, it will not be in the curriculum. Hence they won't be good for any sort of college credit at the majority of undergraduate and graduate universities.
As for a master's degree: the officer pipeline offers paid graduate programs through Naval Postgraduate School and Naval War College. Both require a department head tour, so he'd be looking at ~10 years of commissioned service minimum. With a math degree, he could attempt to ask to do Operations Research at NPS, which is a pretty decent program. The NWC does not have degree programs that would help your son with a post-Navy career and is generally reserved for O-4 and above.
However, no assignment in the Navy is guaranteed. Your son could ask for NPS and be sent to work making powerpoints in the Pentagon for his shore duty. Odds of your son getting what he wants are greatly enhanced by doing a good job and being pleasant for the CO to work with. Additionally, NPS is detrimental to aviation community career paths, if your son chooses to go that route, because he'll get non-observed fitreps when he's about to go to the O-4 screening board.
He likes the idea of military, training and direction. Any advice?
1) Allow your son to take charge of his own career. Kick his ass into reading the stuff you read and asking his own questions instead of you doing it for him. If he likes the idea of the military, then get him used to acting like an adult.
2) Your son should stop talking to enlisted Navy/AF recruiters. They don't know what STEM means because their job is to put sailors/airmen into the Navy/USAF and that doesn't require a 4-year college degree, let alone a STEM degree.
3) Based on what you said, your son should apply for Engineering Duty Officer (EDO) if he's eligible. The Navy has a master's at MIT or NPS built into the career path. If he's not eligible due to poor grades, he could go conventional Surface Warfare Officer (SWO) and attempt to lateral transfer to EDO after, assuming that they'd let him with those grades. SWO is a 4 year commitment, and they do accept people with sub 3.0 GPAs if they can do well on the ASTB and put together strong recommendations/essay/extra-curriculars. If he gets denied the lat xfer or is simply not eligible, he can either leave the service and use the GI bill to offset $18,700/year of graduate school costs, or he could roll the dice and try to get NPS on his shore duty.
4) If he doesn't like the idea of doing 4 years as a SWO with a longshot of lat transferring, he could apply for aviation. Again, the community will take him if he does extremely well on the ASTB, but their physical requirements are more stringent -- 20/40 vision or better in each eye, no sinus issues, and a handful of other things that are more thorough which I'm not completely familiar with. Pilot is a ~10 year commitment (8 years post winging, which takes about 2 years) and NFO is ~8 years (6 years post winging).
4) Enlisting will not give your son the experience and opportunities he seeks.
5) Your son screwed his college education with a 2.96 GPA, and the military won't be able to erase that.