Admission
Selection to USNTPS is highly competitive. Military aviators are evaluated by a selection board which takes into account flight qualification, professional performance, academic background, and the needs of the service. Engineers are similarly evaluated but prioritize experience, performance, and flight suitability.
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Attendees normally have a BS degree in engineering, physical science, or math but this is not absolutely required. Those without requisite math or engineering courses can make themselves more competitive by completing correspondence courses or attending a local college/university. Don't second-guess what the board is looking for--if you don't apply you can't get picked. Over 1000 hours of flight time is desired at the time class convenes but, again, this is not a firm requirement.
There is also a cooperative program with the Naval Postgraduate School which leads to a Masters Degree.
And the answer is Yes!