How to Use Time Productively - Self Study, Schools, et al

[MAAntonius]

Ladies and Gentlemen of PhysicsForum,

This is an awesome venue filled with great resources. I look forward to expanding my abilities within the realm of sciences by using the resources listed here and occasional consultation with the really generous posters who are far more experienced than I ever will be.

As mentioned in my introductory thread, I'm active Navy, basically permanent-shore/desk job, but work some gnarly shifts that rotate more frequently than the length of a single semester. That is all to preface that I don't see myself able to take any courses at a Brick & Mortar institution near me because even if I'd registered for night courses, I could very inconveniently be thrown on a swing shift peri-semester. As it stands, I possesses a mere Associate's and aim first to learn as much about math as possible in the remaining 4 years of my enlistment, and peripherally prepare myself optimally for a B&M BS at a great school.

I've read the following threads on this site:
1) https://www.physicsforums.com/threads/bs-in-mathematics-online.267655/
2) https://www.physicsforums.com/threads/online-mathematics-courses.685335/

From them I've ascertained that an online degree in math is a true inhibitor to future achievement in the field in a lot of ways. I was never a fan of such courses before, but am largely considering due to the military. They emphasize the value of pursuing any degree whatsoever and using Tuition Assistance (which caps at $250/unit, $4500 per year) "or suffering the consequences."

A fellow Marine and I have deemed far more valuable to expand our knowledge and ability rather than ascend the ladder of education without attaining many real qualifications. To this end, we've shared Logic textbooks (from the Philosophy side of symbolic and predicate logic), work a bit out of Spivak's Calculus, and are seeking as many resources as possible. Is it a wise approach to use our time to try to come out of the military as ~26 year old "super-prepared sophomores/Juniors in a BS program" but not pursue credit?

I've also seen Micromass's excellent "Self-Study of Mathematics" thread. "Should I Become a Mathematician" has a wonderful list of books to delve into. With nearly 4.5 years, I think I can sacrifice some of my Arabic and French from work to really get my head into the "better" parts of mathematics I failed to reach for before. I appreciate any input that can be provided on these endeavors, but especially look forward to criticism (and I have a thick skin, so lay in if needed!) on the degree/no degree/etc. matters.

Thanks for reading and any input you all may have.

All the best,
MAA

 

[WWGD]

Hi, I am not sure, but I hope this will help.
I have considered applying the 20-80 law : In certain situations/environments, 20% of the input produces 80% of the output; this can be used to improve productivity. So it comes down to effectively-administering your attentional states. If you learn to recognize the attentional state you are in at a given moment (i.e., are you sharp, is your mind more-or-less receptive ), you may be able to effectively-decide what are the best tasks to do at that moment; you don't want to , e.g., waste a period of time when you're well-awake and sharp to do rote work, nor do you want to do the converse: try to learn difficult material when you're either tired, or not mentally sharp (or both.). It takes some training to recognize your mental states and then allot the time effectively. OF course, with more advanced training, one may change one's mental state, but this is kind of far out. HTH.

 

[MAAntonius]

That's great advice, WWGD. I've tried to exploit those principles by planning my daily schedule out in a really regimented way... fundamentally, I can get a lot more good quality work done academically if I do so before my work day and commitments begin, so rising at 4am and having 2-3 hours of "me" time gives me a much better opportunity to pursue what I want than waiting until after a rigorous day of work.

Doing so simply on a so called microscale, and thinking about it in the midst of the day, isn't something I'd considered before, thanks!

And just as a generic update, I got some good advice from a physics grad student and am working on Larson's Calculus and Kolmann's Elementary Linear Algebra to make myself better prepared once I do get the shot at entering an undergrad math program.

Thanks for your time and input!