[nightski]

I'm in the demographic you describe, yet I've had a hard time finding resources to develop that "mathematical maturity" short of going back to graduate school. Which I'd love to do, but am at a point in my career where that would be devastatingly expensive to my future since these are the prime earning and wealth building years.

I wish there was more of a self directed way to achieve this.

[ghufran_syed]

I just finished an MS in math and statistics a long time after doing a non-mathematical undergrad degree. I feel a lot of what is called mathematical maturity is actually getting comfortable doing proofs, which I think is hard to learn while also learning more advanced math. I would recommend working through "Mathematical proofs" by Polimeni/Chartrand/Zhang. Unlike math at an earlier level, you can't just check your answers against the official ones to see if you made a mistake - writing proofs is more like writing essays, the grammar is the easy bit, it's the process of putting the arguments together in the right detail and the right order that's important and hard to do without feedback. So you also need to get feedback from mathematicians on your proofs if possible. The best way to do that if you don't have a buddy who happens to be a mathematician is to learn to use LaTeX and ask questions on math.stackexchange.com.

An alternative is to do the proof and abstract algebra courses via (asymmetric) distance learning at https://westcottcourses.com/courses.html

I know someone who took these courses and felt like they got good feedback on their homeworks from the profs running the course.

Feel free to get in touch if you want to chat, I spent a long time trying to self-learn this stuff before starting my math MS, so happy to help in any way I can!

[marai2]

Since it's seems like you were already motivated and interested in learning Math on your own, how would you describe what your learnings were before you enrolled in formal studies? In other words if you could travel back in time to talk to yourself before you made the decision to enroll in a Master's program, what would the younger you have asked the older you and what would be the response? For example I'm thinking a reply might be like "well you're going to miss out on opportunities xyz by commiting to a Master's program, but because I know you and know you wouldn't be happy without satisfying your desire to learn Math in a more formal study the trade of is worth it. And you don't know this yet but when you start learning about P,Q,R you'll really get a kick out of it" :-)

[nightski]

Thank you for the resources, it is greatly appreciated!

[wenc]

Just curious, the topic above aside: what would you say is the main reason behind why you'd like to strive for "mathematical maturity"?

(from what you wrote, I gather it's not for reasons of vocation?)