How do I learn about digital signal processing to start my ...

I am 30 years old. I have a Bachelors of Psychology. I've been working as a software engineer for 10 years. I would like to learn more about digital signal processing, synthesizers, and the mathematics of audio. Why? I would like to start my own company that writes and sells virtual instruments. I have a deep/expert understanding of software, but I am light on audio programming/mathematics.
I've finished Calculus I as part of my psychology degree. What options do I have, either formally or informally, to study and learn about the mathematics of digital signal processing? I am open to complete formal training (getting another bachelors in Mathematics) to complete informal training (reading books and making it happen on my own). I have lots of questions here -- for example, can an adult take classes at a university without enrolling in a degree program?
I know this is a broad question, but I'd like to get a general pulse on how somebody at my age, with my experience, with my goals, could proceed with his dream to start writing virtual instruments.
Thank you so much!

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