> How to Learn Advanced Mathematics Without Heading to University
I wonder if it's even possible. Learning maths requires much work, time and dedication. Doing so alone must be very difficult.
There are several things universities provide that are hard to replicate alone: a degree, which gives you access to a job, motivation, learning environment, and "peace of mind".
What I mean by peace of mind is that, when you're a student, your job is to study, that's what you're expected to do and normally your degree will give you access to a job (esp. if your university is reputable).
Now suppose someone learns advanced maths on their own. There's a huge opportunity cost. Not only it takes a lot of time, and the few lucrative jobs that make use of maths are in finance. I suspect financial institutions are very conservative and rarely recruit someone without a proper academic background.
An other thing when learning things alone, is that your job is twofold. You must be teacher and student at the same time. You need to find the material, impose yourself some pacing, decide when it's ok to move on etc... It may be ok when you want to learn a new technique in a field you already know, but something as broad as "learning advanced mathematics" seems impossible.
I wonder if it's even possible. Learning maths requires much work, time and dedication. Doing so alone must be very difficult.
There are several things universities provide that are hard to replicate alone: a degree, which gives you access to a job, motivation, learning environment, and "peace of mind".
What I mean by peace of mind is that, when you're a student, your job is to study, that's what you're expected to do and normally your degree will give you access to a job (esp. if your university is reputable).
Now suppose someone learns advanced maths on their own. There's a huge opportunity cost. Not only it takes a lot of time, and the few lucrative jobs that make use of maths are in finance. I suspect financial institutions are very conservative and rarely recruit someone without a proper academic background.
An other thing when learning things alone, is that your job is twofold. You must be teacher and student at the same time. You need to find the material, impose yourself some pacing, decide when it's ok to move on etc... It may be ok when you want to learn a new technique in a field you already know, but something as broad as "learning advanced mathematics" seems impossible.