Does anyone with more experience than me foresee problems with this approach? Has this been tired before? How did it work?
I foresee (minor) problems. Nothing too serious, but it might be useful to be aware of the existence of problems with this approach. Most notably:
Many (sub)fields use only a single model out of a larger, overarching theory. Most of the times you want to skip the grand theory to get immediate results from a single model (so that’s a plus for your approach), but sometimes having someone show you the similarities between different theories explicitly can be very useful. By going for depth rather than breadth it might be hard to compare, contrast and most importantly merge pieces of knowledge from different fields. For clarity: I’m talking about really, really general mathematics here (for example learning linear algebra rather than the algorithm for the Fast Fourier Transform).
I personally found that in general it is quite hard to figure out which math you need to fully understand a certain result if you don’t already know the math. If you start with an overly ambitious goal (for example if you start with the Einstein equations of General Relativity and say to yourself: ‘Lets backtrack to see which math I need’) I suspect that you will have trouble figuring out which math to learn.
All in all these points are only minor—most useful math is relatively simple (it’s called the simple math for a reason), and you already seem to plan to start with pretty general mathematics (e.g. learning statistics rather than just the linear least squares algorithm). But sometimes learning the math before you have a goal can be useful.
I personally found that in general it is quite hard to figure out which math you need to fully understand a certain result if you don’t already know the math. If you start with an overly ambitious goal (for example if you start with the Einstein equations of General Relativity and say to yourself: ‘Lets backtrack to see which math I need’) I suspect that you will have trouble figuring out which math to learn
Noted, but I do have the advantage of being able to ask. The next post will ask, “for each topic, formula, or problem on this list, what math do I need to know to understand and solve it?”
I foresee (minor) problems. Nothing too serious, but it might be useful to be aware of the existence of problems with this approach. Most notably:
Many (sub)fields use only a single model out of a larger, overarching theory. Most of the times you want to skip the grand theory to get immediate results from a single model (so that’s a plus for your approach), but sometimes having someone show you the similarities between different theories explicitly can be very useful. By going for depth rather than breadth it might be hard to compare, contrast and most importantly merge pieces of knowledge from different fields. For clarity: I’m talking about really, really general mathematics here (for example learning linear algebra rather than the algorithm for the Fast Fourier Transform).
I personally found that in general it is quite hard to figure out which math you need to fully understand a certain result if you don’t already know the math. If you start with an overly ambitious goal (for example if you start with the Einstein equations of General Relativity and say to yourself: ‘Lets backtrack to see which math I need’) I suspect that you will have trouble figuring out which math to learn.
All in all these points are only minor—most useful math is relatively simple (it’s called the simple math for a reason), and you already seem to plan to start with pretty general mathematics (e.g. learning statistics rather than just the linear least squares algorithm). But sometimes learning the math before you have a goal can be useful.
Noted, but I do have the advantage of being able to ask. The next post will ask, “for each topic, formula, or problem on this list, what math do I need to know to understand and solve it?”