| Some notes from an older person: The best approach will vary based on topic, age, and constraints (e.g. professional with kids). When I was a teenager, I learned Calc I, II, III and a first course of differential equations. I retained most of it. When I decided to take more advanced math courses later on (just a few years later), I was always saddened by my inability to retain much after the course was over. I kept wondering if I'm in my decline (at the old, old age of 25). No - I was not. The nature of the material had changed. Whereas stuff you learn in Calc I and Calc II is material you can easily and often apply in engineering, some random theorem in group theory is not. When you study a theorem in Calc II, the frequency with which that theorem is invoked in the same book is high. When you get to higher math, it does become somewhat broader: Most theorems are invoked only a few times in the book. There's also raw talent vs techniques. Younger me got by with raw talent, but at some point the material you're learning will supersede your talent. You then need to strategize (and different topics may require different strategies). Don't knock raw talent/skills - they can be honed and it may be worth honing them. But broadly: The person who has good systematic study skills will eventually overtake the raw talent person. Most of the approaches that will work if you have all the time in the world will fail you when time becomes constrained. I started using spaced repetition a few years ago and it has been a game changer. I can study things for a bit, take a break for a few months, and mostly can pick up where I left off despite not practicing that material in those months. Having said that, most of Becky's advice is good. The one thing I'd disagree with is: > "Five minutes every day is better than an hour once per week" This definitely depends on the material. You're not going to get far in math on just 5 minutes a day. Some topics will need a lower bound of minimum time per session. |
Last year I taught myself a good deal of category theory, and you're right, five minutes is not really enough to learn most things - but it is enough time to start an exercise - and those five minutes often turn into something longer!