Related: I got two masters degrees, at midlife, after doing other stuff. I also moved back to the USA during that time and found it useful to learn a lot of little things I never needed to think about in Taiwan, like how to fix a car. So, having learned a handful of new skills in the past eight years or so, from car repairs to calculus, as a general heuristic I find doing something independently from beginning to end and fixing the problems along the way the first time teaches about 50% of the knowledge. 2-3 times gets to 75%. 3-5 times gets to 90%. Past the 90% mark, you spend the rest of your life making small improvements in the last 10% of the knowledge.
Basically, you don’t need to do that many Taylor series to see the pattern and grok what’s going on (and have improved your understanding of polynomial representations of calculus, and start getting intuitions when other approaches are used). You don’t need to switch the motor mounts on that many cars to basically get it (and to have learned frankly a lot about similar types of car work). Etc.
That first time, maybe the second in some cases, is the biggest lift and the biggest learning.
Related: I got two masters degrees, at midlife, after doing other stuff. I also moved back to the USA during that time and found it useful to learn a lot of little things I never needed to think about in Taiwan, like how to fix a car. So, having learned a handful of new skills in the past eight years or so, from car repairs to calculus, as a general heuristic I find doing something independently from beginning to end and fixing the problems along the way the first time teaches about 50% of the knowledge. 2-3 times gets to 75%. 3-5 times gets to 90%. Past the 90% mark, you spend the rest of your life making small improvements in the last 10% of the knowledge.
Basically, you don’t need to do that many Taylor series to see the pattern and grok what’s going on (and have improved your understanding of polynomial representations of calculus, and start getting intuitions when other approaches are used). You don’t need to switch the motor mounts on that many cars to basically get it (and to have learned frankly a lot about similar types of car work). Etc.
That first time, maybe the second in some cases, is the biggest lift and the biggest learning.