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by Zeule
3026 days ago
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This answer is absurd, and only true for people with little motivation. Self-learning does require more motivation and "grit" to keep going, and some planning early on, and there is a higher dropout rate. But in many cases, it is the best option. I've found that this is especially true for many parts of STEM fields. It is a far more productive and effective use of time to work through problems than listen to lectures. Of course, it is also helpful to have people you can ask questions when you don't understand as comes with a class, but that can also be found online. I also find that I often understand things I learn on my own more deeply because I can go at my own pace and have more time (time not spent listening to lectures or preparing for exams on a fixed deadline) to draw from a variety of resources. One of the most important skills someone can learn is how to learn, and especially how to solve problems and keep going when it is difficult. For math through high school level/early university, I'd suggest Art of Problem Solving (if you can handle it). It teaches by having people solve problems rather than presenting mathematical techniques to memorize. Some of them are straightforward, but many are tricky problems and fun puzzles with elegant solutions. It helps you gain a good sense for numbers and problem solving, and an appreciation for the beauty of math. The teaching method helps you intuitively understand rules rather than memorize them. They also have a nice gamified online practice system (Alcumus) to go along with the first half of their books. For some higher level, more applied areas like linear algebra there are some good coding-based courses like codingthematrix.com. Project Euler is also another good option for practicing math with programming. |
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