[Math] Self studying math, how can I learn the most

educationreference-requestself-learningsoft-question

I am currently studying Pre-Calculus on my own. I have a few texts I am working with but feel like I could learning a lot more than I am.

When people typically ask these kind of questions the common response for Pre-calculus->Calculus is to watch "Khan Academy" etc.

Is this really a wise approach, especially when confronting future topics? Wouldn't it better to develop more independent, self-sufficient learning strategies beforehand?

I always wonder how mathematicians teach themselves so much knowledge without resources like "Khan Academy", lectures or even teachers. People learned math before the internet, what was the strategy then?

Some other questions:

  • Which is the better source to learn from, video lectures or reading the text? I feel like video lectures are too passive. Would time be better spent doing more exercises and less video lectures?

  • If you watch a video lecture, should it be watched before reading the text or after?

  • Math is quite concise as presented in textbooks, is summarizing the chapter as you read in a notebook effective or unnecessary?

  • Should I completely read chapters before attempting exercises or try questions first and refer to the text as needed?

Final question:
If a person was attempting to learn a topic in math from scratch with minimal knowledge on the content, what is an approach they could apply to learn it that would be both effective and efficient?

Thanks

Best Answer

  • Video lectures are actually better for rapidly getting the intuition than studying directly from a textbook. And that's because the lecturer reduces the effort you have to make to understand, especially if his name is Sal.
  • Yes, textbooks are superior to videos for genuinely learning the material.
  • It depends on how you summarize your chapter. Try to look up for the Feynman technique of learning, I'm sure you'll appreciate it and it will help.
  • Well, you can proceed as follows: ${\text{(1)}}$ Read first the chapter. $\text{(2)}$ Do some simple to medium exercises. ${\text{(3)}}$ Read the same chapter again, but this time more intensively and try to think about what you read a bit more. $\text{(4)}$ Do the hard exercises.

If you are starting a topic from scratch with minimal knowledge on the content, what is an approach that is found to be effective and efficient?

Searching for the best textbook out there and doing the procedure I explained in the last sentences. And for your purpose, i.e. Pre-calculus the best book that I really recommend is this one: Precalculus with unit circle geometry - David Cohen. It discusses lot of aspects from the fundamental theorem of algebra to matrices that you can find in my answer here.

After mastering Precalculus you may have a look at the other undergraduate topics.

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