Mathematics for the Adventurous Self-Learner

Re:Mathematics for the Adventurous Self-Learner by kevstev on Monday February 24, 2020 @12:30PM (#22406126)

Do any of you all have some tips for understanding mathematical notation? I feel this is often poorly explained, and it feels like a language all its own that just does not speak to me. I did pretty well in calculus, but I still don't really understand what the dx was supposed to represent and in reality I was just really good at pattern matching when it wasn't supposed to be there anymore.

I try to read papers now and again with a math orientation, and I quickly get lost when trying to translate the concepts into cryptic formulas, and often when they make the "obvious" transition from step 3 to step 4 I just have no idea how they got there.

I feel this is by far my biggest barrier to understanding most mathematics, and I have thus far found no way to overcome it.

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Re:Mathematics for the Adventurous Self-Learner by bo1024 on Monday February 24, 2020 @01:47PM (#22407043)

I think usually the problem is "almost getting it" and trying to move forward, which means small uncertainties add up and all the sudden one is totally lost without being sure exactly why. So it's important to go back and make sure each piece of notation is crystal clear before moving forward.

Any statement in math is meant to be directly translatable to human language. You should be able to read it out loud in English and know exactly what you mean when you say it.

Unfortunately, sometimes math uses awful notation. For example, df/dx. This is a case where df doesn't mean anything (or at least it's not normally well-defined), and dx doesn't mean anything either (same comment). But the notation as a whole means something. If we write g = df/dx, then we can understand that g is a function whose input is x and output is the slope of f at x.

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Re:Mathematics for the Adventurous Self-Learner by strls on Monday February 24, 2020 @12:44PM (#22406291)

Sounds like you might simply not understand the definitions for these operators and symbols. In other words, it's not a notation problem. I find that it's helpful to mentally replace the symbols like dy/dx, sum, lim, integral, and so on with the concepts they represent. That is, go from operators to definitions.

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Re:Mathematics for the Adventurous Self-Learner by proc0 on Monday February 24, 2020 @02:31PM (#22407512)

3blue1brown channel on calculus:

https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQ...

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