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The lecturer is saying

And my goal is for you to come away feeling like you could have invented calculus yourself. That is, cover all

feeling is countable.

So, is "come away a feeling" more appropriate?

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In this particular context, "come away" means "Be left with a specified feeling, impression, or result after doing something". See also Lexico, Cambridge and others. Cambridge uses

I came away empty-handed.

as an example.

So "feeling" is not a noun, but an adjective. You will be feeling like something.

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