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Should i solve math problems by writing the answers to papers or notebooks with pencils or should i try solving them in my head at undergraduate studies at university?

Also, sometimes after learning theorems, definitions or proofs should i write them on papers or notebooks to confirm than i know them well?

Thank you.

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Write stuff down. If you only do it in your head, you'll fake yourself into thinking you know more than you do. When you force yourself to write things down, you show the steps and ensure you really know them all. Clear writing is clear thinking.

In addition, it gives you more investment in the answer, especially when you check your drill homework and mark a check or an ex next to written work.

Also it mimics what you have to do for exams.

P.s. It is fine to write the steps quickly. In fact speed--not spastic, but with some pace--is desirable. ( https://www.youtube.com/watch?v=BqWqzvnbnjU ) But get the whole explication down. Yes. In writing. Own it!

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