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- Mar 10, 2012

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I have been reading Linear Algebra Done Right by Axler. By the time I reached to the exercises at the end of chapter 5, I started realizing that I was not able to solve the exercises "from scratch". The exercises seemed trivial if I used some key results from the chapter but when I tried to think naturally and "originally" I either was not able to get anywhere or I discovered some fantastic new (usually long) solution at the cost of spending a lot of time on the question; where the former occurred more frequently. (And this also goes for Abstract Algebra and other mathematical disciplines).

Now here's my question. What according to you is the right way to do it? Mugging a few results makes things a lot easier that just tackling the question with having zero prior knowledge.

How do you guys do it? How much do you think your previous problem solving experience matters to you? How much do you depend on theorems or results you have previously read?