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Reading Mathematics (2002) [pdf]

172 点作者 kercker超过 7 年前

5 条评论

johnbender超过 7 年前
Beyond notation and ordering, I have had the best results reading and comprehending complex concepts, including mathematics, by taking the following suggestion to the extreme:<p>&gt; Read with pencil and paper in hand, making up little examples for yourself as you go on.<p>I like to find a difficult question that I can answer with an understanding of the material. This acts as a litmus test of my understanding and a forcing function.<p>The question can be almost anything, but a general approach I use is to write a &quot;compiler&quot; that maps some concept from the material to a concept I already understand (this normally takes the form of a denotational semantics). Then the question would be, &quot;How can I interpret X as Y?&quot; This technique has its limits since the material can&#x27;t be too far afield from something I already know and the idea isn&#x27;t novel but it has been effective for me. The critical bit is forcing myself to write down a fairly comprehensive mapping function. This gets me into the dark corners of my understanding very quickly and adds new questions to answer.
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tw1010超过 7 年前
Funny how utterly natural and subconsious this stuff becomes after a while. I almost felt like commenting something snyde about how superfluous it is to make it this explicit, but then I realized that it was only a few years ago that it made my consious brain totally overwhelmed.
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Improvotter超过 7 年前
Right now I&#x27;m studying for my math final for computer engineering. This really does speak to me as I often don&#x27;t understand certain parts of the chapter and just skip ahead to the exercises and then I try to reflect back to the theory. Thank god that I don&#x27;t have to learn a single proof though.<p>Alright, back to studying.
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sergj超过 7 年前
From which book is this?
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josephhurtado超过 7 年前
Useful, to the point, non controversial, and short. AWESOME.