I am an engineer student from Norway who is not that fascinated with "engineering maths", so I am trying to work through Spivak's Calculus book on my own. I know that there is no "how to" manual for grokking concepts. But I wonder if anyone has used writing as a tool to understand complex concepts. The reason I ask is i bumped into this essay about writing, and I was wondering how that relates to my epic battle with Spivak's book. Any thoughts?
(answer I gave in MathOverflow yesterday, for those who didn't see it)
During the late 1980s to mid 1990s (roughly), there was a strong push in the U.S. for "writing across the curriculum" in high school and college mathematics courses. A lot was written about this in various MAA and NCTM publications, but I don't have a list of references to offer. However, the following google searches appear to bring up much that may be of interest:
If a deeper understanding of mathematical concepts is what you're after, then writing is essential. I'd argue that if you can't explain a concept in words, then you don't really understand it.
You don't have to look far for your answer, either. Take a look at the profiles of some of the users with a huge reputation scores and peruse their answers to questions. You'll see a lot of nice, thorough, (and often clever) explanations in words. This comes from being able to write about mathematical concepts (along with ability to write in general).
As Beni commented, write! And don't just write an equation. If it's hard or unnatural at first, start by writing in purely mathematical terms/symbols, but then step back, look at what you have on the paper/screen, and start asking 'What..', 'Why...', 'How...' questions.
'What do I learn from this equation?'
'What happens if I change this one parameter?'
'Why is it of this form?'
'How can I prove this?'
It can be laborious at times, but (I claim) it's necessary.