tag:blogger.com,1999:blog-4962147044562211522.post7061786261779667724..comments2014-07-19T19:00:15.161-07:00Comments on Cantabridgienne in Beverly: In Which We are Much CalmerCantabridgiennehttp://www.blogger.com/profile/14591198017344758776noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-4962147044562211522.post-52970603862162708132011-03-08T00:16:39.002-08:002011-03-08T00:16:39.002-08:00Learning mathematics by reading most explanations ...Learning mathematics by reading most explanations of it is a bit like reading an SF short story collection and then trying to sell to Asimov's.<br /><br />If you're lucky, your book will contain a lucid explanation that is the end result of a long "try this, no that didn't work; try something else" cycle that lays all the steps out in order as though choosing what to do next is as natural as breathing. If you're unlucky, the explanation will become forced and unnatural in it's adherence to a strict methodology that the authors made up themselves, and that they mistakenly think is just the one true way to do this kind of math.<br /><br />In neither case are you going to be given an understanding of the path to the final explanation and the many revisions and reworkings that happened on the way to building the chain of logic that now marches from A to B. Nor are you likely to get much discussion of other viable routes from A to B or other routes that seem good initially but that must be abandoned for one reason or another.<br /><br />So *of course* you need to do math yourself in order to learn it. Nothing else is going to get you to feel out the conceptual territory that lies right next to the territory of the book's tidy paths so that you can find your own way when you need to later.dtmhttps://www.blogger.com/profile/08695928927082149527noreply@blogger.com