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This is a problem I always had in university. Higher math always seemed to start with "the definition of X is Z etc." and I would never know what's the purpose
by ofrzeta 7y ago
This is a problem I always had in university. Higher math always seemed to start with "the definition of X is Z etc." and I would never know what's the purpose of doing this. When I attended a talk of Gilbert Strang many years later it was eye opening because it was a totally different approach that always accompanied theoretical concepts with a concrete interpretation.
Actually I now think it might also be a cultural thing. If you take a look at the approaches the English Wikipedia takes vs. the German Wikipedia take explaining a vector space you'll know what I mean:
https://en.wikipedia.org/wiki/Vector_space#Introduction_and_definition https://en.wikipedia.org/wiki/Vector_space#Introduction_and_...
https://de.wikipedia.org/wiki/Vektorraum#Definition https://de.wikipedia.org/wiki/Vektorraum#Definition
- big_chungus 7y agoI'd second the point on different cultures doing it differently. One of my profs once said he had a book written by two mathematicians, one German and another Italian. It was fairly evident who had worked on which part. He also mentioned that the "old style" German books would almost apologize if they "had" to use just a few pictures to illustrate something.
- dkarl 7y agoI had a math professor who told me that advanced math books are like Hoyle's Rules of Games. There are two ways you can use Hoyle's Rules of Games. You can memorize the rules of bridge and stop there, but then you will have a pretty dull experience. Or you can use the book as a tool to start playing bridge, and it will open you up to a rich and engaging activity.