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Groups are just the abstraction of "transformations of something", the usual example being "symmetries" but it leaves out a bunch of other natural ideas like tr
by pfortuny 14y ago
Groups are just the abstraction of "transformations of something", the usual example being "symmetries" but it leaves out a bunch of other natural ideas like translations, movements, etc.
Any teacher not mentioning "shape" when explaining group theory is either a bad teacher or a bad teacher.
- paulrademacher 14y agoGroup theory can be taught and appreciated without the geometric approach, but instead as a pure abstract concept. Different textbooks reflect this: Herstein is very abstract, Dummit and Foote uses probably more geometric examples, and Fraleigh relies heavily on geometric cases. I've personally always preferred the Herstein/abstract approach.
- pfortuny 14y agoOh certainly: that is the way I studied and enjoyed it but a book is not a teacher. I am not claiming books should always be "imagination" driven, on the contrary. But teachers should.