Use multiple textbooks if you can. Often a definition or theorem doesn’t quite gel until I’ve read multiple presentations of it.
Google is your friend. For example, this blog post is the best explanation of normal subgroups I’ve ever seen. When you combine it with this Math Exchange thread, this web page from John Baez, and Wikipedia, you can actually learn a lot about normal subgroups without even opening a textbook.
This is probably exclusive to how I learn, but I find that going through a text book linearly is, in general, horribly boring. You are typically given a collection of defintions, which you are supposed to memorize and trust that they will eventually become important. Then you prove theorems about the properties of these minimally-motivated definitions, and if you persist long enough you’ll eventually make it to an interesting result and see that the definitions were indeed useful. I can’t learn like that; my eyes glaze over. Instead I skim places like Wikipedia for topics that seem interesting and not too far out of reach, and then I learn only the things that I need to understand the topic. Essentially, I try to learn like a package manager, installing only the depencies I need for the package I’m currently interested in. I mention this only because I spent a lot of time trying and failing to make my way systematically through math textbooks before I found this method, which seems to work for me.
Scattered thoughts:
Use multiple textbooks if you can. Often a definition or theorem doesn’t quite gel until I’ve read multiple presentations of it.
Google is your friend. For example, this blog post is the best explanation of normal subgroups I’ve ever seen. When you combine it with this Math Exchange thread, this web page from John Baez, and Wikipedia, you can actually learn a lot about normal subgroups without even opening a textbook.
This is probably exclusive to how I learn, but I find that going through a text book linearly is, in general, horribly boring. You are typically given a collection of defintions, which you are supposed to memorize and trust that they will eventually become important. Then you prove theorems about the properties of these minimally-motivated definitions, and if you persist long enough you’ll eventually make it to an interesting result and see that the definitions were indeed useful. I can’t learn like that; my eyes glaze over. Instead I skim places like Wikipedia for topics that seem interesting and not too far out of reach, and then I learn only the things that I need to understand the topic. Essentially, I try to learn like a package manager, installing only the depencies I need for the package I’m currently interested in. I mention this only because I spent a lot of time trying and failing to make my way systematically through math textbooks before I found this method, which seems to work for me.