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What was your favorite proof or Eureka moment you remember?
Mine was about normal subgroups (##gNg^{-1}\subseteq N##). You learn the definition and prove a few properties and go to the next subject. I remember that I once tried to teach the concept to someone and in the middle of my explanations I all of a sudden realized, that this definition isn't just convenient, but necessary to get a well defined group structure on ##G/N##. Since then I know that being forced to explain something to others (while constantly asking your self why this is true what you are just talking about) is a really good way to learn something.What were your Eureka moments?
Mine was about normal subgroups (##gNg^{-1}\subseteq N##). You learn the definition and prove a few properties and go to the next subject. I remember that I once tried to teach the concept to someone and in the middle of my explanations I all of a sudden realized, that this definition isn't just convenient, but necessary to get a well defined group structure on ##G/N##. Since then I know that being forced to explain something to others (while constantly asking your self why this is true what you are just talking about) is a really good way to learn something.What were your Eureka moments?