On Sat, 21 Mar 2009, Kyle Klipowicz wrote:
I took Modern Algebra as my first course in "Higher Math." Big mistake. Learning to do proofs this way is a big headache, especially if you have a curmudgeonly teacher!
I don't know what kind of prof you had, but Group Theory tends to need proofs that start from the very scratch. You can hardly skip any step or make any assumptions. Making proofs at this level is very akin to programming in low-level languages like machine language and assembly language: you need to go in the little details, and all you have are little details put together. Fortunately, other courses (and perhaps other parts of the same course) are higher-level than that: I don't need to re-prove every little thing. But it's often not very clear in what level of detail I have to go. As a really bored student, I constantly tested the limits of what I can submit in an exam, and I'd say that they were quite tolerant of my terse proofs.
For your learning process, perhaps it has more to do with the teacher being curmudgeonly than about the actual topic that you use for learning how to prove things.
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