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Originally Posted by Urchin
I really like LeGrange's theorem and everything it implies
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That's on my short list of favorite theorems, if not at the top.
Quote:
Originally Posted by nemo
I haven't taken abstract algebra or complex analysis yet, but my advisor says I'll love them. I've read a great deal about both topics, but I've been too busy lately to self-educate myself much. How have you guys liked those courses?
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Complex analysis is like real analysis but confined to R2 and making specific use of the definitions of e and i. Should be fun for you. I never took a real analysis class (advanced calc. and complex analysis were the closest I got) because I was Discrete Math major. I bought a couple of Real Analysis and Topology books later, but I haven't gotten around to reading them yet.
After spending that much time in analysis-land, abstract algebra will be a cake-walk for you. It is a lot of fun too, a lot of applications to number theory (and to seemingly every branch of mathematics).
I got math as an auxiliary degree while focusing on computer engineering. So I missed out on a lot of the analysis classes. Part of me wants to go back to school for a math degree focused on analysis.
I especially want to cover some heavy-duty set theory, topology, real analysis and measure theory.
Another part of me want to go back and study non-linear dynamics, chaos theory, catastrophe theory and the like. After spending time as an EE masters and all the assumptions of linear dynamics, I can't help but wonder how the non-linear world is described.