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AdrianZ

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Today I was studying Euclidean rings and I found the subject very beautiful and subtle and I guess by the end of today I'll try to solve some problems on Euclidean rings.

Having said all of these things, my favorite area of mathematics is geometry, but I also love abstract algebra, analysis and topology. The name algebraic geometry suggests that it must be an interesting field that links geometry to algebra. Is that true?

What is algebraic geometry about? What are the main theorems in algebraic geometry? What are the applications of algebraic geometry in pure mathematics and applied mathematics or in physics? Is there any book that explains algebraic geometry for an undergraduate student? What are the prerequisites to study algebraic geometry? Is it a good idea that I study algebraic geometry now?

Thanks in advance