I'm currently studying abstract algebra from Herstein's interesting book "Topics in algebra", I've learned different definitions so far and I've solved most of the problems covered in the book. I've so far studied groups, subgroups of them, normal subgroups, quotient groups, isomorphism theorems, products of groups, conjugacy classes and the conjugacy class equation and I've understood theorems like Cauchy theorem, but so far I've excluded Sylow theorem from my group theory knowledge because I find a bit hard to for self studying. In rings, I've got acquainted with basic definitions and I've gone further and realized that every domain can be extended to a field and I've understood results like R/M is a field if and only if M is a maximal ideal provided that R is a commutative ring with a multiplication identity element. I've also studied the ring of polynomials with coefficients in F from Herstein's "topics in algebra" and Hoffman-Kunze linear algebra book.(adsbygoogle = window.adsbygoogle || []).push({});

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

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# What's algebraic geometry good for?

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