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I graduated with a bachelor of electrical engineering and I like to start a phd program in algebraic geometry at Brown university or another similar university. During my undergraduate, in addition to engineering math courses, I have taken abstract algebra, real and complex analysis, differential equation, linear algebra, and vector calculus.

Given my background, how can I start a phd program in algebraic geometry? How should I transition to a phd program in algebraic geometry?

I know that my math background is very poor but I want to know what I need to do so I can do a phd in algebraic geometry?

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    Go visit Brown and talk to a few faculty in the math department to see what they would advise. You may have a worse opinion of your math background than necessary. I also wonder why you chose algebraic geometry, but that is something to explore with the faculty. – Buffy Apr 14 at 13:13
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    Why algebraic geometry? How were you motivated to choose the topic? Why not persistent homology (topology from samples), discrete Morse theory or computational geometry? I am asking because these topics are all linking abstract mathematical concepts with (esp. computational) applications closer to everyday life, and therefore may be more accessible to you but still offer a route into more challenging mathematical understanding. – Captain Emacs Apr 14 at 14:07

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