I was wondering how much background knowledge is needed to do research in some subfield of algebra. I am currently working on an application for a summer research program, and I need to choose a subfield of mathematics to research, but I'm not too sure whether research in algebra would be possible with only a read of Dummit and Foote and Artin's text on Algebra. Also, is linear algebra still a topic that is currently being researched? And finally, is ring theory something I could possibly handle with only background knowledge from the two texts listed above?

  • $\begingroup$ Research level mathematics is well beyond most upper year undergraduate/early graduate level texts. You'll get the foundation, but you won't have nearly enough background to do research. $\endgroup$ – Cameron Williams Nov 28 '15 at 6:40
  • $\begingroup$ Are you applying to an REU? What program specifically? I did an REU this summer so if you want more information about that, I can help you. Not too sure about your other quesitons. $\endgroup$ – Ethan Alwaise Nov 28 '15 at 6:50
  • $\begingroup$ I'm currently in high school. I'm applying to RSI. $\endgroup$ – thkim1011 Nov 28 '15 at 7:05

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