As I've mentioned recently, I'm trying to write an undergraduate abstract algebra textbook that's readable by humans,1 because I think that somebody should.
Well part of the motivation for writing the book is that there are lots of abstract algebra books out there that seem to have been written for people who either already understand this stuff very well already (the Éléments de mathématique series by the Bourbaki collective are some of the most extreme examples of this type) or for confident students who are prepared to hack away at something until they understand it. I think it's probably fine to expect PhD students to put a bit of work in to understand something (although that still doesn't excuse overly terse or opaque exposition) but there are a lot of students who get turned off entire branches of mathematics because their confidence gets damaged by unsympathetic or unclear lectures or books.
In particular, I want my book to be understandable by these less confident students as well, so I'd be grateful for any insights you can share from that perspective. Some of it might still be a bit complicated: in some places I assume that the reader has at least some familiarity with things like matrices, vectors, complex numbers and functions. But I do plan to include an appendix which gives a brief overview of that sort of stuff too.
In particular, I want my book to be understandable by these less confident students as well, so I'd be grateful for any insights you can share from that perspective. Some of it might still be a bit complicated: in some places I assume that the reader has at least some familiarity with things like matrices, vectors, complex numbers and functions. But I do plan to include an appendix which gives a brief overview of that sort of stuff too.
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