What are some interesting polynomial books, which doesn't requires any prerequisite except basic high school algebra, but develops and introduces interesting stuff (eg: Fields/Rings/Interesting sides of Galois theory) in a historically motivated way ?
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1$\begingroup$ Stillwell's Elements of Algebra comes to mind. It's not specifically about polynomials, but it does cover the basics of Galois theory in a historically motivated way, and its prerequisites are modest. $\endgroup$– user169852Commented Oct 18, 2017 at 16:16
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$\begingroup$ @Bungo I have Stillwells' "Mahtematics and its history", and the book is...fantastic ! Nice suggestion, please add it as an answer. $\endgroup$– katana_0Commented Oct 18, 2017 at 16:44
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3 Answers
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The great giant in this category is Polynomials by Barbeau. This is actually a problem book, and the reader must be willing to follow an interesting guided path of problems through many a various aspects of polynomials. Ideas related to Galois theory are introduced, but the book stays very elementary.
answered Oct 18, 2017 at 16:23
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1$\begingroup$ Thanks for the suggestion. Yes, I have read that book, but I didn't have much patience going through it because as the book is very old (from 1975), the problem are not very challenging/ don't require more than one hour thinking, and a lot of problems are very straightforward exercises. (Compare that to the problems in Problems from the book by Titu Andreescu, the problems there are so .....ing hard... :) (BTW I didn't downvote the answer) $\endgroup$– katana_0Commented Oct 18, 2017 at 16:40
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The Fundamental Theorem of Algebra, by Benjamin Fine and Gerhard Rosenberger (Springer-Verlag, 1997), is quite interesting.
answered Oct 18, 2017 at 16:17
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Since you mentioned in a comment that you like Stillwell's Mathematics and Its History (as do I), I think you would also enjoy his book Elements of Algebra. It's not specifically about polynomials, but it does cover the basics of Galois theory in a historically motivated way, and its prerequisites are modest. In particular, you don't need any previous exposure to abstract algebra. He develops the basics of groups, rings, and fields as needed, and only after motivating the concepts first.