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 ?
2026-04-08 19:15:24.1775675724
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Interesting polynomial books
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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.
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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.
The Fundamental Theorem of Algebra, by Benjamin Fine and Gerhard Rosenberger (Springer-Verlag, 1997), is quite interesting.