Correct order of books for a beginner

Question

what should be the order of the books in which a beginner should do the following books in algebra:
-1.E.J. Barbeau POLYNOMIALS
-2. Polynomials and Polynomial Inequalities (Graduate Texts in Mathematics) - (Springer) - Peter Borwein -Tamas Erdely.
3.Geometry of Polynomials - (American Mathematical Society) - Morris Marden
And if you guys know of any other book then share it.
And in functional equations the following:
1.Functional Equations and Inequalities in Several Variables - (World Scientific Publication) - Stefan Czerwik.
2.Lectures on Functional Equations - (Academic Press) - J. Aczel.

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3.Functional Equations: A Problem Solving Approach - (Prism Books) - B.J. Venkatchala.

Answer 1

In the sense that there might be someone who will go through all three polynomial books at some time, that order would likely be Barbeau's Polynomials, which can be read by a high school student, Polynomials and Polynomial Inequalities, Geometry of Polynomials. Although I should mention that the last two don't have a dependence chain or anything, so it doesn't really matter which of the two you take first. But there are many, many, many things to be learned between Barbeau and the others, like calculus, algebra, algebraic geometry, and some analysis. It would be inappropriate for me to suggest that Barbeau would adequately prepare you for the other two.

I'm not familiar with the functional analysis books.

Answer 2

Except for Barbeau's book, those references cover a random selection of advanced subjects and a beginner will find them hard to read, because they assume other intermediate subjects as background. If your goal is to gain mathematical knowledge starting from the basics, or improve at the olympiad type of problem-solving ability, any of the last five books on the list would be a very inefficient investment.

Barbeau's book has a strong problem-solving slant and is intended for beginners, but it is limited to the elementary, 18th century type of algebra. It is more a compendium of exercises from contests and journals.