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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.


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

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    [tag:reference-request] should not be used as a standalone tag; see [meta](http://meta.math.stackexchange.com/questions/2498/the-meta-tags).2012-08-06
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    This because I want to strengthen my algebra and number theory and geometry and calculus and trigonometry and everything that a high school typical maths curriculum includes but do not want myself to have limited knowledge that my school provides. And that is why I am looking for good books in these two branches (sadly,I do not have sufficient sources for them)2012-08-06
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    You will strengthen your skills by practice of problems, not by cramming massive amounts of knowledge. I am a postgraduate mathematician and I have never had need for this many books on polynomials and inequalities. Some of these books are written to contain many specific results in these areas that are not suitable for high school students.2012-08-06
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    @OldJohn there are no functional analysis books on that list...it is olympiad style functional equations that the OP is probably interested in2012-08-06
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    Quite right - my mistake - I will delete my pointless comment!2012-08-06

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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.

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    There are no functional analysis books in that list!2012-08-06
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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.

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    The last item, on functional equations, is not visible online but seems to be another competition-based source like Barbeau's. So it may be accessible to a beginner, but not necessarily connected to deeper theory.2012-08-07