By algebraic inequalities I mean inequalities like Cauchy's inequality, the AM-GM inequality etc. I need it for the International Mathematics Olympiad (IMO), so I hope I can find some books that introduce inequalities on that level. While I can only find problems on websites like M.SE. or AoPS (most of which are almost unintelligible to me), I want a book that provides a detailed, reader-friendly approach to that subject. Any recommendations? Thanks in advance.
2026-04-07 00:47:30.1775522850
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What are some good books on algebraic inequalities?
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$1$. Garling - Inequalities
$2$. Cvetkovski - Inequalities
$3$. Zawaira - A Primer for Mathematics Competitions
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The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by J. Michael Steele.
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With the note that certain algebraic inequalities require some calculus to derive and/or grasp the full context:
$1$ Hardy, Littlewood, Polya - Inequalities;
$2$ Beckenbach, Bellman - Inequalities.
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Old and New Inequalities Volume 1 - Titu Andreescu
Old and New Inequalities Volume 2 - Vo Quoc Ba Can et.al.
Algebraic Inequalities - Vasile Cirtoaje
Secrets in Inequalities - Pham Kim Hung [Volume 1 and 2]
Inequalities with Beautiful Solutions - Vo Quoc Ba Can et.al.
To my best knowledge, all the problems presented in the above mentioned books are solved.
Basics of Olympiad Inequalities (Samin Riasat)
www.aam.org.in/site/st_material/14.pdf
It's a free pdf document and it is very useful.