Inequalities

1. Basic (Elementary) Inequalities and Their Application
Zdravko Cvetkovski

2. Inequalities Between Means (with Two and Three Variables)
Zdravko Cvetkovski

3. Geometric (Triangle) Inequalities
Zdravko Cvetkovski

4. Bernoulli’s Inequality, the Cauchy–Schwarz Inequality, Chebishev’s Inequality, Surányi’s Inequality
Zdravko Cvetkovski

5. Inequalities Between Means (General Case)
Zdravko Cvetkovski

6. The Rearrangement Inequality
Zdravko Cvetkovski

7. Convexity, Jensen’s Inequality
Zdravko Cvetkovski

8. Trigonometric Substitutions and Their Application for Proving Algebraic Inequalities
Zdravko Cvetkovski

9. Hölder’s Inequality, Minkowski’s Inequality and Their Variants
Zdravko Cvetkovski

10. Generalizations of the Cauchy–Schwarz Inequality, Chebishev’s Inequality and the Mean Inequalities
Zdravko Cvetkovski

11. Newton’s Inequality, Maclaurin’s Inequality
Zdravko Cvetkovski

12. Schur’s Inequality, Muirhead’s Inequality and Karamata’s Inequality
Zdravko Cvetkovski

13. Two Theorems from Differential Calculus, and Their Applications for Proving Inequalities
Zdravko Cvetkovski

14. One Method of Proving Symmetric Inequalities with Three Variables
Zdravko Cvetkovski

15. Method for Proving Symmetric Inequalities with Three Variables Defined on the Set of Real Numbers
Zdravko Cvetkovski

16. Abstract Concreteness Method (ABC Method)
Zdravko Cvetkovski

17. Sum of Squares (SOS Method)
Zdravko Cvetkovski

18. Strong Mixing Variables Method (SMV Theorem)
Zdravko Cvetkovski

19. Method of Lagrange Multipliers
Zdravko Cvetkovski

20. Problems
Zdravko Cvetkovski

21. Solutions
Zdravko Cvetkovski

Keywords: Mathematics, Algebra, Popular Science in Mathematics/Computer Science/Natural Science/Technology, Mathematics Education, Popular Science, general