Inequality

The subject of mathematical inequalities is tied closely with optimization methods. While most of the subject of inequalities is often left out of the ordinary educational track, they are common in mathematics Olympiads.

Famous inequalities

Here are some of the more famous and useful inequalities, as well as general inequalities topics.

• Arithmetic Mean-Geometric Mean Inequality
• Cauchy-Schwarz Inequality
• Chebyshev's Inequality
• Geometric inequalities
• Holder's inequality
• Isoperimetric inequalities
• Jensen's inequality
• Minkowski inequality
• Power mean inequality
• Rearrangement Inequality
• Schur's inequality
• Triangle inequality
• Trigonometric inequalities
• Trivial inequality

Problem solving tactics

substitution, telescoping, induction, etc. (write me please!)

Resources

Books

Intermediate

• Introduction to Inequalities
• Geometric Inequalities

Olympiad

• The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities by J. Michael Steele.
• Problem Solving Strategies by Arthur Engel contains significant material on inequalities.
• Inequalities by G. H. Hardy, J. E. Littlewood, G. Pólya.

Articles

Olympiad

• Inequalities by MIT Professor Kiran Kedlaya.
• Inequalities by IMO gold medalist Thomas Mildorf.

Classes

Olympiad

• The Worldwide Online Olympiad Training Program is designed to help students learn to tackle mathematical Olympiad problems in topics such as inequalities.

See also

• Mathematics competitions
• Math books