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 Mathematical Olympiads.
Contents
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
- Chebyshevs inequality
- Geometric inequalities
- Holders inequality
- Isoperimetric inequalities
- Jensens inequality
- Minkowski inequality
- Power mean inequality
- Schurs inequality
- Triangle inequality
- Trigonometric inequalities
- Trivial inequality
Problem solving tactics
substitution, telescoping, induction, etc. (write me please!)
Resources
Books
Intermediate
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.
