Texts and Readings in Mathematics

This book is an introduction to basic topics in inequalities and their applications. These include the arithmetic mean-geometric mean inequality, Cauchy-Schwarz inequality, Chebyshev inequality, rearrangement inequality, convex and concave functions and Muirhead's theorem. More than 400 problems are included in the book and their solutions are explained. A chapter on geometric inequalities is a special feature of this book. Most of these problems are from International Mathematical Olympiads and from many national mathematical olympiads.

The book is intended to help students who are preparing for various mathematical competitions. It is also a good source book for graduate students in consolidating their knowledge of inequalities and their applications.

The author has been involved in training Indian students for mathematical olympiads for more than 25 years.

1 Some basic inequalities
2 Techniques for proving inequalities
3 Geometric inequalities
4 Applications involving inequalities
5 Problems on inequalities
6 Solutions to problems
7 Bibliography
8 Abbreviation
9 Index