Inequalities

This book discusses about the basic topics on 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. The book contains over 400 problems with their solutions. 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 who are consolidating their knowledge of inequalities and their applications.

Auteur

B.J. VENKATACHALA is professor emeritus at the Homi Bhabha Centre for Science Education-Tata Institute of Fundamental Research (HBCSE-TIFR), India. Earlier, he held several administrative and academic positions, such as a scientist at the Indian Institute of Science, Bengaluru; lecturer at the University of Mysore; reader at Kuvempu University, Shimoga; a scientific officer at the Department of Atomic Energy, Government of India, where he took charge of the mathematical Olympiad activity in India. He later joined HBCSE-TIFR, where he was completely involved in selecting and training students for International Mathematical Olympiad (IMO) for nearly 25 years, until his retirement in 2015. He has contributed to Olympiad literature in the form of problems and books. He was also the leader of the Indian team to IMO several times.

Contenu

Chapter 1. Some basic inequalities.- Chapter 2. Techniques for proving inequalities.- Chapter 3. Geometric inequalities.- Chapter 4. Applications involving inequalities.- Chapter 5. Problems on inequalities.- Chapter 6. Solutions to problems.