PROVING VARIOUS MATHEMATICAL INEQUALITIES FOR OLYMPIADS
Abstract
Mathematical inequalities play a pivotal role in problem-solving within mathematical olympiads. This paper explores diverse techniques for proving inequalities, emphasizing their practical application in competitive settings. By presenting classical and advanced methods such as AM-GM, Cauchy-Schwarz, and Jensen's inequalities, the paper provides a comprehensive guide for students preparing for olympiads. A systematic approach to understanding and solving inequality problems is discussed, alongside illustrative examples.
Keywords
Mathematical Inequalities, Olympiad Problem-Solving, AM-GM InequalityHow to Cite
References
Hardy, G. H., Littlewood, J. E., & Pólya, G. (1952). Inequalities. Cambridge University Press.
Engel, A. (1998). Problem-Solving Strategies. Springer.
Titu Andreescu and Razvan Gelca (2000). Mathematical Olympiad Challenges. Birkhäuser.
Uzbekistan Academy of Sciences (2001). Foundations of Mathematical Inequalities. Tashkent: Fan Publishing.
Karimov, N. (2010). Advanced Problem Solving in Algebra and Geometry. Tashkent: O‘qituvchi.
Rashidov, M. (2005). Mathematical Methods in Olympiad Preparation. Tashkent: Sharq Publishing.
Sobirov, U. (2015). Convex Functions and Their Applications. Tashkent: Yangi Nashr.
Olimov, K., & Ergashev, S. (2012). Applied Inequalities in Modern Mathematics. Tashkent: O‘qituvchi.
Mirzayev, J. (2008). Methods of Mathematical Analysis. Tashkent: Universitet Nashriyoti.
Khakimov, B. (2019). Geometry and Inequality Problem-Solving. Tashkent: Fan Publishing.
Saidov, A. (2021). Mathematical Theory and Olympiad Applications. Tashkent: Nashr.
License
Copyright (c) 2024 Tilagov Axmadqul Abduazimovich, Tilagova Buvgilos Saidqulovna
This work is licensed under a Creative Commons Attribution 4.0 International License.