Inequalities: A Mathematical Olympiad Approach
- ISBN-10
- 303460050X
- ISBN-13
- 9783034600507
- Series
- Inequalities
- Category
- Mathematics
- Pages
- 220
- Language
- English
- Published
- 2010-01-01
- Publisher
- Springer Science & Business Media
- Authors
- Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado
Description
This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.
Get the book
Other editions
-
- 2012-12-06
- 711 pages
- Ebook
- Springer Science & Business Media
-
- 2012-01-06
- 444 pages
- Ebook
- Springer Science & Business Media
-
- 2010-11-25
- 909 pages
- Ebook
- Springer Science & Business Media
Similar books
-
Savage Inequalities: Children in America's Schools
By Jonathan KozolIn Savage Inequalities, Kozol delivers a searing examination of the extremes of wealth and poverty and calls into question the reality of equal opportunity in our nation's schools.
-
Inequalities for Differential and Integral Equations
For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course.
-
Inequalities
By G. H. Hardy, G. Polya, J. E. LittlewoodThis classic of the mathematical literature forms a comprehensive study of the inequalities used throughout mathematics.
-
Equations and Inequalities: Elementary Problems and Theorems in Algebra and Number Theory
By Jiri Herman, Radan Kucera, Jaromir SimsaWhile it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here.
-
Concentration Inequalities: A Nonasymptotic Theory of Independence
By Gabor Lugosi, Stéphane Boucheron, Pascal MassartDescribes the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory.
-
General Inequalities 7: 7th International Conference [on General Inequalities] at Oberwolfach, November 13-18, 1995
By Wolfgang Walter, Catherine Bandle, William N. EverittNote on Wirtinger's inequality Horst Alzer Abstract In this note we refine the following theorem due to W. Wirtinger : If f has period 27 and satisfies $ 2 * f ( x ) dx = 0 , then 27 [ $ * ( z ) dx < " 1 * s ( ) with strict inequality ...
-
Inequalities in Statistics and Probability: Proceedings of the Symposium on Inequalities in Statistics and Probability, October 27-30, 1982, Lincoln, Nebraska
By Ingram Olkin, Yung Liang Tong5 ( 1984 ) , 1-3 INTRODUCTION BY Y. L. TONG University of Nebraska As noted by Pólya ( 1967 ) , " Inequalities play a role in most branches of mathematics and have widely different applications . " This is certainly true in statistics ...
-
Differential and Integral Inequalities
By Wolfgang WalterIn 1964 the author's mono graph "Differential- und Integral-Un gleichungen," with the subtitle "und ihre Anwendung bei Abschätzungs und Eindeutigkeitsproblemen" was published. The present volume grew out of the response...
-
Health inequalities: Persistence and change in modern welfare states
By Johan P. MackenbachEuropean Union Statistics on Income and Living Conditions survey (EU-SILC) 98b, 185n6 evidence health inequality ... 50, 51 explanation of health inequalities 97 analyses 97,98b exploitative nature of capitalism 142–43 farmers 16 ...
-
Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications
By Baasansuren Jadamba, Akhtar A. Khan, Joachim GwinnerDOI: 10.1201/9781315228969-4 4.1 Illustrative Examples 4.2 Linear Variational Inequalities 4.2.1 Some Basic Results 4.2.2 Regularization for Linear Variational Inequalities 4.2.3 Recession Approach for Linear Variational Inequalities ...