2009, by Viet Publishing.
The book aims, first, to provide students with a comprehensive and minute system of typical inequality demonstration methods and techniques, ranging from classical to modern ones, which, due to the fact that their importance remains unchanged throughout the flow of time, can be considered as “diamonds in mathematical inequalities”. This main purpose is accomplished by a number of valuable mathematic samples with interesting “lead-ins” and, most importantly, a dialectic viewpoint on each solving method. The major goal of the authors is, therefore, to helping students to acquire multitude of mathematical tools and methods in solving inequalities, then, be able to achieve excellence in this field. Besides, on utilizing a new approach in presenting familiar mathematical facts, the authors also hope to highlight in readers’ mind the importance of a good mathematical inequality-based thinking in developing their creativeness as well as their ability to critically evaluate changes in life.
The success of this book will also mean the publication of the authors’ other books on other fields of secondary mathematics.
Diamonds in classical mathematical inequalitiesAM-GM inequalities
Cauchy-Schwarz inequalities
Holder inequalities
Minkowski inequalities
Chebyshev inequalities
Diamonds in modern mathematical inequalitiesSchur inequalities
Muirhead inequalities
Permutation inequalities
Diamonds of analytic methodFermat theorem (Derivative method)
Lagrange theorem
Bernoulli inequalities
Diamonds in mathematical inequalitiesJensen inequalities
Karamata inequalities
Vasile Cirtoaje inequalities (RCF, LCF and LCRCF theorem)
Popoviciu inequalities
Riman theorem (Integral method)
Diamonds in contemporary inequalitiesUCT method
SOS method
GMV method
ABC method
Equal variable method
Geometricalize Algebra method
Divide and conquer method
Some creations on mathematical inequalitiesSelective papers on inequalities
Nice solutions to selective inequalities
Challenging problems