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The book features selected techniques in the field. Inequalities
from each section are ordered increasingly by the number of
variables and the degree of difficulty. Each problem has at least
one complete solution, and many problems have multiple solutions,
useful in developing the necessary array of mathematical machinery
for competitions.
This book is a sequel to the 116 Algebraic Inequalities from the
AwesomeMath Year-round Program and 118 Inequalities for Mathematics
Competitions. It delves into other elementary techniques but also
powerful methods and generalizations for constrained optimization
in the theory of inequalities. In the first section, the reader
will encounter each of Abel's, Newton's, Maclaurin's, and Blundon's
inequalities, the method of mathematical induction, the "mixing"
and "stronger mixing" variable methods, and the method of Lagrange
multipliers. The next sections are dedicated to the proposed
problems, which are divided into introductory and advanced. Each
problem is given at least one complete solution, and many problems
have multiple solutions.
This book would certainly help Olympiad students who wish to
prepare for the study of inequalities, a topic now of frequent use
at various competitive levels. The inequalities from each section
are ordered increasingly by the number of variables: one, two,
three, four, and multi-variables. Each problem has at least one
complete solution and many problems have multiple solutions, useful
in developing the necessary array of mathematical machinery for
competitions.
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