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Questions of maxima and minima have great practical significance,
with applications to physics, engineering, and economics; they have
also given rise to theoretical advances, notably in calculus and
optimization. Indeed, while most texts view the study of extrema
within the context of calculus, this carefully constructed problem
book takes a uniquely intuitive approach to the subject: it
presents hundreds of extreme value problems, examples, and
solutions primarily through Euclidean geometry. Written by a team
of established mathematicians and professors, this work draws on
the authors' experience in the classroom and as Olympiad coaches.
By exposing readers to a wealth of creative problem-solving
approaches, the text communicates not only geometry but also
algebra, calculus, and topology. Ideal for use at the junior and
senior undergraduate level, as well as in enrichment programs and
Olympiad training for advanced high school students, this book's
breadth and depth will appeal to a wide audience, from secondary
school teachers and pupils to graduate students, professional
mathematicians, and puzzle enthusiasts.
As a sequel to 113 Geometric Inequalities from the AwesomeMath
Summer Program, this book extends the themes discussed in the
former book and broadens a problem-solver's competitive arsenal.
Strategies from multiple fields, such as Algebra, Calculus, and
pure Geometry provide the reader with varied methods useful in
mathematics competitions. Starting with the fundamentals such as
the triangle inequality and ""broken lines'', the book progresses
increasingly to more sophisticated machinery such as the Averaging
Method, Quadratic Forms, Finite Fourier Transforms, Level Curves,
the Erdoes-Mordell and Brunn-Minkowski Inequalities, as well as the
Isoperimetric Theorem, to name a few. Rich theory and
generalizations accompany the aforementioned topics to supply the
reader with a rigorous exploration of fields associated with
geometric inequalities.
For the curious reader looking to sharpen their arsenal of
mathematical strategies on the Olympiad level, 113 Geometric
Inequalities from the AwesomeMath Summer Program is a valuable
addition. This problem-solving methodology prompts key ideas in
other domains such as calculus or complex numbers as the solutions
are usually nonstandard in a geometric sense. Nevertheless, trying
your hand at these types of inequalities consolidates your
mathematical reasoning while exposing you to a broad range of
problems, all teeming with insightful inequality-type solutions.
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