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**PREFACE : **

Convexity provides a wide-ranging introduction for final year
undergraduates and graduate students. Convex sets and functions are
studied in the Euclidean space IRn, thus allowing an exposition
demanding only an elementary knowledge of analysis and linear algebra,
and enabling concepts to bemotivated through simple geometric examples.
The fundemental ideas of convexity are natural and appealing, and does
not have to travel far along its path, before meeting significant,
aesthetically pleasing results. It develops geometric intuition, and is a
showcase for displaying interconnections amongst different parts of
mathematics, inaddition to have ties with economics, science and
engineering. Despite being an active research field, it abounds in
unsolved problems having an instant intuitive appeal. One distinctive
feature of the book is the diverse applications that it highlights:
number theory, geometric extremum problems, combinatorial geometry,
linear programming, game theory, polytopes, bodies of constant width,
the gamma function, minimax approximation, and linear, classical and
matrixinequalities. Several topics make their first appearance in a
general introduction to convexity, while a few have not appeared outside
research journals. The account has a self-contained treatment of
volume, thus permitting a rigorous discussion of mixed volumes, is
operimetry and Brunn-Minkowskitheory. Full solutions to most of the 241
exercises are provided and detailed suggestions for further reading are
given.

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