This book attempts to bridge the gap between the principles of pure
mathematics and the applications in physical science. After the
Moebius inversion formula had been considered as purely academic,
or beyond what was useful in the physics community for more than
150 years, the apparently obscure result in classical mathematics
suddenly appears to be connected to a variety of important inverse
problems in physical science.This book only requires readers to
have some background in elementary calculus and general physics,
and the prerequisite knowledge of number theory is not needed. It
will be attractive to our multidisciplinary readers interested in
the Moebius technique, which is a tiny but important part of the
number-theoretic methods. It will inspire many students and
researchers in both physics and mathematics. In a practical
problem, continuity and discreteness are often correlated, and few
textbooks have given attention to this wide and important field as
this one.Clearly, this book will be an essential supplement for
many existing courses such as mathematical physics, elementary
number theory and discrete mathematics.
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