This book attempts to bridge the gap between the principles of pure mathematics and the applications in physical science. After the Mbius 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 prerequisite knowledge of number theory is not needed. It will be attractive to our multidisciplinary readers interested in the Mbius 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 textbook have given attention to this wide and important field as this book.

Clearly, this book will be an essential supplement for many existing courses such as mathematical physics, elementary number theory and discrete mathematics.