数学反演思想及其发展

In this thesis, the author intends to discuss the ideological differentiae and mutual relations among the inversion transformation, the series reversion, the inverse problem theory, the method of relation mapping inversion, and the inversion set theory. The author points out that method of relation mapping inversion comprises series reversion, while series reversion includes inversion transformation, therefore, method of relation mapping inversion and inverse problem theory could unified into inversion set theory within finite set. The author also illustrates the applications of inversion set theory in the inverse problem theory (joint inversion).