This transcript transforms mathematics from geometrization to materialization of space. It is classic evolution of complex algebra A. Cauchy into space. It gives mathematical foundation to the core physic theories; gives them a completely new interpretation in complex space. Table of contents: Problems of contemporary mathematics. Extension of complex variable of A.L. Cauchy into space. Functions of complex spatial variable. Functions differentiability. Implementation of integral theorems of A.L. Cauchy in space. Connectivity of complex space. Implementation of integral theorems in space....

The book is a continuation of research completed in "Numeric field. Introduction into theory functions of complex spatial variable." The concept of a numeric field, developed on the algebra of the laws of the real and complex numbers, provided the basis for developing the concept of coordinate axes of physical reality. The complex space changes the geometric representation of a material point, line, surface, and so on. The line is the epsilon tunnel in space. The point being the intersection of the lines becomes a spatial volume (in the simplest representation it is a sphere). A beam of light...