Mathematics is considered as an important and necessary component of universal culture, as an example of the structure of knowledge "weapons for reflection." It is interpreted primarily as a model for building concepts, equally important for any humanitarian discipline. Sections intended for students of economic specialties are highlighted. The fundamental feature of the book is increased attention to (mathematical) logic and conceptual issues, therefore, it includes remarkable discoveries of mathematics of the 20th century. (including the foundations of computer science - discrete mathematics, algorithms and recursion).