Lecture: Introduction to mathematical cartography, the concept of the original surface in cartographic projection, coordinate systems. The concept of regular surface-to-surface mapping and
cartographic projection. Elements of the theory of distortions in cartographic projections: particular scale, main scale and elementary scale of mapping distortions. Elementary scale of length distortion
as a function of the directional angle. Tissot's theorem I - the concept of principal directions of a mapping. Tissot's theorem II - the concept of an ellipse of projection distortions. Extreme length
distortion in the principal directions of the projection. Elementary scale of field distortions. The concept of meridian convergence, distortions of directions and extreme distortions of angles. Map
projections reductions. Classification of cartographic projections depending on local projection distortions. Classification of cartographic projections depending on the shape of graticules- the class of
multi-conical projections. Perspective map projections. Theoretical foundations of conformal mappings: isometric coordinates, theorem on conformal mappings, elementary length scale in conformal
mappings and meridian convergence. General characteristics of cartographic projections used in geodesy and cartography. Gauss-Krüger mapping and its analytical forms. Project: Construction of a
mapping grid in a given projection. Study of the nature of mapping distortions: lengths, directions, angles, surfaces. Determining the reduction of the geodetic figures in map projections
