A1 Orthogonal projections (to one plane, Monge's projection, axonometry, topography) - principles, basic construction, applications.

A2 Skew projections (to one plane, skew axonometry) - principles, basic construction, applications.

A3 Central projections (central projection, linear perspective, perspective axonometry) - principles, basic construction, applications.

A4 Perspective affinity and its using as a tools in solving problems in descriptive geometry. Plane intersection of prismatic and circle cylindrical surface.

A5 Perspective collineation and its application to solve problems in descriptive geometry. Plane intersection of the pyramid and the circular cone.

A6 Geometric base of photogrametry. Internal and external orientation of a scan. Reconstruction from one orthogonal and one skew image.

A7 Classification and principles of cartographic projections (planar, cylindrical, conic, other). Planar cartographic projections (orthographic, stereographic, gnomonic).

A8 CAD systems as a tool for creating and work with technical drawings (principles, standards and practical use).

A09 Torsion of a curve. Frenet's formulas.

A10 Singular points of planar curves.

A11 The first fundamental form of a surface and computation of the lengths, angles and area on a surface.

A12 Dupin's indicatrix and conjugate directions in the tangent plane of a surface.

A13 Principal directions and curvatures of a surface, Weingarten mapping.

A14 Gaussian curvature of surfaces.

A15 Ideals in commutative rings (particularly in rings of polynomials).

A16 Affine and projective algebraic varieties. Associated ideal of an algebraic variety.

A17 Zariski's topology. Decomposition of algebraic variety into irreducible components.

A18 Coordinate ring variety. Morphisms and rational varieties.

A19 Ordering of monomes in polynomial rings. Algorithm of division, Gröbner's base ideal, calculations in algebraic geometry, applications of Gröbner base.

A20 Quadratic surfaces of revolution. Basic problems of descriptive geometry on quadratic surfaces of revolution.

A21Helix and its properties. Construction of the tangent, osculation plane and center of curvature in projections methods.

A22 Quadratic surfaces, definition, constructions, basic properties. Ruled surfaces, non-ruled surfaces, their affine classification (ellipsoids, paraboloids, hyperboloids).

A23 Developable surfaces, constructions and applications in technical practice. Helicoid surface as a developable surface. Construction, properties and developing into a plane.

A24 Non-developable ruled surfaces. Chasles theorem and its applications (conoids, helicoid). Tangent plane of non-developable ruled surfaces.

A25 Helicoid surfaces. Linear and cyclic helicoid surfaces. A helicoid as a conoid.

A26 Non-ruled surfaces of technical practice (wedge, sum, cyclical). Basic properties and examples of their application.

A27 Hermit and Bezier segment, their properties and evaluation algorithms.

A28 Hermit cubic splines - construction, properties, examples of endpoint conditions.

A29 B-spline curves, knot sequence, construction, modeling of B-spline curves.

A30 Beta-spline curves, continuity conditions, properties of a segment, modeling of a curve.

A31 Construction of rational curves, rational Bézier curves and their modeling.

A32 Surfaces determined by the boundary conditions - Coons patches. Construction and mathematical description of ruled, bilinear and bicubic patches.

A33 Tensor product surfaces, properties of Bézier bicubic patch.

B01 Applying didactic principles in teaching of descriptive geometry.

B02 Organization of curriculum plans and creation of curriculum topics in descriptive geometry.

B03 Applications of education methods in descriptive geometry.

B04 Specifics of problem solutions in descriptive geometry (complete solution, construction problems).

B05 Steps and tools of development of spatial imagination.

B06 Development of logical reasoning. Complete sorting with examples in descriptive geometry.

B07 Education in descriptive geometry (axioms, definitions, theorems).

B08 Functions and techniques of proving in descriptive geometry.

B09 Organizational forms of education in descriptive geometry at schools.

B10 Descriptive geometry and modern means of education.