Algebraic curves and surfaces are determined by polynomial equations. The order respectively the degree of a curve or surface is given by the maximal sum of exponents. The order has an geometric interpretation in \(\mathbb{R}^3\): The intersection of a surface of order \(n\) and a line has a maximal number of /(n/) points.

Combinatorical Geometry

In the field of combinatorial geometry one studies properties of countable geometric objects.

Topology

Topology is the study of mathematical objects and their properties which persist under deformation.

Kinematics and Mechanics

Kinematics describes the movement of points, objects, and groups of objects. Mechanic deals with the behavior of objects under certain forces.

Differential Geometry

In differential geometry one studies the properties of geometric objects, which don't rely on any parametrization.

Algebra

Analysis, Trigonometric und Taylor Series, Orthogonal Functions, Transcendental Configurations, Probability Theory

Theory of Functions of Complex Variables

In complex theory of functions one studies differentiable mappings into the complex numbers.

Differential Equations, Extension and Oscillation Processes, Wave Theory

Differential equations are equations which contain a function and it's derivatio(s). They describe standard phenomenons as movement. Expension and oscillation can be described and analysed by partial differential equations.