Mathematics

Originally, algebra dealt with solving algebraic equations such as . Formulas for solving equations with a degree of at most four were developed over the years, and finally it was proved that equations of a higher degree cannot be solved with the help of radicals (i.e. with the help of terms consisting of roots of the coefficients).

In the beginning of the 19th century, the development of modern algebra began: Thenceforward, the analysis of algebraic structures – which are sets of elements for which at least one algebraic operator is defined – became more and more important. Some examples for such algebraic structures are:

• groups
• rings
• integral domains
• unique factoriation domains
• principal ideal domains
• euclidean rings
• fields
• vector spaces
• lattices
• etc.

The course "Algebra", which is usually attended in the third semester, offers a closer look at these algebraic structures.

Before that, one generally attends two introductory courses treating the subjects of linear algebra and analytic geometry which cover (of course) some aspects of algebra as well as of geometry:

• The course "Linear Algebra and Analytic Geometry I" deals with vector spaces, matrices and determinants, linear mappings and the basics of affine and projetive geometry.
• The course "Linear Algebra and Analytic Geometrie II" deals with sesquilinear forms, inner products, quadrics and linear optimization (among others).

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