Classical algebraic structures and their applications

Master's seminars

Several basic algebraic structures are studied. In particular: groups and semigroups, rings and algebras,

modules, matrices and linear representations. Classical results and open problems are discussed and a variety of applications is presented.

Several basic algebraic structures are studied. In particular: groups and semigroups, rings and algebras,

modules, matrices and linear representations. Classical results and open problems are discussed and a variety of applications is presented.

References will be given at the first meeting.

1. Knows the selected aspects of classical algebraic structures,

which are discussed at the seminar, their relationships, as well as the place the referred issues in the broader theory and reference to selected open problems.

2. Is able to clearly present the appropriate parts of the theory of

some algebraic structures and discuss them in a creatively

transformed way. He can produce sub-questions and hypotheses,

seek their solutions and fill in the gaps in the available

studies of selected issues.

3.. Knows his own limitations on existing knowledge of selected

issues discussed at the seminar, and the need of futher developments.

4. Can independently search for literature on the issues that

are discussed at the seminar and present synthetically a selected material.

Can independently search for literature on the issues that are discussed at the seminar, also in English, and present synthetically a selected material.

5. Knows examples of applications of algebraic structures and their properties in other areas of mathematics, including solving important problems formulated in a language of school mathematics

.

6. Can interact with other participants of the seminar, lead

joint discussions on issues they are working on, can share his own thoughts on discussed problems.

Grade based on presented talks and other activities on a seminar