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Objectives and competences

Learning fundamental algebraic concepts and abstract thinking.

Content (Syllabus outline)

An overview of algebraic structures: semigroups, groups, rings, fields, vector spaces, algebras. Substructures. Generators. Direct products and sums. Examples of groups and rings: the integers, the integers modulo n, the quaternions, matrix rings and linear groups, rings of functions, polynomial rings, symmetric groups, dihedral groups. Homomorphisms: basic notions and examples. Cayley's theorem. Field of fractions. Quotient structures: normal subgroups and quotient groups, ideals and quotient rings, isomorphism theorems. Finite groups: Lagrange's theorem, Caucy's theorem, group actions, Sylow theorems, simple groups, finite Abelian groups.

Learning and teaching methods

- Lectures - Tutorial

Intended learning outcomes - knowledge and understanding

Knowledge and Understanding: - The knowledge of basic algebraic structures and their substructures, homomorphisms, and quotient structures. - Understanding the basics of the theory of finite groups.

Intended learning outcomes - transferable/key skills and other attributes

Transferable/Key Skills and other attributes: - The obtained knowledge is a prerequisite for a study of almost any area of mathematics.

Readings

M. Brešar, Uvod v algebro, DMFA, 2018. M. Brešar, Undergraduate algebra. A unified approach, Springer, 2019. D. S. Dummit, R. M. Foote, Abstract Algebra, Prentice-Hall International, Inc., 1991. J. Gallian: Contemporary Abstract Algebra, Brooks/Cole, 2013. I. Vidav, Algebra, DMFA, 1980.

Prerequisits

Linear algebra

  • red. prof. dr. MATEJ BREŠAR

  • Written exam or 2 written test: 50
  • Oral examination: 50

  • : 60
  • : 45
  • : 135

  • Slovenian
  • Slovenian