# 401-2003-00L Algebra I

Semester | Autumn Semester 2017 |

Lecturers | E. Kowalski |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | Introduction and development of some basic algebraic structures - groups, rings, fields. |

Learning objective | Introduction to basic notions and results of group, ring and field theory. |

Content | Group Theory: basic notions and examples of groups; Subgroups, Quotient groups and Homomorphisms, Sylow Theorems, Group actions and applications Ring Theory: basic notions and examples of rings; Ring Homomorphisms, ideals and quotient rings, applications Field Theory: basic notions and examples of fields; finite fields, applications |

Literature | J. Rotman, "Advanced modern algebra, 3rd edition, part 1" http://bookstore.ams.org/gsm-165/ J.F. Humphreys: A Course in Group Theory (Oxford University Press) G. Smith and O. Tabachnikova: Topics in Group Theory (Springer-Verlag) M. Artin: Algebra (Birkhaeuser Verlag) R. Lidl and H. Niederreiter: Introduction to Finite Fields and their Applications (Cambridge University Press) B.L. van der Waerden: Algebra I & II (Springer Verlag) |