# 401-2004-00L Algebra II

Semester | Spring Semester 2019 |

Lecturers | R. Pandharipande |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | The main topics are field extensions and Galois theory. |

Objective | Introduction to fundamentals of field extensions, Galois theory, and related topics. |

Content | The main topic is Galois Theory. Starting point is the problem of solvability of algebraic equations by radicals. Galois theory solves this problem by making a connection between field extensions and group theory. Galois theory will enable us to prove the theorem of Abel-Ruffini, that there are polynomials of degree 5 that are not solvable by radicals, as well as Galois' theorem characterizing those polynomials which are solvable by radicals. |

Literature | Joseph J. Rotman, "Advanced Modern Algebra" third edition, part 1, Graduate Studies in Mathematics,Volume 165 American Mathematical Society Galois Theory is the topic treated in Chapter A5. |

Prerequisites / Notice | Prerequisites is Rahul Pandharipande's course "Algebra I" or similar, in Rotman's book ideally Chapter A3 and A4. |