as of 9/19/2019 |

**RINGS, FIELDS AND GALOIS THEORY (ADVANCED)** |

Country - Partner Institution - Programs: | Australia - University of Sydney - 'Australian Universities' |

UC Course Subject | Mathematics |

Number & Suffix: | 122 |

Full UC Title: | RINGS, FIELDS AND GALOIS THEORY (ADVANCED) |

Transcript Title: | RINGS/FIELDS&GALOIS |

UC QTR Units - Division: | 6.0 - Upper Division |

Course Description: | This course investigates the modern mathematical theory that was originally developed for the purpose of studying polynomial equations. The philosophy is that it should be possible to factorize any polynomial into a product of linear factors by working over a "large enough" field (such as the field of all complex numbers). Viewed like this, the problem of solving polynomial equations leads to the problem of understanding extensions of fields. This in turn leads into the area of mathematics known as Galois theory. The basic theoretical tool needed for this program is the concept of a ring, which generalizes the concept of a field. The course begins with examples of rings, and associated concepts such as subrings, ring homomorphisms, ideals, and quotient rings. These tools are then applied to study quotient rings of polynomial rings. The final part of the course deals with the basics of Galois theory, which gives a way of understanding field extensions. |

Language of Instruction: | English |

Partner Title: | RINGS, FIELDS AND GALOIS THEORY (ADV) |

Partner University Department: | Mathematics |

Partner University Course Number: | MATH3962 |