SYLLABUS

Mathematics 4140

Abstract Algebra 2

This is a rough guide to the topics we will cover.

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Mathematics 4140

Abstract Algebra 2

Week 1 |
Ending Friday January 20 |
Review linear algebra, vector
spaces. Section 18, 19 (Rings, integral domains and
fields) |

Week 2 |
Ending Friday January 27 |
Section 20, 22, 23 (Fermat's and
Euler's Theorems, rings of polynomials, and
factorization) |

Week 3 |
Ending Friday February 3 |
Section 26, 27, 45 (Homomorphisms
and factor rings, prime and maximal ideals, and UFDs) |

Week 4 |
Ending Friday February 10 |
Section 46, 47 (EDs and Gaussian
integers) |

Week 5 | Ending Friday February 17 |
Section 29, 30, 31 (Extension
fields, vector spaces, and algebraic extensions) |

Week 6 | Ending Friday February 24 |
Section 32, 33. (Geometric
constructions and finite fields) |

Week 7 | Ending Friday March 2 |
Review for Midterm I, Wednesday
March 7. |

Week 8 | Ending Friday March 9 |
Section 48 (Automorphisms of
fields) |

Week 9 | Ending Friday March 16 |
Section 49, 50 (Isomorphism
extension theorem, normal extensions) |

Week 10 | Ending Friday March 23 |
Section 51, 52 (Separable and
inseparable extensions) |

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SPRING BREAK |

Week 11 | Ending Friday April 6 |
Review, Midterm II, Friday April
6 |

Week 12 | Ending Friday April 13 |
Section 53, 54 (Galois theory, and examples) |

Week 13 | Ending Friday April 20 |
Section 55, 56 (Cyclotomic
extensions and quintics) |

Week 14 | Ending Friday April 27 |
Section 16, 17, 36 (Group actions
on sets, and the Sylow Theorems) |

FINAL EXAM |
SATURDAY MAY 5, 4:30 PM - 7:00 PM |

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