# 14-1100/Navigation

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Welcome to Math 1100!
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# | Week of... | Notes and Links |
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1 | Sep 8 | About This Class; Monday - Non Commutative Gaussian Elimination; Thursday - the category of groups, automorphisms and conjugations, images and kernels. |

2 | Sep 15 | Monday - coset spaces, isomorphism theorems; Thursday - simple groups, Jordan-Holder decomposition series. |

3 | Sep 22 | Monday - alternating groups, group actions, The Simplicity of the Alternating Groups, HW1, HW 1 Solutions, Class Photo; Thursday - group actions, Orbit-Stabilizer Thm, Class Equation. |

4 | Sep 29 | Monday - Cauchy's Thm, Sylow 1; Thursday - Sylow 2. |

5 | Oct 6 | Monday - Sylow 3, semi-direct products, braids; HW2; HW 2 Solutions; Thursday - braids, groups of order 12, Braids |

6 | Oct 13 | No class Monday (Thanksgiving); Thursday - groups of order 12 cont'd. |

7 | Oct 20 | Term Test; Term Test Solutions on Monday, HW3; HW 3 Solutions; Thursday - solvable groups, rings: defn's & examples. |

8 | Oct 27 | Monday - functors, Cayley-Hamilton Thm, ideals, iso thm 1; Thursday - iso thms 2-4, integral domains, maximal ideals, One Theorem, Three Corollaries, Five Weeks |

9 | Nov 3 | Monday - prime ideals, primes & irreducibles, UFD's, Euc.DomainPID, Thursday - Noetherian rings, PIDUFD, Euclidean Algorithm, modules: defn & examples, HW4, HW 4 Solutions |

10 | Nov 10 | Monday - R is a PID iff R has a D-H norm, R-modules, direct sums, every f.g. module is given by a presentation matrix, Thursday - row & column reductions plus, existence part of Thm 1 in 1t3c5w handout. |

11 | Nov 17 | Monday-Tuesday is UofT's Fall Break, HW5, Thursday - 1t3c5w handout cont'd, JCF Tricks & Programs handout |

12 | Nov 24 | Monday - JCF Tricks & Programs cont'd, tensor products, Thursday - tensor products cont'd |

13 | Dec 1 | End-of-Course Schedule; Monday - tensor products finale, extension/reduction of scalars, uniqueness part of Thm 1 in 1t3c5w, localization & fields of fractions; Wednesday is a "makeup Monday"! |

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See Non Commutative Gaussian Elimination |