Notes on Math 541: Modern Algebra @ University of Wisconsin-Madison

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# Course Website

# Textbook

Abstract Algebra, by Dummit and Foote, Third Edition, 2004

# Lecture Notes

Week 1 | |
---|---|

1/24 | Divides, Equivalence Relations |

1/26 | Well-ordering of Z |

Week 2 | |

1/29 | Division Algorithm, gcd |

1/31 | Euclidean Algorithm |

2/2 | Equivalence Class, Z/nZ, Group |

Week 3 | |

2/5 | Group, Well-definedness, Z/nZ |

2/7 | (Z/nZ)*, Properties of Group |

2/9 | Order, Symmetric Group |

Week 4 | |

2/12 | Symmetric Group, Cycle |

2/14 | Homomorphism, Isomorphism |

2/16 | Order, Homomorphism, Subgroup |

Week 5 | |

2/19 | Dihedral Groups, Subgroup |

2/21 | Cyclic Group, lcm, Order of g^a |

2/23 | Cyclic Subgroup, Generating Set of a Group |

Week 6 | |

2/26 | Finitely Generated Group |

2/28 | Coset, Normal Subgroup |

3/2 | Exam 1 |

Week 7 | |

3/5 | Quotient Group, Index, Lagrange’s Theorem |

3/7 | Corollaries of Lagrange’s Theorem |

3/9 | The First & Second Isomorphism Theorems |

Week 8 | |

3/12 | The Third Isomorphism Theorem |

3/14 | Transposition, Sign of Permutation |

3/16 | Homework 6, The Correspondence Theorem |

Week 9 | |

3/19 | Sign of Permutation, Alternating Group |

3/21 | Subgroups of A_4, Group Action, Orbit, Stabilizer |

3/23 | Orbit, Stabilizer, Cayley’s Theorem |

Week 10 | |

4/2 | Conjugacy Class, The Class Equation |

4/4 | Cauchy’s Theorem, Recognizing Direct Products |

4/6 | Homework 8, Properties of Finite Abelian Group |

Week 11 | |

4/9 | Fundamental Theorem of Finite Abelian Groups |

4/11 | Definition of Ring |

4/13 | Exam 2 |

Week 12 | |

4/16 | Properties of Ring, Zero-Divisor, Unit |

4/18 | Field, Product Ring, Integral Domain |

4/20 | Product Ring, Finite Domain and Field, Subring |

Week 13 | |

4/23 | Polynomial Ring, Ideal, Principal Ideal |

4/25 | Examples of Ideals, Quotient Ring |

4/27 | Isomorphism Theorems for Rings |

Week 14 | |

4/30 | Generating Ideal, Maximal Ideal, Prime Ideal |

5/2 | Prime Ideal, Euclidean Domain |

5/4 | Review, Galois Theory |