Final Study Problems are listed below the schedule.

Date | Link to Lecture Notes | Notes |
---|---|---|

Monday, August 20 | 1. Integers | |

Wednesday, August 22 | 2. Polynomials | Supplement |

Friday, August 24 | 3. Permutations | |

Monday, August 27 | 4. Vectors: span and independence | |

Wednesday, August 29 | 5. Bases and matrices | Hurricane Isaac |

Friday, August 31 | 6. Linear maps and matrix notation | |

Monday, September 3 | Labor Day Holiday | |

Wednesday, September 5 | 7. Dual spaces | |

Friday, September 7 | 8. Double dual, quotient spaces | |

Monday, September 10 | 9. Products, sums and UMP | |

Wednesday, September 12 | 10. Determinants | |

Friday, September 14 | 11. Eigenvalues and eigenvectors | |

Monday, September 17 | Class cancelled (campus security threat) | |

Wednesday, September 19 | 12. Inner product spaces | Supplemental project |

Friday, September 21 | 13. Orthonormal bases | |

Monday, September 24 | 14. Adjoints | |

Wednesday, September 26 | 15. Inroduction to groups | |

Friday, September 28 | 16. Quotient groups, homomorphisms, cosets | |

Monday, October 1 | 17. G-sets | |

Wednesday, October 3 | 18. Congugacy classes | |

Friday, October 5 | 19. Products and semidirect products | |

Monday, October 8 | 20. Categories | |

Wednesday, October 10 | 21. Modules & Abelian Groups (Free Objects) | |

Friday, October 12 | 22. Modules & Abelian Groups (Sums) | |

Monday, October 15 | 23. Morphisms of free modules and matrices | |

Wednesday, October 17 | 24. Abelian Groups (Classifying fin. gen. ones) | |

Friday, October 19 | 25. Abelian Groups (Classifying fin. gen. ones) | |

Monday, October 22 | 26. Commutative Rings: Intro. | |

Wednesday, October 24 | 27. Com. Rings: Examples in number theory | |

Friday, October 26 | 28. Com. Rings: Units and zero-divisors | |

Monday, October 29 | 29. Com. Rings: Ideals (prime and maximal) | |

Wednesday, October 31 | 30. Factorization in Domains | |

Friday, November 2 | 31. Factorizationin Polynomial Rings 1 | |

Monday, November 5 | 32. Factorization in Polynomial Rings 2 | How about A[[x]]? |

Wednesday, November 7 | 33. Cyclic Modules and F[x]-modules | |

Friday, November 9 | 34. Cyclic F[x] modules | |

Monday, November 12 | 35. Analysis of a single linear endomorphism | |

Wednesday, November 14 | -- | |

Friday, November 16 | 36. Analysis . . . endomorphism (cont.) | |

Monday, November 19 | 37. Cayley-Hamilton Theorem and applications | |

Wednesday, November 21 | Review Problems (Modules) | |

Friday, November 23 | Thanksgiving Holiday | |

Monday, November 26 | 38. Sylow Theorems | |

Wednesday, November 28 | Other topics or review problems | |

Friday, November 30 | Other topics or review problems |

Study Problems (from "June 2, 1999 Algebra Exam Syllabus")

- Groups: G1, G2, G6, G7, G9, G17, G22, G23, G25, G26
- Rings: R1, R2, R4, R5, R6, R7, R10, R13, R19, R25
- Modules: G3, G16, G19, M1, M2, M3, M4, M5, M6, M9
- Linear Algebra: L15, L16, L19, L28, L39