Home Page of Alistair Savage | Department of Mathematics and Statistics | Virtual Campus | Sessional Dates |

The syllabus will be updated as the course progresses. Unless otherwise indicated, section numbers and exercises refer to the text *Linear Algebra* by Sterling K. Berberian.

Date |
Text Sections |
Material
| Recommended Exercises ^{*} |

Sep 9 | Lecture notes only | Sets with operations (magmas) | Exercises in notes only |

Sep 13 | A.4 | Fields | Exercises in notes only |

Sep 16 | 1.3 | Vector spaces: definition and examples | Page 14: Exercises 1, 3, 4 |

Sep 20 | 1.3–1.6 | Some properties of vector spaces, linear combinations, subspaces | Page 17: Exercises 1–5; Page 19: Exercises: 1, 4–8 |

Sep 23 | 1.6 | Subspaces | Page 22: Exercises (3)–(5), (8), (10), (11), (13), (16), (17) |

Sep 27 | 2.1, 2.2 | Linear mappings | Page 28: Exercises (1)–(4), (7); Page 31: Exercise (3) |

Sep 30 | 2.2, 2.3 | Kernel, image, vector spaces of linear mappings | Page 31: Exercises (1), (2), (4)–(6); Page 35: Exercises (2), (3), (11)–(16), (19), (20) |

Oct 4 | 2.3, 2.4 | Isomorphisms | Page 35: Exercises (9), (10), (21), (23), (24); Page 39: Exercises (2), (5)–(11), |

Oct 7 | 2.4, 2.5 | Isomorphisms, equivalence relations | Page 45: Exercises (2)–(5) |

Oct 14 | 2.5 | Equivalence relations, partitions | Page 45: Exercise (7) |

Oct 18 | 2.6, 2.7 | Quotient vector spaces, the first isomorphism theorem | Page 48: Exercises (1)–(6); Page 50: Exercises (1)–(6) |

Oct 21 | Midterm exam (covers material up to and including lecture of October 18) |
||

Nov 1 | 3.1–3.3 | Generating sets, linear dependence/independence | Page 54: Exercises (1)–(4); Page 57: Exercises (3)–(5), (7), (8); Page 59: Exercises (1)–(7), (12) |

Nov 4 | 3.3, 3.4 | Linear dependence/independence, finitely generated vector spaces | Page 59: Exercises (9), (11), (13); Page 65: Exercises (1), (4), (6) |

Nov 8 | 3.4, 3.5 | Basis | Page 65: Exercise (7); Page 71: Exercises (1)–(3), (5)–(8), (11), (13), (18) |

Nov 11 | 3.5 | Dimension | Page 71: Exercises (9), (10), (12), (14), (20) |

Nov 15 | 3.6–3.8 | Conservation of dimension, dimensions of spaces of linear maps | Page 76: Exercises (1)–(5), (7)–(12), (14); Page 80: Exercises (3), (6), (7); Page 83: Exercises (2), (3), (7), (8), (10) |

Nov 18 | 3.9 | Student course evaluations. Linear functionals and dual spaces |
Page 89: Exercises (2), (3), (5)–(7), (10), (12), (13) |

Nov 22 | 4.1–4.9 | Matrices | Page 101: Exercises (1)–(5), (7)–(12) |

Nov 25 | 4.10 | Change of basis, similar matrices, inner product spaces | Page 128: Exercises (2), (3), (6)–(8) |

Nov 29 | 5.1 | Orthogonality, Gram-Schmidt algorithm | Page 135: Exercises (1), (3)–(9) |

Dec 2 | 5.2–5.4 | Discussion of final exam. Duality revisited, adjoints | Page 140: Exercises (1), (2), (4), (6), (7); Page 146: (1), (3), (4), (7) |

Dec 6 | 6.4–6.7 | Characteristic polynomials, diagonalizing symmetric matrices | Page 171: Exercises (1)–(3); Page 176: Exercise (1); Page 181: Exercise (1) |

Dec 8 | N/A | Review | N/A |