The following is a **tentative** syllabus for the course.
This page will be updated irregularly. On the other hand, the weekly syllabus
contained in the Homework assignments page will always be accurate.

week | Date | Sections | Brief Description |
---|---|---|---|

1 | 3/30 M | Introduction to Mathematical Proofs | |

4/1 W | 1.1-1.2 | Vectors and Vector Spaces | |

4/3 F | 1.2 | Vector Spaces (cont.) | |

2 | 4/6 M | 1.3 | Subspaces |

4/8 W | 1.4 | Linear Combinations and System of Linear Equations | |

4/10 F | 1.5 | Linear Dependence and linear Independence | |

3 | 4/13 M | 1.6 | Bases and Dimension |

4/15 W | 2.1 | Linear Transformations | |

4/17 F | 2.1 | Null Spaces and Ranges | |

4 | 4/20 M | 2.2 | Matrix Representation |

4/22 W | 2.3 | Composition of Linear Transformations | |

4/24 F | 2.4 | Invertibility | |

5 | 4/27 M | 2.4 | Isomorphisms |

4/29 W | 2.5 | Change of Coordinate Matrix | |

5/1 F | 3.1 | Elementary Matrix Operations and Elementary Matrices | |

6 | 5/4 M | 3.2 | The Rank of a Matrix and Matrix Inverses |

5/6 W | 3.3 | System of Linear Equations (Theoretical) | |

5/8 F | 3.3 | System of Linear Equations (Computational) | |

7 | 5/11 M | 4.1 | Determinants of Order 2 |

5/13 W | 4.2 | Determinants of Order n | |

5/15 F | 4.3 | Properties of Determinants | |

8 | 5/18 M | 5.1 | Eigenvalues and Eigenvectors |

5/20 W | 5.1 | Eigenvalues and Eigenvectors (cont.) | |

5/22 F | 5.2 | Diagonalizability | |

9 | 5/25 M | 5.2 | Diagonalizability (cont.) |

5/27 W | 6.1 | Inner Products and Norms | |

5/29 F | 6.2 | Gram-Schmidt Process | |

10 | 6/1 M | 6.3, 6.4 | Normal and Self-adjoint Operators |

6/3 W | 6.5 | Unitary and orthogonal operators |