Class | Date | Sections | Brief Description |
---|---|---|---|

1 | Monday, 1/22 | 1.1 | Introduction, Overview of Linear Algebra |

2 | Wednesday, 1/24 | 1.2 - 1.3 | Mathematical Statements, Quantifiers (For all, There exists), Negations |

3 | Friday, 1/26 | 1.3 - 1.4 | Alternations of Quantifiers, Mathematical Definitions |

4 | Monday, 1/29 | 1.4 | Evens and Odds, Contrapositives and Contradictions |

5 | Wednesday, 1/31 | 1.5 | Sets, Constructing Sets, Subsets |

6 | Friday, 2/2 | 1.5 - 1.6 | Set Equality, Set Operations, Functions |

7 | Monday, 2/5 | 1.6 - 1.7 | Injective, Surjective, and Bijective Functions |

8 | Wednesday, 2/7 | 1.7 - 2.2 | Inverse Functions, Solving Equations, Vectors in R^2 |

9 | Friday, 2/9 | 2.3 | The Span of Vectors in R^2 |

10 | Monday, 2/12 | 2.3 - 2.4 | Bases, Linear Transformations: Definitions and Examples |

11 | Wednesday, 2/14 | 2.4 | Linear Transformations: Properties and Bases |

12 | Friday, 2/16 | 2.4 - 2.5 | Operations on Linear Transformations, The Standard Matrix |

13 | Monday, 2/19 | - | First Exam |

14 | Wednesday, 2/21 | 2.5 | The Standard Matrix, Examples (Rotations, Projections, Reflections) |

15 | Friday, 2/23 | 2.6 | Matrix Algebra |

16 | Monday, 2/26 | 2.7 | The Range and Null Space of a Linear Transformation |

17 | Wednesday, 2/28 | 2.7 - 3.1 | Inverses of Matrices, Coordinates and Change of Basis |

18 | Friday, 3/1 | 3.2 | Matrices with Respect to Other Coordinates |

19 | Monday, 3/4 | 3.2 - 3.3 | Changing Coordinates, Eigenvalues and Eigenvectors |

20 | Wednesday, 3/6 | 3.3 | Characteristic Polynomial, Diagonalization |

21 | Friday, 3/8 | 3.3 - 3.4 | Diagonalization, Determinants |

22 | Monday, 3/11 | 3.4 - 4.1 | Determinants, Vector Spaces |

23 | Wednesday, 3/13 | 4.1 | Vector Spaces, Subspaces |

24 | Friday, 3/15 | 4.1 - 4.2 | Spans, Linear Systems |

- | - | - | Spring Break |

25 | Monday, 4/1 | 4.2 | Solving Linear Systems, Augmented Matrices, Echelon Forms |

26 | Wednesday, 4/3 | - | Second Exam |

27 | Friday, 4/5 | 4.2 | Reduced Echelon Form, Spans in Polynomial and Function Spaces |

- | Monday, 4/8 | - | Class Canceled |

28 | Wednesday, 4/10 | 4.3 | Spanning Sequences |

29 | Friday, 4/12 | 4.4 | Linearly Independent Sequences |

30 | Monday, 4/15 | 4.5 | Bases and Coordinates |

31 | Wednesday, 4/17 | 4.5 | Trimming Spanning Sequences to Bases |

32 | Friday, 4/19 | 4.6 | Dimension |

33 | Monday, 4/22 | 5.1 | General Linear Transformations, Matrices |

34 | Wednesday, 4/24 | 5.1 - 5.2 | Matrices, The Range and Null Space of a Linear Transformation |

35 | Friday, 4/26 | 5.2 | Rank and Nullity |

36 | Monday, 4/29 | - | Third Exam |

37 | Wednesday, 5/1 | 5.2 | Injective and Surjective Linear Transformations, Invertible Matrices |

38 | Friday, 5/3 | 5.3 | Determinants |

39 | Monday, 5/6 | 5.3 | Determinants, Cofactor Expansions |

40 | Wednesday, 5/8 | 5.4 | Eigenvalues and Eigenvectors |

41 | Friday, 5/10 | - | Markov Chains, Fitting Lines to Data |