**Instructor:** John Voight

**Course on canvas.dartmouth.edu.**⇗

## Course Summary

Date | Details | Due |
---|---|---|

Mon Sep 11, 2023 | Finite-dimensional vector spaces | 12:50pm to 1:55pm |

Tue Sep 12, 2023 | Matrices, change of basis | 1:20pm to 2:10pm |

Wed Sep 13, 2023 | Bases, sums and direct sums, free vector spaces | 12:50pm to 1:55pm |

Fri Sep 15, 2023 | Quotients, factors through, rank-nullity | 12:50pm to 1:55pm |

Mon Sep 18, 2023 | Exact sequences, splitting | 12:50pm to 1:55pm |

Wed Sep 20, 2023 | Duals, pullback | 12:50pm to 1:55pm |

Assignment Weekly Homework #1 | due by 5pm | |

Mon Sep 25, 2023 | Annihilators, bilinear forms | 12:50pm to 1:55pm |

Wed Sep 27, 2023 | Kernels, symmetric bilinear forms, orthogonal group | 12:50pm to 1:55pm |

Assignment Weekly Homework #2 | due by 5pm | |

Fri Sep 29, 2023 | Diagonalization, adjoints, real inner product spaces | 12:50pm to 1:55pm |

Mon Oct 2, 2023 | Sesquilinear forms, unitary, Hermitian, complex inner product spaces | 12:50pm to 1:55pm |

Wed Oct 4, 2023 | Diagonalizability, upper triangularizability | 12:50pm to 1:55pm |

Assignment Weekly Homework #3 | due by 5pm | |

Mon Oct 9, 2023 | Normal operators, spectral theorem | 12:50pm to 1:55pm |

Tue Oct 10, 2023 | SVD, matrix factorizations | 1:20pm to 2:10pm |

Wed Oct 11, 2023 | Tensor products | 12:50pm to 1:55pm |

Assignment Weekly Homework #4 | due by 5pm | |

Fri Oct 13, 2023 | Tensor products continued, multilinear forms | 12:50pm to 1:55pm |

Mon Oct 16, 2023 | Symmetric and exterior powers, determinants | 12:50pm to 1:55pm |

Wed Oct 18, 2023 | Algebras | 12:50pm to 1:55pm |

Assignment Weekly Homework #5 | due by 5pm | |

Fri Oct 20, 2023 | Categories, functors | 12:50pm to 1:55pm |

Mon Oct 23, 2023 | Natural transformations, universal properties | 12:50pm to 1:55pm |

Wed Oct 25, 2023 | Modules, free modules, quotients, isomorphism theorem | 12:50pm to 1:55pm |

Assignment Weekly Homework #6 | due by 5pm | |

Fri Oct 27, 2023 | Exact sequences, splitting, projective modules, tensor products | 12:50pm to 1:55pm |

Mon Oct 30, 2023 | Modules over PIDs | 12:50pm to 1:55pm |

Wed Nov 1, 2023 | Canonical forms | 12:50pm to 1:55pm |

Assignment Weekly Homework #7 | due by 5pm | |

Fri Nov 3, 2023 | Linear representations, decomposable, Maschke's theorem | 12:50pm to 1:55pm |

Mon Nov 6, 2023 | Operations on linear representations | 12:50pm to 1:55pm |

Wed Nov 8, 2023 | Characters, Schur's lemma | 12:50pm to 1:55pm |

Fri Nov 10, 2023 | Character tables, orthogonality | 12:50pm to 1:55pm |

Mon Nov 13, 2023 | Wrap up | 12:50pm to 1:55pm |

Assignment Weekly Homework #8 | due by 5pm | |

Tue Nov 14, 2023 | Assignment Daily Homework | due by 1:20pm |

Mon Nov 20, 2023 | Assignment Final Exam (due) | due by 8am |