I want our classroom, the collaborations between my students outside class, and the mathematics department as a whole, to be an environment where students feel able to share their ideas. I want to provide a space where questions are very welcome, especially on basic points.

Please ask all questions you have; remember that every question you have is likely a question that many share. Please share your insights and suggestions, partial or complete. Please treat your peers questions, comments and ideas with respect.

You may collaberate on homework, but you must write up and turn in your own problem set, and you must disclose any people with whom you worked.

You are free to seek help from me, from each other (disclosed as above), and from the tutors at the Mathlab. You absolutely

Plans for future weeks are my best estimate of my schedule but are not guaranteed. I will not change assignments (except to correct errors) once they are less than one week from their due date.

Dates | Topics | Handouts and Lecture Notes | Assigned reading | Assignments |

January 6 | Review of vectors, matrices | Basics of vectors and matrices Worksheet from Jan 6 Lecture notes for Jan 6 | ||

January 11, 13 | Review of image, kernel, invertible matrices row operations, row reduced echelon form | Slides for Jan 11 Slides for Jan 13 | Skim 1.1, read 1.2-1.6 | Problem Set 1 Solution Set 1 |

January 18, 20 | Abstract vector spaces, subspaces, linear independence, spanning, bases, dimension | The axioms of a field Slides for Jan 18 Slides for Jan 20 (edited) | Read 1.1 and 2.1-2.3 | Problem Set 2 Solution Set 2 |

January 25, 27 | Coordinates, quotient spaces | Slides for Jan 25 Slides for Jan 27 (up to slide 25) | Read 2.4, 2.6 and appendix A.4 | Problem Set 3 Solution Set 3 |

February 1, 3 | Linear transformations, the rank-nullity theorem | Slides for Feb 1 Problems for Feb 3 | Read 3.1-3.4 | Problem Set 4 Solution Set 4 |

February 8, 10 | Dual vector spaces, transpose | Slides for February 8 Miro for Feb 10 | Read 3.5 and 3.7 | Exam on February 10. Exam solutions. |

February 15, 17 | Dual vector spaces, transpose, orthogonal complement | Slides for February 15 Miro for Feb 15 Slides for February 17 Miro for Feb 17" | Reread 3.5 and 3.7 | Problem Set 5 Solution Set 5 |

February 22, 24 | Determinants | Slides from February 22 Whiteboard drawing from February 22 Slides from February 24 | We'll skip Chapter 4 and come back to it. Read 5.2-5.4 | Problem Set 6 Solution Set 6 |

March 1,3 | Spring Break! | No assignment | ||

March 8, 10 | More on determinants, start eigenvalues and eigenvectors | Problems from March 8 Miro from March 8 Problems from March 10 Miro from March 10 | Read 5.6-5.7 | Problem Set 7 Solution Set 7 |

March 15, 17 | Characteristic and minimal polynomial, triangularization | Slides from March 15 Slides from March 17 Whiteboard from March 17 | Read 6.1-6.4 | Problem Set 8 Solution Set 8 |

March 22, 24 | Direct sum decompositions coming from eigenspaces | Slides from March 22 Problems from March 22 and 24 Miro for March 22 and 24 Mathematica notebook from March 24 PDF export of Mathematica notebook from March 24 | Read 6.6-6.8 | Problem Set 9 Solution Set 9 |

March 29, 31 | Review, start inner products | Whiteboards from March 29 Slides from March 31 Problems from March 31 Miro from March 31 | Exam on March 29. Exam solutions. | |

April 5, 7 | Orthonormal bases, orthogonal projection, Gram-Schmidt algorithm | Slides from April 5 Problems from April 7 Miro for April 7 Slides from April 7 | Read 8.1-8.4 | Problem Set 10 Solution Set 10 |

April 12, 14 | Complex numbers, Hermitian, unitary and normal operators | Slides for April 12 Slides originally meant for April 14, but used on April 12 Miro from April 14 Problems from April 14 | Read 8.5 | Problem Set 11 Solution Set 11 |

April 19 | Review | Whiteboards for April 19 | Final exam 10:30-12:30 Thursday, April 28 Mason Hall 3437 |