**MATH 19620 (Linear Algebra)** is a linear algebra course taught at the University of Chicago, targeted primarily at economics and other social science majors. I taught the course twice, once in Spring 2012-13, and once in Autumn 2013-14 (these were successive academic quarters, with a summer break in between). I’ll include links to lecture notes and other material on this page. The course materials below are for the most recent version of the course I taught, namely the one in Autumn 2013-14.

#### Alternative learning recommendations

If you’re interested in recommendations for learning linear algebra, see Cognito Mentoring’s linear algebra learning recommendations page, to which I was a primary contributor.

#### Textbook

The textbook for the course was Linear Algebra with Applications (5th Edition) (Featured Titles for Linear Algebra (Introductory)) [Hardcover] by Otto Bretscher. I’ll refer to it as “the textbook” or “the book” or “Bretscher” below and in the lecture notes and quizzes. However, the notes are largely independent of the textbook, and do not require you to buy or own the textbook. Having the 4th Edition will also suffice.

#### My personal teaching experience

You can read a detailed answer I wrote on Quora about my personal experience.

#### Full downloads

Later in this page, links to each of the lecture notes, quizzes, and review sheets are available. If, however, you want to download *all* the lecture notes or *all* the quizzes, saving each link can be a pain. The links below can be useful if you want to download in bulk. Note that page numbers as shown on the pages are for individual files, not for the combined file.

- Single PDF with all lecture notes.
- Single PDF with all quizzes.
- Single PDF with all quiz solutions.
- Single PDF with all review sheets.

#### Opening remarks about linear algebra

Linear algebra: beware (PDF, 1 page)

#### Lecture notes plus quizzes

To determine the chronological order of quizzes, please use the dates in the quiz titles. Quizzes related to a given topic may not all have been administered at the time the topic was taught. Some quizzes were deliberately delayed in order to facilitate spaced repetition.

For solutions to any quiz, add `-solns` to the part of the URL just before the `.pdf` at the end of the URL. For instance, the solutions file for the quiz with URL `http://files.vipulnaik.com/math-196/10-18-linear-systems-rank-dimension-considerations.pdf` has URL `http://files.vipulnaik.com/math-196/10-18-linear-systems-rank-dimension-considerations-solns.pdf`

#### Quizzes providing glimpses into application areas not directly covered

- Using linear systems for measurement: Meant to consolidate linear transformations and hint at ideas behind factor analysis and principal component analysis.
- Linear dynamical systems and stochastic matrices: Linear dynamical systems, Stochastic matrices. These quizzes covered the ideas of eigenvalues and eigenvectors.
- Applications to calculus: Linear transformations: seeds for reaping later (note: this also included some questions paving the way for similarity of linear transformations), Image and kernel: applications to calculus, Subspace, basis, and dimension: applications to calculus.

#### Review sheets

Basic review sheets are unions of executive summaries of the corresponding lecture notes. Advanced review sheets include error-spotting exercises and other practice material.

Review sheet for … |
Sections of book covered |

midterm 1 (basic) | 1.1-1.3, 2.1 |

midterm 1 (advanced) | 1.1-1.3, 2.1 |

midterm 2 (basic) | 2.2-2.4, 3.1 |

midterm 2 (advanced) | 2.2-2.4, 3.1 |

final (basic) | 3.2-3.4, 4.1, 4.2, 5.3 |

final (advanced) | 3.2-3.4, 4.1, 4.2, 5.3 |