Discover Linear Algebra is an open-access linear algebra textbook that uses a discovery-based approach to introduce students to this beautiful subject. The philosophy of this treatment is to allow the undeniable core ideas and patterns of linear algebra to reveal themselves to the student.
Each chapter begins with a set of guided-discovery activities suitable for use as in-class group activities, as pre-class preparatory explorations, or for self-study. The exposition in the remainder of each chapter reflects and expands upon these introductory explorations, beginning with an informal Concepts section, followed by a section of Examples, and ending with a more formal Theory section of theorems and proofs. Please see the book's preface (two-semester version; one-semester version) for a little more detail on the organization and pedagogical approach of the book.
Discover Linear Algebra is free as in “freedom” — released under the GNU Free Documentation License (GFDL), you are free to use, copy, redistribute, and/or modify this textbook. (Though that freedom comes with some responsibilities; see the full text of the GFDL, included as an appendix to the textbook.) If you wish to make use of this work under a different license, please contact the author using the contact info below.
Two-semester version: Discover Linear Algebra — Winter 2021 Edition
One-semester version: Discover Linear Algebra: A first course in linear algebra — 2023 Edition
One-semester electronic PDF version (for viewing on-screen): Discover Linear Algebra: A first course in linear algebra — 2023 Electronic PDF Edition
One-semester print PDF version (for printing double-sided): Discover Linear Algebra: A first course in linear algebra — 2023 Print PDF Edition
Github repository for the PreTeXt document source code: github.com/jjrsylvestre/dla
I usually recommend 3,000 Solved Problems in Linear Algebra (Lipschutz) as an inexpensive supplementary textbook for students to use as a source of solved practise problems. The following page contains chapter-by-chapter lists of recommended practise problems from this supplementary text for the one-semester version of Discover Linear Algebra: A first course in linear algebra.
Practise Problem Lists for DLA1
Chapter-by-chapter WeBWorK problem sets for the one-semester version of Discover Linear Algebra. The problem sets are not balanced — some chapters have a lot of problems, some only a few. The average is 8 problems per set. This may seem low, but is based on the philosophy that large numbers of repetitive, algorithmic, calculation-based "drill" problems are best left as practise problems (see above).
WeBWorK Problem Sets for DLA1 (.zip file)
(Unzip into your WeBWorK course's templates directory, import the .def files in the Hmwk Sets Editor , and then adjust the opening/closing dates for each set.)
During the pandemic I seized the opportunity to fully "flip" my linear algebra courses and recorded lecture videos for each chapter. Note that these are intended to be watched after students have attempted the corresponding Discovery Guide.
Videos for One-Semester Version
Additional Videos for Two-Semester Version
Jeremy Sylvestre
University of Alberta, Augustana Campus
jeremy.sylvestre@ualberta.ca