cover of Linear Algebra by Hefferon

Linear Algebra by Jim Hefferon is a text for a first undergraduate course. It is Free. Use it as the main book, as a supplement, or for independent study.

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Text highlights

  • Standard coverage Linear systems and Gauss's method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues.
  • Developmental approach The book proves all of the results but does not start by assuming that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and many exercises. The goal is to raise each student's level of mathematical maturity.
  • Extensive exercise sets Each subsection has a wide range of exercises, from routine verifications to a few challenges. The book of solutions gives the answer to every one, completely worked. And, clicking on a problem takes you to its answer while clicking on the answer takes you back to the problem.
  • Popular Used in hundreds of classes at many schools, as well as by thousands of people for independent study.
  • Applications Each chapter finishes with four or five short supplemental topics for reading or projects, or for small group work.
  • Extras There are beamer slides for classroom presentations, a lab manual using Sage, and videos. For more, see the page for instructors.
  • Prerequisite One semester of calculus.
  • Free Everything is Freely available, including the LaTeX source. You can also buy a paper copy of the book.
  • Reviews Some from: the Mathematical Association of America, the American Institute of Mathematics, the Open Textbook Library, The Assayer, a longstanding site about free texts.
  • Award winning Recipient of the 2020 Solow Award from the Mathematical Association of America, for “impact on undergraduate education in mathematics.”