My text Linear Algebra is free for downloading, It covers the material of an undergraduate first linear algebra course. You can use it either as a main text, or as a supplement to another text, or for independent study.
When I started teaching linear algebra I found three kinds of texts. There were applied mathematics books that avoid proofs and cover the linear algebra only as needed for their applications. There were advanced books that assume that students can understand their elegant proofs, and understand how to answer the homework questions having seen only one or two examples. And finally, there were books that spend a good part of the semester doing elementary things such as multiplying matrices and computing determinants, and then suddenly change level to working with definitions and proofs.
Each of these three types was a problem in my classroom. The applications were interesting, but I wanted to primarilyy focus on the linear algebra. The advanced books were beautiful, but my students were not ready for them. And, the level-switching books, resulted in a lot of grief. My students thought that these were like the calculus books that they had seen before, where there is material labelled `proof' that they have skipped in favor of the computations. By the time that the level switched in this type of book, no amount of prompting on my part could convince them otherwise and the semesters ended unhappily.
That is, while I wish I could say that my students now perform at the level of the advanced books, I cannot. However, we can instead work steadily to bring them up to it, over the course of our program. This means stepping back from rote computations of the application books in favor of an understanding of the mathematics. It means proving things and having them understand, e.g., that matrix multiplication is the application of a linear function. But it means also avoiding an approach that is too advanced for the students; the presentation must emphasize motivation, must have many exercises, and must include problem sets with many of the medium-difficult questions that are a challenge to a learner without being overwhelming. And, it means communicating to our students that this is what we are doing, right from the start.
There is only one review that I know of.
The files are current as of 2001-Oct-09. To have a look at the PDF files you need Adobe Acrobat.
If you just want a quick look, try the second chapter. The first chapter may be misleading because it is necessarily computational but the second chapter shows clearly what the book works on: bridging between high school mathematics with its reliance on explicitly-given algorithms and upper division college mathematics with its emphasis on concepts and proof.
Naturally, I'd be glad for any comments or interest in trying it out. It's been class-tested here and elsewhere, and I'm delighted to have it on student's desks, doing what it is for. Around here, running off double-sided copies and comb-binding them costs students $20.00 (we include the Preface, Table of Contents, Appendix, and Index to make 449 pages. With the Answers to Exercises at 213 pages the total is $25.00).
In addition to the book, the answers to the exercises, and the source, you can get some materials that were contributed by others. If you in turn have something that you are able to share please write me. Anything is welcome, from a suggestion about a better way to prove a result or make an example, to an entire Topic or subsection. In particular, your used exams or problem sets would be very welcome, especially if you can contribute the TeX or LaTeX source, so that a user could cut or paste. Several people have asked me about a Topic on eigenvectors and eigenvalues in Quantum Mechanics. Sadly, I don't know any QM. Can you help?
Naturally, all contributions will be gratefully acknowledged (or anonymous, if you like).
If you find the book useful, drop me a note in the mail.
In particular, if you use it in a class, a letter on letterhead
to the address below would be great.
Jim Hefferon
Mathematics, Saint Michael's College
Winooski Park
Colchester, VT USA, 05439
Some people don't believe me when I tell them that I'm working in here.
The page above. The page maintainer is Jim Hefferon. Last revision: 2001-Oct-09.
This site Joshua is located in the Mathematics Department of Saint Michael's College in Colchester, Vermont USA.
Open Source software is a great idea. This project would not have gotten done without it.
(Credit for the logo to Matt Ericson.)