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FREE Video Lectures

So... you think my lectures are annoying?!? Well... maybe you like Gil Strang's style better? The "Essence of linear algebra" looks very promising as well.

• Gil Strang (Massachusetts Institute of Technology): 34 Lectures (Recorded Live Fall 1999)
• "Essence of linear algebra" YouTube Series (First Video Posted 8/4/2016)

FREE Textbook Resources

Textbooks are expensive! ("No joke, Sherlock!") Also, learning styles, preparation, and needs differ. I am not saying that any of the below resources fully will replace the textbook selected for the course, but they may serve as either additional resources giving a slightly different point of view of the material; or as stop-gap replacements if you decide that the textbook is to expensive.

These resources have NOT YET been fully vetted, and are provided for "adults and entertainment purposes only." However, the long-term goal is to migrate the class to a more cost-effective text.

If you decide to use (or not use) any of these texts I am very interested in your opinion on what was good/bad about it; your input is very much appreciated!

• Interactive Linear Algebra (Dan Margalit, and Joseph Rabinoff)
• A First Course in Linear Algebra (Robert Beezer) [Alternative Link]
  A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form.PDF versions are available to download for printing or on-screen viewing, an online version is available, and physical copies may be purchased from the print-on-demand service at Lulu.com. GNU Free Documentation License
• Linear Algebra (Jim Hefferon) [Alternative Link]
  Linear Algebra is free for downloading, It covers the material of an undergraduate first linear algebra course.
• Linear Algebra, Theory and Applications (Kenneth Kuttler) [Alternative Link]
  From the preface: "This is a book on linear algebra and matrix theory. While it is self-contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however." A solutions manual to the exercises in the textbook is included.
• Linear Algebra Done Wrong (Sergei Treil) [Alternative Link]
  Brown University has two introductory linear algebra courses. This text is used in the honors course that emphasizes proofs. The book's title suggests that it is not the typical approach to linear algebra even among those books that are more theoretical. For example, the concept of a basis is treated as more fundamental than the concept of linear independence, and linear transformations are introduced before solving systems of linear equations. Especially noteworthy is the motivation and development of determinants. As the author states in the preface: I spent a lot of time presenting a motivation for the determinant, and only much later give formal definitions. Determinants are introduced as a way to compute volumes. It is shown that if we allow signed volumes, make the determinant linear in each column, and assume some very natural properties, then we do not have any choice and arrive at the classical definition of the determinant.
• Linear Algebra (WikiBooks) [Alternative Link]
  This is a free, online wikibook, so its content is continually being updated and refined. According to the authors, "Linear algebra is a branch of algebra in mathematics concerned with the study of vectors, vector spaces, linear transformations, and systems of linear equations. Vector spaces are very important in modern mathematics. Linear algebra is widely used in abstract algebra and functional analysis. It has extensive applications in natural and social sciences, for both linear systems and linear models of nonlinear systems."
• Linear Algebra [Alternative Link]
  'What this book is: This "textbook" (+videos+WeBWorKs) is suitable for a sophomore level linear algebra course taught in about twenty-five lectures. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors. Our goal in writing it was to produce students who can perform computations with linear systems and also understand the concepts behind these computations. For more details, see the Table of Contents or the Preface.Homework: This book is designed to be used in conjunction with online homework exercises written in the WeBWorK system. These exercises help the students read the lecture notes and learn basic computational skills. There are also in-depth conceptual problems at the end of each lecture, designed for written assignments. See the homework page for more information about homework or to obtain access to the online homework exercises.'
• Linear Algebra (David Cherney, Tom Denton, and Andrew Waldron) [Alternative Link]
  The general layout of content in the units proceeds, wherever possible from the concrete representation of the concepts to their abstract forms. Unit 1 begins with a treatment of systems of linear equations and their solutions. This is followed by a section that introduces vectors and matrices and dwells quite a lot on operations on these and the theory and properties of determinants. The relatively more abstract concept of vector spaces is treated next. The theory and properties of Linear transformations closes this unit. Unit 2 introduces the notions of eigenvalues and eigenvectors. The diagonalisation property is demonstrated and proved. Each unit has a maximum of four activities, one of which focuses on mathematics education, pedagogics and didactics. This helps students not only to focus on mathematical content, but also to focus on their goal as teachers of mathematics in the secondary school.