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• Understand the concept of a real vector space from an algebraic and a geometric point of view. The student will master related concepts such as bases and linear independence, norms, inner products, and so forth.
• Understand the most important maps between vector spaces -- the linear transformations. The successful student will be able to describe their structure and describe it in terms of ranks, nullspaces, etc.
• Understand how to manipulate matrices and explain the correspondence between matrices and linear transformations.
• Understand what eigenvalues are, why they are interesting, and why one would want to compute them.
• See applications of all of the above to engineering and physical and social sciences. To give just one example --- at the heart of Google search is an eigenvalue. (The student will not master this over the course of only one semester! If you give it thirty years, maybe. But people are developing new applications for linear algebra all the time.)
• Develop their ability to understand and explain rigorous mathematics and prove simple statements. This is a 500-level math class, and as such proofs will be required on homeworks and exams. If you have limited background in proofs, then this course will help bolster it.

• The course will probably say little about the very interesting and important questions when doing linear algebra in the "real world" -- which involves imprecise measurements and computational precision issues. The student who would like to see this beautiful topic emphasized should instead take Math 526.
• The course will develop only a minimal amount of formalism -- so the vector space axioms, fields other than R, infinite-dimensional vector spaces, inner products other than the "obvious" one coming from geometry, etc. will not be talked about much. This material would be more appropriate in a more advanced course. Please see me at the end of the term, or pursue a relevant term project, if you would be interested in learning more about these aspects of the subject.

Warning. You should expect 5-8 hours of homework a week in this class, which is more than most other instructors assign; in my experience there is no other way to learn the material. Your consistent effort will certainly lead to improved understanding, and it will almost certainly lead to you earning high grades.

The book is available by clicking the link above, click on the link above to download a PDF. It is completely free. You can also purchase a cheap printed copy if you like.

Thanks to the author for making this high quality material available for free! If you enjoy his books, please consider contacting them directly and saying so.