The coverage is standard: linear systems and Gauss' method, vector
spaces, linear maps and matrices, determinants, and eigenvectors and
eigenvalues. Prerequisites: A semester of calculus. Students with three
semesters of calculus can skip a few sections. Applications: Each
chapter has three or four discussions of additional topics and
applications. These are suitable for independent study or for small
group work. What makes it different? The approach is developmental.
Although the presentation is focused on covering the requisite material
by proving things, it does not start with an assumption that students
are already able at abstract work. Instead, it proceeds with a great
deal of motivation, many computational examples, and exercises that
range from routine verifications to (a few) challenges. The goal is, in
the context of developing the usual material of an undergraduate linear
algebra course, to help raise the level of mathematical maturity of the
class.
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