This text covers a standard first course: Gauss’s Method, vector spaces, linear maps and matrices, determinants, and eigenvalues and eigenvectors. In addition, each chapter ends with some brief topics, such as applications. What sets it apart is careful motivation, many examples, and extensive exercise sets. Together, these help each student master the material of the course and also help an instructor develop that student’s level of mathematical maturity.
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For a quick look, I suggest the second chapter. The first chapter is necessarily computational but the second chapter shows more clearly what the book works on: bridging between lower-division mathematics with its reliance on explicitly-given algorithms, and upper division college mathematics with its emphasis on concepts and proof.
Jim Hefferon is an Associate Professor and Department Chair of the Mathematics Department at Saint Michael's College in Colchester, Vermont.
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