Matrix Groups for Undergraduates

See our review of the first edition. The second edition includes two new chapters, on Homogeneous Manifolds and Roots. According to the back cover, these were added to “allow for an easier transition to the general theory of Lie groups.” Adding these is certainly a good idea, though they are definitely more difficult.

Since the book is probably too long to be covered in a semester, I regret that there is no “dependence graph” for the chapters. There are lots of exercises. This remains one of the most attractive options for a senior seminar for mathematics majors.

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Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College, where he has often taught a senior seminar on matrix groups.