Linear Algebra

Author : Jim Hefferon, Saint Michael's College
Publication Date : May 2006

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Book Excerpts:

This book helps students to master the material of a standard undergraduate linear algebra course.

The material is standard in that the topics covered are Gaussian reduction, vector spaces, linear maps, determinants, and eigenvalues and eigenvectors. The audience is also standard: sophmores or juniors, usually with a background of at least one semester of Calculus and perhaps with as much as three semesters.

The help that it gives to students comes from taking a developmental approach - this book's presentation emphasizes motivation and naturalness, driven home by a wide variety of examples and extensive, careful, exercises. The developmental approach is what sets this book apart, so some expansion of the term is appropriate here.

The aim of this book's exposition is to help students develop from being successful at their present level, in classes where a majority of the members are interested mainly in applications in science or engineering, to being successful at the next level, that of serious students of the subject of mathematics itself.

Helping students make this transition means taking the mathematics seriously, so all of the results in this book are proved. On the other hand, this book cannot assume that students have already arrived, and so in contrast with more abstract texts, this book gives many examples and they are often quite detailed.

Review(s):

The Assayer:

"Many of the homework problems relate directly to these real-life applications. This is in welcome contrast to the usual, dreary set of "drill and kill" problems without any real context. The drudgery is also reduced by the explicit introduction of computer algebra systems in the first chapter. Many of the problems explicitly state that they are to be solved on a computer, and the assumption that the students will use computers has also allowed Hefferon to include many realistic problems that result in larger matrices than could be handled by hand."

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