Linear Algebra

Reviewed by Bruce Lundberg, Chair, and Professor of Mathematics, Colorado State University - Pueblo on 2/1/18

Comprehensiveness rating: 4

Treats the standard topics in Linear Algebra, plus Linear Optimization (Simplex Method and applications), and the SVD. An exploratory introductory first chapter is non-standard but interesting for engaging students right away in seeing and asking about the meaning of Linear Algebra. The Index is adequate and has links to pages cited. There was no collected glossary. Cross product is assumed, but then stated a few pages later, and not covered (not untypical for LA books).

Content Accuracy rating: 4

Apart from a number of typo's, the mathematical accuracy looks high.

Relevance/Longevity rating: 3

The material covers the standard topics, but the exercise sets and some terms, notations can be nonstandard. The treatment of hyperplanes, and exercises about them were hard for students (and the other faculty they sought help from). The matrix and vector entry superscript-subscript notation is neat for preparing engineers for tensor analysis notations, but is non-standard and somewhat confusing for students at the introductory level.
Longevity depends on the direction the LA curriculum for engineers evolves.

Clarity rating: 3

The treatment of hyperplanes, and exercises about them were hard for students (and the other faculty they sought help from). The matrix and vector entry superscript-subscript notation is neat for preparing engineers for tensor analysis notations, but is non-standard and somewhat confusing for students at the introductory level.
Longevity depends on the direction the LA curriculum for engineers evolves.

The lack of clarity to other faculty and to students could be an artifact of the non-standard exposition, problems and notations. Faculty just jump in to help, looking for notations they know. When they have to read through the text, and the students see faculty "do not know how to do the problems", this gives the limping ones an excuse or scandal.

That said, this very quality can cause the more capable and motivated students to learn more, and make cheating or mimicry harder for students to carry off.

Consistency rating: 3

This is hard to tell for sure, without a very careful and thoughtful read and use. But, my impression is that the four author effort shows somewhat in a lack of pedagogical consistency.

Modularity rating: 3

This is difficult. I would have to skip some sections and chapters in my course, but the non-standard exposition and problems assume the perspectives and exposition of former chapters.

Organization/Structure/Flow rating: 3

It seems a bit odd or non-standard that Matrices come after vector spaces and after linear transformations. But I think this works in the spirit of the text, which seems to be to introduce the topics after motivation and applied context has been developed.

Interface rating: 5

Text interface is of high quality.

Grammatical Errors rating: 4

The writing, apart from some typos, is good.

Cultural Relevance rating: 5

The text is culturally relevant and respectful.

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