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    A First Course in Linear Algebra

    Reviewed by Christopher Phan, Assistant Professor, Winona State University on 8/21/16

    Comprehensiveness rating: 5

    This book includes a good selection of topics for a semester-long linear algebra course.

    Content Accuracy rating: 5

    I did not notice any errors. The open-source model allows any errors to be corrected promptly.

    Relevance/Longevity rating: 5

    Most of the material is basically timeless. The book does include computer code that can be used with SageMath, an open-source computer algebra system. Because SageMath is open-source, it should be possible to obtain a copy indefinitely.

    Clarity rating: 5

    The book is easy to read, with practical examples sprinkled throughout. In addition, in the electronic version, the interface makes it easy to refer to previous theorems or examples.

    Consistency rating: 5

    The author uses consistent terminology and notation throughout.

    Modularity rating: 5

    The book is more modular than most other math texts. For example, theorems are not numbered, but given abbreviations, so that they would not need to be renumbered should you choose to adopt and incorporate sections into another text. Of course, some sections depend on results or material from others, which cannot be avoided in a math text. (But even then, the interface makes referring to the previous material easy.)

    Organization/Structure/Flow rating: 5

    The book is organized well. The author moves from concrete to more abstract concepts, starting with matrices and column vectors before moving on to abstract vector spaces and linear transformations. For example, eigenvectors are described before linear transformations. This organization is pleasant to follow.

    Interface rating: 5

    The interface in the electronic version is a selling point of the book. Every time a previous theorem or definition is invoked, the reader can click a link and view that previous theorem or definition without actually navigating to that page. Likewise, the book includes instruction on using the SageMath computer algebra system. The electronic version includes a direct interface to SageMath (through the SageMath Cell Server) which allows code to be run directly from the book.

    Grammatical Errors rating: 5

    I did not notice any grammatical or spelling errors.

    Cultural Relevance rating: 5

    I did not notice anything that was culturally insensitive or offensive.

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