Algebra is applied in many computing technologies and related fields (such as, for instance, networking). For me, the closest examples contain: quantum computing, network routing, and error-control coding. In this book, Ferrante Neri elaborates on this algebraic background, providing a very good starting point for undergraduate students who wish to gain a basic understanding of the theories behind the most exciting parts of contemporary information technology (IT) technologies.

The book covers all of the classical aspects of linear algebra: matrices (chapter 1), systems of linear equations (chapter 2), geometric vectors (chapter 3), complex numbers (chapter 4), preliminaries of geometric algebra (chapter 5), overview of basic algebraic structures such as groups and rings (chapter 7), vector spaces (chapter 8), and linear mappings (chapter 10). The material related to linear algebra is appended with a short introduction to set theory in chapter 1, computational complexity in chapter 10, as well as graph theory in chapter 11.

As Neri’s work is a self-contained textbook, everything is explained from scratch and all of the chapters finish with exercises to test the reader’s understanding of just the presented material. While I like Neri’s approach, I would expect a way of lecturing more resembling, for example, Moon’s presentation of mathematical background for signal processing [1] or Trivedi in his handbook on stochastic modeling necessary in the reliability or queueing theory adopted for computational sciences [2]. While the mathematical fields are different in these three books, I think that the mode of lecture where the mathematical background is explained first and then the engineering applications are presented in some of today’s most prominent computer science examples is most effective for a contemporary engineering student having a utilitarian rather than essential way of learning things. While I sympathize with the latter philosophy of teaching, I am aware of the limited attractiveness of a book following it. On the other hand, in the case of Neri’s work, some examples of this kind are present; for example, Huffman coding and Polish notations are shown in chapter 10. Additionally, there is a whole chapter (12) devoted to solving electrical circuits with respect to linear algebra methods. However, as a practicing lecturer on mathematical applications in engineering, I would like to see, for instance, more examples related to the areas mentioned in the first paragraph of my review.