This second edition of Wallis’ concisely written textbook on finite mathematics can be a valuable resource for freshmen and sophomores. An economy of language lends elegance and clarity to this text, which is unusual among comparable texts that I work with. The sequence in which topics are presented convinces me, however, that it would be awkward in the classroom. Additional lectures would be required, and probably also reordering the sections. Such situations, I find, often confuse and unsettle a student already on the margins of his or her confidence and works against encouraging students to read ahead and do independent study. The book can nevertheless be helpful for parents or students seeking a resource to supplement a required textbook during the first couple of years of pre-calculus college algebra.

As usual with comparable works, the book leads off with set theory. I very much appreciate that Wallis immediately connects this to solution sets, instead of waiting until half-way into the text. However, a tangent is taken into summation notation and principles before returning to cover such set basics as union, intersection, and Venn diagrams. Arithmetic and geometric sequences are never explored in detail, or even introduced. Wallis also introduces probability sooner than most comparable textbooks. In his approach, standard deviation comes before the combinatorial basis of probability. Similarly, after a quick exhibition of probability measures, including the unnamed inclusion-exclusion principle, the text is into Bernoulli trials before counting basics. As a result, the student is confronted with determining the probability that a netted butterfly is striped or female sections prior to meeting the ideal urn and its monochrome marbles.

Wallis adds material that I believe is crucial to introduce to the target audience. For many business or liberal arts majors, this text contains most if not all of the mathematics they will learn before they enter the workforce with an Associate’s Degree. Unlike many textbooks that may be chosen for them, Wallis includes a very good, not merely cursory, introduction to Bayes. There is also an entire chapter on Graph Theory going as far as Hamiltonian cycles and colorings. (This is perhaps further than is necessary for these students.) There is also an entire chapter on Game Theory. Wallis also ties together nicely the general form of the linear equation with the dot product by way of introducing matrix multiplication. I feel there was a missed opportunity to underscore the applicability to sales figures matrix examples previously presented, but I appreciate the rarely seen vector topics for students at this level.

Finally, there is the subject of graphical solutions to equations and systems. Wallis calls this The Geometric Method and largely relegates this to a later, dedicated chapter and rarely broaches the topic elsewhere. I feel this is a disservice to the student at this level, because very often the crucial “aha!” moment can be sparked with a Cartesian presentation. As a result, Wallis concludes the text with a chapter on exponential growth without comment or display of the unique curve, let alone having it come at the tail of an enlightening parade of fully explored basic graph forms.

Tom Schulte teaches finite mathematics and more at Oakland Community College in Michigan.