A Cool Brisk Walk Through Discrete Mathematics
Stephen Davies, University of Mary Washington
Copyright Year: 2019
Last Update: 2020
Publisher: University of Mary Washington
Conditions of Use
Comprehensiveness is not necessarily the point of the text, as it is principally concerned with offering Computer Science students an entrance into discrete mathematics that meshes well with CS courses they are likely to have taken. The chapter... read more
Comprehensiveness is not necessarily the point of the text, as it is principally concerned with offering Computer Science students an entrance into discrete mathematics that meshes well with CS courses they are likely to have taken. The chapter on graph theory, for example, mainly concerns graph algorithms and graphs as data structures.
I noticed no issues with the accuracy of the material presented.
The book seems quite relevant for the niche it inhabits as a part of a CS program, for majors. I am less sure about its applicability outside of that context: you could still use it as a set of course notes to supplement with additional topics from other sources to deploy it in a Mathematics program, but at that point you might want to consider another resource first.
The writing style is very colloquial, while keeping some focus on formality and notation. It is directed to the student, though the instructor will have no trouble understanding the rationale of the presentation.
The text does go back and forth a bit in some ways: only the first few chapters have exercises included, for instance. The later chapters also feel more like stand-alone modules designed to cover the requisite bases of topics that may be needed down the road for subsequent courses. The writing style is consistent, though, and while I was reading through it, at no point did I feel as though I had been thrown for a loop.
I would not rate it as especially modular. One reason for this is that definitions are largely presented in-line, called out in bold text. As a result, the sections have a sturdy feel to them – they are not easily broken up! It also very much deemphasizes proofs, prior to the chapter dedicated to them. If you wanted to emphasize them more heavily in the earlier chapters you could move that section up, but you would then also have to go and track the relevant proofs down elsewhere for the other chapters (or reproduce them yourself, of course).
As someone who feels that many possible permutations of the topics in a course on discrete mathematics can be reasonable, I have no objection to the organization here.
Die-hards might object to the fact that not every figure seems to have been produced in LaTeX, but I found it to be sufficiently clear. In terms of being accessible to student readers, though, the format might be somewhat intense for students with less experience reading math texts. The way that some sections require the reader to keep tabs on essential details from several paragraphs ago may be assuming a level of familiarity and skill that, in my experience, many undergraduates struggle with. If I adopted this textbook, I would have to think about how much reading I would feel comfortable requiring of my students, and how much of the text could be instead interpreted as course notes to build lessons from.
I did not detect noticeable grammatical issues.
In keeping with the informal style, the book relies on a lot of pop culture references to things like Star Trek that serve as comfort food to a lot of CS and Math faculty. This would give me some pause about assigning it to students to read. I would not say that any of the discussions or exercises with that flavor were problematic in and of themselves, but I am increasingly leery of adding any additional barriers that might only apply to someone whose first language is not English, say, or even just the many students whose cultural frame of reference is very different from that of someone who was watching American television in the 1990s. One other noticeable thing about the framing of the examples is that the author typically refers to his own family when human subjects are needed. This is again not an objectionable thing to do in a course, but it is frequent enough that for me it would be an issue. If you were to adopt the book as course notes you would likely want to reframe most of these occurrences anyway, though, and that would be an opportunity to add a more diverse cast of characters.
It is also worth mentioning that the book links to the author’s website, where he has made available an extensive series of video lectures covering the entire book. He also encourages instructors using his materials to contact him to receive supporting homework assignments, quizzes, group projects and exams, which I unfortunately did not do in time to make my deadline for this review. The exercises included in the book are more of a self-check for a student reading along. As I am not sure I would ask students to read through the chapters themselves, I think they could be readily repurposed into classroom activities.
Table of Contents
- 1 Meetup at the trailhead
- 2 Sets
- 3 Relations
- 4 Probability
- 5 Structures
- 6 Counting
- 7 Numbers
- 8 Logic
- 9 Proof
About the Book
A Cool, Brisk Walk Through Discrete Mathematics, an innovative and non-traditional approach to learning Discrete Math, is available for low cost from Blurb or via free download.
About the Contributors
Stephen Davies, Ph.D, Computer Science Department, University of Mary Washington