Spiral Workbook for Discrete Mathematics
This book covers the main topics in a discrete mathematics text. It does not include an analysis of algorithms, graphs, trees, and other topics that would be of interest to computer science students. The presentation of logic and the techniques for writing proofs are thorough and nicely laid out. The problems presented to the students have sufficient variety. New definitions could be included in the summary of the section in which they are presented.
The mathematical content is accurate, though there are a few instances where definitions in this text deviate a bit from those presented in mathematics textbooks. For example, I have read mathematical books that define a function, f, with domain A and co-domain B as a subset of AxB satisfying two properties: for every element of A, a, there exists an element of B, b, such that (a, b) is an element of f, and if (a, b) and (a, c) are elements of f, then b = c. In this textbook, the graph of a function is defined this way (sort of), but functions are not presented as a collection of ordered pairs when initially being defined. These differences can be used to point out the importance of learning definitions and terminology, and using those definitions to create and explore conjectures.
The textbook covers traditional material included in a discrete mathematics class. It includes examples and problems that are typically used in other textbooks in this field. This textbook does not include examples that are particularly modern, or that reference "pop culture" which helps with longevity.
The text is very well written. The material on formulating proofs is extremely well written, and could be incorporated into any course that helps students make the transition from computational mathematics to abstract mathematics. The explanations are clear, the examples highlight what students should do and what they should avoid. Common mistakes are pointed out with clear explanations and examples. The format of the mathematical steps involved in solving a problem makes it easy to follow along and understand the calculations being presented. There are a few proofs that include the word "obviously" as a reason, however, and it would be helpful to have all definitions presented similarly to how theorems are stated (blocked to stand out and labeled as such).
Consistent terminology and notation is used throughout the book.
The sections are broken up into subsections that fit a particular topic and do not include an excessive amount of material.
Each subsection presents a topic and explores the ideas in more depth. The sequence of subsections in a chapter follows a natural progression that is typical for a discrete mathematics textbook. Each chapter is well-organized and the content being discussed builds on previously presented ideas.
Some of the "hands-on exercises" are split over two pages, making it difficult to understand the task needing to be practiced (for example, exercise 6.2.1). The experience of scrolling through the pdf file was as expected. Leaving space between the hands-on exercise problems reflect that it is a workbook that will be printed, but if a student only accesses the text as a pdf file, the space is not needed. There are pros and cons to each arrangement.
The explanations and presentation of material use correct grammar and spelling. I did not see any glaring errors (grammatical or typographical).
This is a standard mathematics textbook without references to "pop culture" or terminology that could be considered offensive. It does not contain images of events or people with the potential for being problematic in the future. On the other hand, having specific examples of how the concepts being introduced are relevant to computer science (for example, RSA encryption, hash functions etc...) could help motivate students to learn this material.
Overall, I thought that the foundations of mathematics are well-presented. The advice to students in the Introduction could be shared in every math class! The material is clearly presented, there are ample hands-on exercises, and students would benefit from reading this textbook. Including a few applications of the material being covered would strengthen the textbook, and including topics related to an analysis of algorithms (and big-Oh notation), graphs and trees would complete the topics presented in a typical discrete mathematics class.