The Discrete Math Workbook

This “Workbook: A Companion Manual for Practical Study” is not a textbook yet can augment study and even self-study in discrete mathematics if used strategically. It is a “substantial collection of classroom-tested exercises.” Each chapter opens with a list of definitions, theories and perhaps an example that reads tersely like notes taken during a lecture. There is little in the way of development or motivation in the presentation which is more a gallery of subject-related facts. Consider the initial and typical “Fundamentals of Mathematical Logic” chapter which dispenses with its fundamentals in less than six pages. This is backed up by about fifty-six pages of exercise and detailed “Answers, Hints, Solutions”. This is the format for each chapter so that the Set Theory chapter breathlessly moves from the definition of a set to Russel’s paradox in a half-dozen pages followed by over thirty exercises and solutions. The most detailed and developed material resides in the final chapters on sorting and parallel processing. These chapters cover areas in the theory of computer science through analysis of algorithms presented in pseudocode.

The authors are from Voronezh State University, one of the main universities in Central Russia. Many passages read like improvable translations, such as:

In the case E is the equivalence relation on A, then various equivalence classes form a partition on A…. Partial order on the set A is a reflective, antisymmetric, or transitive relation of P.

Exactly which various classes? So, the partial order is not defined as narrowly as reflexive, anti-symmetric and transitive relation? Well, certainly as a study aid this is compact and broad in scope for discrete topics if not recommended as a sole or definitive guide to the topic’s fundamentals.

Tom Schulte is the mathematics instructor for Upper Iowa University’s New Orleans Center located in the Jackson Barracks, the headquarters of the Louisiana National Guard.