Jon von Neumann once said, “In mathematics you don’t understand things. You just get used to them.” Reviewing definitions and procedures and working out solutions to problems are two ways to achieve understanding by getting used to mathematical things. Concise computer mathematics provides an excellent vehicle for participating in these two tasks and for moving toward understanding. Since it stresses brevity over detail and breadth over depth, the book is ideally suited as an adjunct to a course in computer mathematics or as a refresher for someone with some background in computer mathematics.
The book is divided into 12 short, crisply written chapters. Each opens with an abstract, a set of keywords, and a brief treatment of the theoretical background of the subject. Each chapter concludes with a collection of problems or questions to solidify mastery or to provoke thought. The topics covered are sets, relations and functions, logic, proofs and arguments, vectors, matrices, graph theory, number theory, calculus, and numerical methods. The chapter on sets and numbers illustrates the power and limitations of the book. The opening abstract, which functions as a quick overview of the chapter, starts with a brief definition of sets and then quickly mentions the usefulness of sets in problem solving. The four keywords are each also titles of sections, and thus they serve as chapter guides. Keeping the number of keywords to single digits helps focus on what is essential and avoids cluttering details. In four subsequent pages, the book sets out definitions of terms and operations and provides the rationale for the basic number sets. Given the space limitation and the philosophy of the book, the chapter is a set of notes on sets, but those notes are essential and can be amplified by an instructor or a motivated reader. The chapter concludes with problems and their solutions, but the solutions, as is typical of the book, do not include narrative explanations.
The book fulfills its purpose of providing a distilled treatment of the mathematics most commonly used in computer science. It is of most value to computer science students who need a place to find a succinct treatment of the topics covered.