Discrete Mathematics with Applications

Rating:
Summary: The right mix of computer applications and mathematics
Review: Discrete mathematics for the sophomore or junior level computer science major is a blend of mathematics and computer science and neither can really take second place to the other. While more ink is devoted to the mathematics, the computer applications are necessary to provide the appropriate context. In this area, Koshy has hit the target. Some computer applications are embedded in the text and a list of computer applications is given at the end of each chapter. Enough to be of value, but not so many as to be overwhelming. Lists of writing projects and supplementary readings are also available for the instructor who wishes to include a research component.
Formal proofs are not an integral part of the text, which is a tactic that I approve of. The students that I have in discrete mathematics are generally not capable of understanding a formal proof and the purpose of the class is to introduce the mathematics so that they can use it. As a mathematician, I am strongly in favor of teaching formal proofs, but only at the appropriate time. The general philosophy in the mathematics major is to avoid formal proofs until the students are in linear algebra, which is generally taken after a two- semester calculus sequence. If we allow our math majors to avoid formal proofs until their third course in the major, it is absurd to expect the computer science majors to do them in their first.
The coverage is standard. The sequence is logic, set theory, functions, mathematical induction, recursion, combinatorics, relations, graphs, trees, digraphs, formal languages and Boolean algebra. I am in general approval of the sequence, although I would have placed relations before functions. Pseudocode similar to Pascal is used to express the algorithms, and it is heavily documented. Large numbers of exercises are included and answers to the odd-numbered ones are given at the end.
This book strikes the right balance in terms of rigor and detail and I will be adopting it for use the next time I teach discrete mathematics.