4/e
Bernard Kolman
Robert C. Busby , both of Drexel University
Sharon Cutler Ross , Georgia Perimiter College
Published November 1999 by Engineering/Science/Mathematics
Copyright 2000, 505 pp.
Cloth ISBN 0-13-083143-3
Summary
More than any other book in this field, this book ties together discrete topics with a
theme. Written at an appropriate level of understanding for those new to the world of
abstract mathematics, it limits depth of coverage and areas covered to topics of genuine
use in computer science. KEY TOPICS: Chapter topics include fundamentals, logic, counting,
relations and digraphs, trees, topics in graph theory, languages and finite-state
machines, and groups and coding. MARKET: For individuals interested in computer science
and other related fields - looking for an introduction to discrete mathematics, or a
bridge to more advanced material on the subject.
Table of Contents
1. Fundamentals.
Sets and Subsets. Operations on Sets. Sequences. Division in the Integers. Matrices.
Mathematical Structures.
2. Logic.
Propositions and Logical Operations. Conditional Statements. Methods of Proof.
Mathematical Induction.
3. Counting.
Permutations. Combinations. The Pigeonhole Principle. Elements of Probability. Recurrence
Relations.
4. Relations and Digraphs.
Product Sets and Partitions. Relations and Digraphs. Paths in Relations and Digraphs.
Properties of Relations. Equivalence Relations. Computer Representation of Relations and
Digraphs. Operations on Relations. Transitive Closure and Warshall's Algorithm.
5. Functions.
Functions. Functions for Computer Science. Growth of Functions. Permutation Functions.
6. Order Relations and Structures.
Partially Ordered Sets. Extremal Elements of Partially Ordered Sets. Lattices. Finite
Boolean Algebras. Functions on Boolean Algebras. Circuit Design.
7. Trees.
Trees. Labeled Trees. Tree Searching. Undirected Trees. Minimal Spanning Trees.
8. Topics in Graph Theory.
Graphs. Euler Paths and Circuits. Hamiltonian Paths and Circuits. Transport Networks.
Matching Problems. Coloring Graphs.
9. Semigroups and Groups.
Semigroups. Products and Quotients of Semigroups. Groups. Products and Quotients of
Groups.
10. Languages and Finite-State Machines.
Languages. Representations of Special Grammars. And Languages. Finite-State Machines.
Semigroups, Machines, and Languages. Machines and Regular Languages. Simplification of
Machines.
11. Groups and Coding.
Coding of Binary Information and Error Detection. Decoding and Error Correction.
Appendix A: Algorithms and Pseudocode.
Appendix B: Experiments in Discrete Mathematics.
