
Discrete Mathematical Structures, 4/e
Bernard Kolman
Robert Busby, both of Drexel University
Sharon Ross, Georgia Perimiter College
Coming November, 1999 by Prentice Hall Engineering/Science/Mathematics
Copyright 2000, 550 pp.
Cloth
ISBN 0130831433

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For one/twoterm, freshman/sophomorelevel courses in Discrete
Mathematics.
More than any other book in the field, this text ties together
discrete topics with a theme. Written at an appropriate level of rigor—with
a strong pedagogical focus—it limits depth of coverage and areas
covered to topics of genuine use in computer science. An emphasis
on both basic theory and applications provides students with a firm
foundation for more advanced courses.
NEW— More emphasis on proofs—Includes
a “Tips on Proofs” unit in each chapter. The new unit discusses
the proof techniques associated with the topics of that chapter.
 Offers students more dialogue about reading, understanding,
and constructing proofs.
NEW—Extensively redesigned exercise sets—More
routine exercises as well as more challenging problems are given.
The dialogue on proof and proof techniques continues here with exercises
that require students to complete partial proofs and analyze proof
strategies. More exercises require explanations or justifications.
NEW—Chapter Tests—Solutions to all
questions supplied.
 Gives students the opportunity to self test their knowledge
of chapter concepts.
NEW—The different ways of representing
relations are more thoroughly exploited.
 Enables students with different learning styles to master
the concepts.
NEW—Additional sections in the graph theory
chapter covering transport networks and their applications.
Still the briefest text on the market. An accessible,
concise, and interesting narrative—Devoid of excessive technical
jargon and abstraction.
 Helps students focus on fundamental concepts without
becoming bogged down in special cases, weakly motivated examples,
and applications. Enables instructors to sharpen focus on key
ideas and concepts.
Experiments—Suitable for individual work or group
projects.
 Gives students the opportunity to work with an openended
problem, to develop and test conjectures, communicate their work and
build confidence in their problemsolving skills. Experiments also
foster better conceptual understanding.
Only a limited background in mathematics required—No
calculus.
 Offers students a level of rigor appropriate for beginners.
Algorithms and pseudocode used throughout the text to
illustrate techniques.
Systematic approach—Introduces each new concept
using previously encountered material.
 Provides students with material developed in such a way
to simplify the more complex ideas that follow and lead naturally
to other algebraic structures.
Coding exercises—Provided in each chapter.
 Relate discrete mathematics topics to students' programming
experience. Can also be used in developing programming ideas and skills
before a programming course.
Organization of topics around the concept of a relation—Treats
relations and digraphs as two aspects of the same basic mathematical
idea.
 This fundamental idea is then used as the basis for all
the concepts introduced—including functions, partial orders, graphs,
and algebraic structures.
A focus on topics of genuine use in computer science.
 Limits coverage of abstract algebra and gives applications
to the important topics of finite state machines, and error correcting
and detecting codes.
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.
Binary Operations Revisited. Semigroups. Products and Quotients
of Semigroups. Groups. Products and Quotients of Groups.
10. Languages and FiniteState Machines.
Languages. Representations of Special Languages and Grammars.
FiniteState 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.
