Discrete Mathematical Structures, 4/e
Robert Busby, both of Drexel University
Sharon Ross, Georgia Perimiter College
Coming November, 1999 by Prentice Hall Engineering/Science/Mathematics
Copyright 2000, 550 pp.
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Discrete Mathematics-Computer Science
For one/two-term, freshman/sophomore-level courses in Discrete
More than any other book in the field, this text ties together
discrete topics with a theme. Written at an appropriate level of rigorwith
a strong pedagogical focusit 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 proofsIncludes
a Tips on Proofs unit in each chapter. The new unit discusses
the proof techniques associated with the topics of that chapter.
NEWExtensively redesigned exercise setsMore
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.
- Offers students more dialogue about reading, understanding,
and constructing proofs.
NEWChapter TestsSolutions to all
NEWThe different ways of representing
relations are more thoroughly exploited.
- Gives students the opportunity to self test their knowledge
of chapter concepts.
NEWAdditional sections in the graph theory
chapter covering transport networks and their applications.
- Enables students with different learning styles to master
Still the briefest text on the market. An accessible,
concise, and interesting narrativeDevoid of excessive technical
jargon and abstraction.
ExperimentsSuitable for individual work or group
- 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.
Only a limited background in mathematics requiredNo
- Gives students the opportunity to work with an open-ended
problem, to develop and test conjectures, communicate their work and
build confidence in their problem-solving skills. Experiments also
foster better conceptual understanding.
Algorithms and pseudocode used throughout the text to
- Offers students a level of rigor appropriate for beginners.
Systematic approachIntroduces each new concept
using previously encountered material.
Coding exercisesProvided in each chapter.
- Provides students with material developed in such a way
to simplify the more complex ideas that follow and lead naturally
to other algebraic structures.
Organization of topics around the concept of a relationTreats
relations and digraphs as two aspects of the same basic mathematical
- Relate discrete mathematics topics to students' programming
experience. Can also be used in developing programming ideas and skills
before a programming course.
A focus on topics of genuine use in computer science.
- This fundamental idea is then used as the basis for all
the concepts introducedincluding functions, partial orders, graphs,
and algebraic structures.
- Limits coverage of abstract algebra and gives applications
to the important topics of finite state machines, and error correcting
and detecting codes.
Sets and Subsets. Operations on Sets. Sequences. Division
in the Integers. Matrices. Mathematical Structures.
Propositions and Logical Operations. Conditional Statements.
Methods of Proof. Mathematical Induction.
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.
Functions. Functions for Computer Science. Growth of Functions.
6. Order Relations and Structures.
Partially Ordered Sets. Extremal Elements of Partially Ordered
Sets. Lattices. Finite Boolean Algebras. Functions on Boolean Algebras.
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 Finite-State Machines.
Languages. Representations of Special Languages and Grammars.
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.