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Discrete Mathematical Structures, 4/E
Bernard Kolman, Drexel University
Robert C. Busby, Drexel University
Sharon Cutler Ross, Georgia Perimeter College

ISBN-10: 0130831433
ISBN-13: 9780130831439

Publisher: Pearson
Copyright: 2000
Format: Cloth; 505 pp
Published: 11/23/1999

For one/two-term, freshman/sophomore-level 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. Ex.___

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. Ex.___

NEW - The different ways of representing relations are more thoroughly exploited.
- Enables students with different learning styles to master the concepts. Ex.___

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. Ex.___

Experiments—Suitable for individual work or group projects.
- 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. Ex.___

Only a limited background in mathematics required—No calculus.
- Offers students a level of rigor appropriate for beginners. Ex.___

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. Ex.___

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. Ex.___

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. Ex.___

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. Ex.___

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. Ex.___

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.

Chapter Tests—Solutions to all questions supplied.
- Gives students the opportunity to self test their knowledge of chapter concepts. Ex.___

The different ways of representing relations are more thoroughly exploited.
- Enables students with different learning styles to master the concepts. Ex.___

Additional sections in the graph theory chapter covering transport networks and their applications.

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.

Discrete Math (Mathematics)

Discrete Mathematical Structures, 6/E
Kolman, Busby & Ross
©2009 | Pearson | Cloth; 552 pp | Instock
ISBN-10: 0132297515 | ISBN-13: 9780132297516
Net price: $96.00 (What's this?)Brief Description

Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. Ideal for a one-semester introductory course, this text contains more genuine computer science applications than any other text in the field.

This book is written at an appropriate level for a wide variety of majors and non-majors, and assumes a college algebra course as a prerequisite.

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