Description

Features

• The focus on computer science prepares students for future computer science careers.
• The emphasis on proof lays the foundation for mathematical thinking.
• Clear organization of topics prevents students from being overwhelmed. The authors treat relations and digraphs as two aspects of the same fundamental idea, which is then used as the basis of virtually all the concepts introduced in the book.
• Vignettes of mathematical history open each chapter, providing students with a practical background of how these ideas were developed.
• Additional number theory coverage provides more information on the properties of integers, including base n representations, and gives more contexts for isomorphism.
• Cryptology is explored throughout the book, introducing students to this exciting field.
• Coverage of coding provides students with a full picture of all of its aspects, including efficiency, effectiveness, and security.  A set of coding exercises for each chapter is also included in Appendix C.
• Exercises emphasize multiple representations of concepts, and provide practice on reading and writing mathematical proofs.
• Experiments provide opportunities for in-depth exploration and discovery, as well as for writing and for working in groups. Topics include weighted voting systems, Petri nets, Catalan numbers, and others.
• End-of-chapter material includes Tips for Proofs, a summary of Key Ideas, and a Self-Test, which contains a set of conceptual review questions to help students identify and synthesize the main ideas of each chapter.

New To This Edition

• New sections on Logic, Mathematical Statements, and Logic and Problem Solving help students understand proofs and proof techniques.  Additional exercises help students develop conjectures and how to prove or disprove them.
• More applications, exercises, and figures have been added to help students learn and retain the material.
• New material on fuzzy sets and fuzzy logic introduces students to a topic that is extremely important for modern issues of automated feedback and control of processes.
• Popular puzzles like Sudoku and their underlying mathematical connections form a continuous thread in the text, connecting set theory, Boolean matrices, algorithms and coding, logic, the general construction of proofs, coloring problems and polynomials, and other topics in a way that students will find both interesting and instructive.

Table of Contents

1. Fundamentals

1.1 Sets and Subsets

1.2 Operations on Sets

1.3 Sequences

1.4 Properties of Integers

1.5 Matrices

1.6 Mathematical Structures

2. Logic

2.1 Propositions and Logical Operations

2.2 Conditional Statements

2.3 Methods of Proof

2.4 Mathematical Induction

2.5 Mathematical Statements

2.6 Logic and Problem Solving

3. Counting

3.1 Permutations

3.2 Combinations

3.3 Pigeonhole Principle

3.4 Elements of Probability

3.5 Recurrence Relations 112

4. Relations and Digraphs

4.1 Product Sets and Partitions

4.2 Relations and Digraphs

4.3 Paths in Relations and Digraphs

4.4 Properties of Relations

4.5 Equivalence Relations

4.6 Data Structures for Relations and Digraphs

4.7 Operations on Relations

4.8 Transitive Closure and Warshall's Algorithm

5. Functions

5.1 Functions

5.2 Functions for Computer Science

5.3 Growth of Functions

5.4 Permutation Functions

6. Order Relations and Structures

6.1 Partially Ordered Sets

6.2 Extremal Elements of Partially Ordered Sets

6.3 Lattices

6.4 Finite Boolean Algebras

6.5 Functions on Boolean Algebras

6.6 Circuit Design

7. Trees

7.1 Trees

7.2 Labeled Trees

7.3 Tree Searching

7.4 Undirected Trees

7.5 Minimal Spanning Trees

8. Topics in Graph Theory

8.1 Graphs

8.2 Euler Paths and Circuits

8.3 Hamiltonian Paths and Circuits

8.4 Transport Networks

8.5 Matching Problems

8.6 Coloring Graphs

9. Semigroups and Groups

9.1 Binary Operations Revisited

9.2 Semigroups

9.3 Products and Quotients of Semigroups

9.4 Groups

9.5 Products and Quotients of Groups

9.6 Other Mathematical Structures

10. Languages and Finite-State Machines

10.1 Languages

10.2 Representations of Special Grammars and Languages

10.3 Finite-State Machines

10.4 Monoids, Machines, and Languages

10.5 Machines and Regular Languages

10.6 Simplification of Machines

11. Groups and Coding

11.1 Coding of Binary Information and Error Detection

11.2 Decoding and Error Correction

11.3 Public Key Cryptology

Appendix A: Algorithms and Pseudocode

Appendix B: Additional Experiments in Discrete Mathematics

Appendix C: Coding Exercises

Courses

Discrete Math  (Mathematics)

Author Bios

Bernard Kolman received his BS in mathematics and physics from Brooklyn College in 1954, his ScM from Brown University in 1956, and his PhD from the University of Pennsylvania in 1965, all in mathematics. He has worked as a mathematician for the US Navy and IBM. He has been a member of the mathematics department at Drexel University since 1964, and has served as Acting Head of the department. His research activities have included Lie algebra and perations research. He belongs to a number of professional associations and is a member of Phi Beta Kappa, Pi Mu Epsilon, and Sigma Xi.

Robert C. Busby received his BS in physics from Drexel University in 1963, his AM in 1964 and PhD in 1966, both in mathematics from the University of Pennsylvania. He has served as a faculty member of the mathematics department at Drexel since 1969. He has consulted in applied mathematics and industry and government, including three years as a consultant to the Office of Emergency Preparedness, Executive Office of the President, specializing in applications of mathematics to economic problems. He has written a number of books and research papers on operator algebra, group representations, operator continued fractions, and the applications of probability and statistics to mathematical demography.

Sharon Cutler Ross received a SB in mathematics from the Massachusetts Institute of Technology in 1965, an MAT in secondary mathematics from Harvard University in 1966, and a PhD in mathematics from Emory University in 1976. She has taught junior high, high school, and college mathematics, and has taught computer science at the collegiate level. She has been a member of the mathematics department at DeKalb College. Her current professional interests are in undergraduate mathematics education and alternative forms of assessment. Her interests and associations include the Mathematical Association of America, the American Mathematical Association of Two-Year Colleges, and UME Trends. She is a member of Sigma Xi and other organizations.

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Instructor's Solutions Manual for Discrete Mathematical Structures, 6/E
Kolman, Busby & Ross
©2009  |  Pearson  |  Paper; 180 pp  |  Instock
ISBN-10: 0132297523  |  ISBN-13: 9780132297523
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Discrete Math Workbook: Interactive Exercises
Bush
©2003  |  Pearson  |  Paper; 404 pp  |  Instock
ISBN-10: 0130463272  |  ISBN-13: 9780130463272
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Practice Problems in Discrete Mathematics
Obrenic
©2003  |  Pearson  |  Paper; 275 pp  |  Instock
ISBN-10: 0130458031  |  ISBN-13: 9780130458032
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Allied Health Study Card, 2/E
Forshier
©2006  |  Pearson  |  Study Card  |  Instock
ISBN-10: 0321394747  |  ISBN-13: 9780321394743
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Basic Math Review Card, 2/E
Addison-Wesley
©2006  |  Pearson  |  Study Card; 6 pp  |  Instock
ISBN-10: 0321394763  |  ISBN-13: 9780321394767
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Center for Excellence Sticker
Addison Wesley Higher Education Group
©2000  |  Pearson  |  Unknown / Other  |  Instock
ISBN-10: 0201716275  |  ISBN-13: 9780201716276
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Concept Videos: Algebra
Addison-Wesley
©2008  |  Pearson  |  Multiple Media Package  |  Instock
ISBN-10: 0321517199  |  ISBN-13: 9780321517197
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Concept Videos: Basic Math & Prealgebra
Addison-Wesley
©2008  |  Pearson  |  Multiple Media Package  |  Instock
ISBN-10: 032151758X  |  ISBN-13: 9780321517586
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Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997  |  Pearson  |  Paper; 195 pp  |  Instock
ISBN-10: 0136492037  |  ISBN-13: 9780136492030
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Graphing Calculator Tutorial CD
Addison-Wesley
©2006  |  Pearson  |  CD-ROM Only  |  Instock
ISBN-10: 0321357744  |  ISBN-13: 9780321357748
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Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000  |  Pearson  |  Paper  |  Instock
ISBN-10: 0321069188  |  ISBN-13: 9780321069184
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Prealgebra Review Workbook
Wheel
©2006  |  Pearson  |  Paper; 300 pp  |  Instock
ISBN-10: 0321473329  |  ISBN-13: 9780321473325
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Review of Algebra, A
Howard
©2002  |  Pearson  |  Paper; 224 pp  |  Instock
ISBN-10: 0201773473  |  ISBN-13: 9780201773477
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Spanish Basic Math Study Card
Leonarte
©2007  |  Pearson  |  Study Card  |  Instock
ISBN-10: 0321438582  |  ISBN-13: 9780321438584
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TestGen All-in-One 2005 Package
Addison-Wesley
©2005  |  Pearson  |  CD-ROM Only  |  Instock
ISBN-10: 0321334469  |  ISBN-13: 9780321334466
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