Key Message: Discrete Mathematical Structures, Sixth Edition, offers a clear and concise presentation of the fundamental concepts of discrete mathematics. This introductory book contains more genuine computer science applications than any other text in the field, and will be especially helpful for readers interested in computer science. This book is written at an appropriate level for a wide variety of readers, and assumes a college algebra course as the only prerequisite.
Key Topics: Fundamentals; Logic; Counting; Relations and Digraphs; Functions; Order Relations and Structures; Trees; Topics in Graph Theory; Semigroups and Groups; Languages and Finite-State Machines; Groups and Coding
Market: For all readers interested in discrete mathematics.
| Preface |
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xi | |
| A Word to Students |
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xv | |
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1 | (49) |
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2 | (3) |
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5 | (8) |
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13 | (7) |
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Properties of the Integers |
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20 | (12) |
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32 | (9) |
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41 | (9) |
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50 | (41) |
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Propositions and Logical Operations |
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51 | (6) |
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57 | (5) |
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62 | (6) |
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68 | (7) |
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75 | (3) |
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Logic and Problem Solving |
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78 | (13) |
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91 | (31) |
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92 | (4) |
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96 | (4) |
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100 | (4) |
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104 | (8) |
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112 | (10) |
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122 | (58) |
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Product Sets and Partitions |
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123 | (4) |
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127 | (8) |
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Paths in Relations and Digraphs |
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135 | (6) |
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141 | (7) |
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148 | (4) |
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Data Structures for Relations and Digraphs |
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152 | (7) |
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159 | (10) |
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Transitive Closure and Warshall's Algorithm |
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169 | (11) |
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180 | (37) |
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181 | (9) |
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Functions for Computer Science |
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190 | (10) |
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200 | (5) |
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205 | (12) |
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Order Relations and Structures |
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217 | (53) |
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218 | (10) |
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Extremal Elements of Partially Ordered Sets |
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228 | (5) |
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233 | (10) |
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243 | (7) |
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Functions on Boolean Algebras |
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250 | (4) |
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254 | (16) |
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270 | (35) |
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271 | (4) |
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275 | (5) |
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280 | (8) |
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288 | (7) |
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295 | (10) |
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305 | (39) |
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306 | (5) |
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311 | (7) |
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Hamiltonian Paths and Circuits |
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318 | (3) |
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321 | (8) |
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329 | (5) |
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334 | (10) |
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344 | (42) |
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Binary Operations Revisited |
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345 | (4) |
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349 | (7) |
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Products and Quotients of Semigroups |
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356 | (6) |
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362 | (10) |
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Products and Quotients of Groups |
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372 | (5) |
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Other Mathematical Structures |
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377 | (9) |
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Languages and Finite-State Machines |
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386 | (43) |
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387 | (7) |
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Representations of Special Grammars and Languages |
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394 | (9) |
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403 | (6) |
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Monoids, Machines, and Languages |
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409 | (5) |
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Machines and Regular Languages |
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414 | (6) |
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Simplification of Machines |
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420 | (9) |
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429 | (26) |
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Coding of Binary Information and Error Detection |
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430 | (10) |
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Decoding and Error Correction |
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440 | (9) |
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449 | (6) |
| Appendix A: Algorithms and Pseudocode |
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455 | (12) |
| Appendix B: Additional Experiments in Discrete Mathematics |
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467 | (6) |
| Appendix C: coding Exercises |
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473 | (4) |
| Answers to Odd-Numbered Exercises |
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477 | (38) |
Answers to
Chapter Self-Tests |
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515 | |
| Glossary |
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1 | (1) |
| Index |
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1 | (1) |
| Photo Credits |
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1 | |
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.
