Discrete Mathematical Structures (Classic Version)

About our authors 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.

• Table of Contents Fundamentals 1.1 Sets and Subsets1.2 Operations on Sets1.3 Sequences1.4 Properties of Integers1.5 Matrices1.6 Mathematical StructuresLogic 2.1 Propositions and Logical Operations2.2 Conditional Statements2.3 Methods of Proof2.4 Mathematical Induction2.5 Mathematical Statements2.6 Logic and Problem SolvingCounting 3.1 Permutations3.2 Combinations3.3 Pigeonhole Principle3.4 Elements of Probability3.5 Recurrence Relations 112Relations and Digraphs 4.1 Product Sets and Partitions4.2 Relations and Digraphs4.3 Paths in Relations and Digraphs4.4 Properties of Relations4.5 Equivalence Relations4.6 Data Structures for Relations and Digraphs4.7 Operations on Relations4.8 Transitive Closure and Warshall’s AlgorithmFunctions 5.1 Functions5.2 Functions for Computer Science5.3 Growth of Functions5.4 Permutation FunctionsOrder Relations and Structures 6.1 Partially Ordered Sets6.2 Extremal Elements of Partially Ordered Sets6.3 Lattices6.4 Finite Boolean Algebras6.5 Functions on Boolean Algebras6.6 Circuit DesignTrees 7.1 Trees7.2 Labeled Trees7.3 Tree Searching7.4 Undirected Trees7.5 Minimal Spanning TreesTopics in Graph Theory 8.1 Graphs8.2 Euler Paths and Circuits8.3 Hamiltonian Paths and Circuits8.4 Transport Networks8.5 Matching Problems8.6 Coloring GraphsSemigroups and Groups 9.1 Binary Operations Revisited9.2 Semigroups9.3 Products and Quotients of Semigroups9.4 Groups9.5 Products and Quotients of Groups9.6 Other Mathematical StructuresLanguages and Finite-State Machines 10.1 Languages10.2 Representations of Special Grammars and Languages10.3 Finite-State Machines10.4 Monoids, Machines, and Languages10.5 Machines and Regular Languages10.6 Simplification of MachinesGroups and Coding 11.1 Coding of Binary Information and Error Detection11.2 Decoding and Error Correction11.3 Public Key CryptologyAppendix A: Algorithms and Pseudocode Appendix B: Additional Experiments in Discrete Mathematics Appendix C: Coding Exercises