Discrete Mathematics

Doug Ensley is a full professor at Shippenshburg University with a Ph.D. from Carnegie Mellon.  He is an active participant in national and regional committees determining the future of the discrete math curriculum, and he regularly speaks at Joint Math and MathFest. Winston Crawley is a full professor and chair of the math department at Shippensburg University.  He has a Ph.D. from University of Tennessee-Knoxville.  Crawley developed the undergraduate computer science curriculum at Shippensburg.

• 1 Puzzles, Patterns, and Mathematical Language 11.1 First Examples 11.2 Number Puzzles and Sequences 91.3 Truth-tellers, Liars, and Propositional Logic 241.4 Predicates 401.5 Implications 531.6 Excursion Validity of Arguments 682 A Primer of Mathematical Writing 812.1 Mathematical Writing 822.2 Proofs about Numbers 982.3 Mathematical Induction 1102.4 More about Induction 1222.5 Contradiction and the Pigeonhole Principle 1322.6 Excursion Representations of Numbers 1502.7 Excursion Modular Arithmetic and Cryptography 1663 Sets and Boolean Algebra 1813.1 Set Definitions and Operations 1813.2 More Operations on Sets 1983.3 Proving Set Properties 2103.4 Boolean Algebra 2213.5 Excursion Logic Circuits 2294 Functions and Relations 2484.1 Definitions, Diagrams, and Inverses 2494.2 The Composition Operation 2684.3 Properties of Functions and Set Cardinality 2834.4 Properties of Relations 3014.5 Equivalence Relations 3134.6 Numerical Functions in Discrete Math 3244.7 Excursion Iterated Functions and Chaos 3344.8 Excursion Growth of Functions 3455 Combinatorics 3685.1 Introduction 3695.2 Basic Rules for Counting 3865.3 Combinations and the Binomial Theorem 3985.4 Binary Sequences 4085.5 Recursive Counting 4185.6 Excursion Solving Recurrence Relations 4236 Probability 4406.1 Introduction 4406.2 Sum and Product Rules for Probability 4486.3 Probability in Games of Chance 4606.4 Expected Value in Games of Chance 4666.5 Excursion Recursion Revisited 4756.6 Excursion Matrices and Markov Chains 4827 Graphs and Trees 5057.1 Graph Theory 5067.2 Proofs about Graphs and Trees 5197.3 Isomorphism and Planarity 5337.4 Connections to Matrices and Relations 5467.5 Graphs in Puzzles and Games 5677.6 Excursion Binary Trees 5817.7 Excursion Hamiltonian Cycles and the TSP 596A Rules of the Game 613Cards 613Sports 614Miscellaneous Games 615B Matrices and Their Operations 618Matrix Operations 618Matrix Arithmetic with Technology 620Selected Answers and Hints 625References and Further Reading 682