WebAssign for Shannon, Discrete Mathematics: A Brief Introduction, Single-Term Instant Access,
1st Edition

0. WHAT IS DISCRETE MATHEMATICS WITH EXAMPLES.
What is Discrete Mathematics? Logistic Population Models and the interplay between Discrete and Continuous Systems and Models. The Königsburg Bridge Problem and the Party Problem. Some Useful Definitions.
1. PRELIMINARIES I: SETS.
Sets, subsets and set operations: Unions, Intersections, Complements. Set Equality: Truth Tables, Venn Diagrams and Element Chasing. Set Identities: Associate, Commutative, Absorptive, Identity Laws. DeMorgan’s Laws. Functions and Relations. Relations on a set A and their properties. Equivalence Relations and Modular Arithmetic. Partial Orderings and Hasse Diagrams. Chapter 1 Review.
2. PRELIMINARIES.
Logic and Proof. What is Proof; Conditional Connectives, Converses and Contrapositives. Mathematical Induction. More Mathematical Induction and Strong Induction. Universal and Existential Quantifiers. Recurrence Relations. Chapter 2 Review.
3. COUNTING (WITH DISCUSSIONS OF DISCRETE PROBABILITY).
Introduction: What is counting? The Multiplication Rule. Four questions: How many ways can k objects be selected from n objects? Ordered Samples with and without Repetition, Permutations. Unordered Samples without Repetition: Subsets, Pascal’s Triangle and the
Binomial Theorem. Unordered Samples with Repetition: Multisets (Optional). The Principle of Inclusion and Exclusion. Wrap up on Discrete Probability. Chapter 3 Review.
4. TREES AND OTHER GRAPHS.
Some Definitions and Uses: Graphs, Multigraphs, Network Problems, Transportation Problems. Graphs and Cycles: Adjacency Matrices, the Königsburg Bridge Problem and Euler Cycles. Trees and Spanning Trees: Spanning Tree Algorithm and the Daisy Chain Theorem. Greedy Algorithms: Minimal spanning trees, shortest paths, Prim’s Algorithm, and Dijkstra’s Algorithm. Binary Trees: Search Algorithms, Reverse Polish Notation. Planar Graphs and Euler’s Theorem. Chapter 4 Review.
5. INTRODUCTION TO PROPOSITIONAL CALCULUS, BOOLEAN ALGEBRA AND DIGITAL LOGIC GATES.
Set Theory, Propositional Calculus and Boolean Algebra, what’s the difference? Propositional Calculus. Boolean Algebra. Digital Logic Gates. Karnaugh Maps: Simplifying Boolean Expressions. Chapter 5 Review.
APPENDIX A INFINITE SETS AND COUNTABILITY.
APPENDIX B ANSWERS TO SELECTED PROBLEMS.
Practice Exercises and Problems whose numbers are underlined have answers or solutions in Appendix B. Those marked with * have partial solutions in Appendix B.

• Kathleen Shannon

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