Discrete Mathematics for Computer Science

1. Introduction to Algorithms. 1.1. What are Algorithms? 1.2. Control Structures. 1.3. Tracing an Algorithm. 1.4. Algorithm Examples. 1.5. Problems. 2. Number Representations. 2.1. Whole Numbers. 2.2. Fractional Numbers. 2.3. The Relationship Between Binary, Octal, and Hexadecimal Numbers. 2.4. Converting from Decimal Numbers. 2.5. Problems. 3. Logic. 3.1. Propositions and Connectives. 3.2. Connective Truth Tables. 3.3. Truth Value of Compound Statements. 3.4. Tautologies and Contradictions. 3.5. Logical Equivalence and The Laws of Logic. 3.6 Problems. 4. Set Theory. 4.1. Set Notation. 4.2. Set Operations. 4.3. Venn Diagrams. 4.4. The Laws of Set Theory. 4.5. Binary Relations on Sets. 4.6. Problems. 5. Boolean Algebra. 5.1. Definition of Boolean Algebra. 5.2. Logic and Set Theory as Boolean Algebras. 5.3. Digital Circuits. 5.4. Sums-of-Products and Products-of-Sums. 5.5. Problems. 6. Functions. 6.1. Introduction to Functions. 6.2. Real-valued Functions. 6.3. Function Composition and Inverses. 6.4. Problems. 7. Counting and Combinatorics. 7.1. Addition and Multiplication Principles. 7.2. Counting Algorithm Loops. 7.3. Permutations and Arrangements. 7.4. Combinations and Subsets. 7.5. Permutation and Combination Examples. 7.6. Problems. 8. Algorithmic Complexity. 8.1. Overview of Algorithmic Complexity. 8.2. Time-Complexity Functions. 8.3. Finding Time-Complexity Functions. 8.4. Big-O Notation. 8.5. Ranking Algorithms. 8.6. Problems. 9. Graph Theory. 9.1. Basic Definitions. 9.2. Eulerian and Semi-Eulerian Graphs. 9.3. Matrix representation of Graphs. 9.4. Reachability for Directed Graphs. 9.5. Problems. 10. Trees. 10.1 Basic Definitions. 10.2. Minimal Spanning Trees of Weighted Graphs. 10.3. Minimal Distance Paths. 10.4. Problems. Appendix A: Basic Circuit Design. Appendix B: Answers to Problems.