Discrete Structures

Major Topics

Chapter 1

The Logic of Compound Statements and Quantified Statements

• 1.1 Logical Forms and Equivalences
• 1.2 Conditional Statement Forms
• 1.3 Argument Forms
       Quiz:  Section 1.1 - 1.3
• 1.4 Digital Logic & Circuits
• 1.5 Binary Number Systems and Circuits for Addition
• 1.6 Predicates and Quantifiers
       Quiz:  Section 1.4 - 1.6
• 1.7 More Quantified Statements
• 1.8 Arguments with Quantified Statements
       Quiz: Chapter 1

Chapter 2

Elementary Number Theory, Matrices and Methods of Proof

• 2.1. Direct Proof and Counter Example
• 2.2. Rational Numbers, Divisibility and Quotient-Remainder Theorem
• 2.3. Sequences, Induction and Recursion
• 2.4. Matrix Algebra
       Quiz: Chapter 2

Chapter 3

Set Theory, Counting

• 3.1. Set Theory Basics
• 3.2. Set Properties and Definitions
• 3.3. Paradox and Puzzles
• 3.4. Counting, Permutations and Combinations
         Quiz: Chapter 3.1-3.4
• 3.5. Formulas Involving Combinations
• 3.6. The Inclusion Exclusion Principle
• 3.7. The PigeonHole Principle

• 4.1. Introduction to Functions
• 4.2. Application of Functions: Finite State Automata (Optional)
• 4.3. Advanced Functions

       Quiz: Section 4.1 - 4.3
• 4.4. More Advanced Functions
• 4.5. Relations

       Quiz: Chapter 4

Chapter 5

Graphs, Trees

• 5.1. An Introduction to Graphs
• 5.2  Connectivity of Graphs
• 5.3  Matrix Representations of Graphs
• 5.4  Introduction to Trees

       Quiz: Chapter5