# Topics in Mathematics

#### Chapter 1: Topics in Logic

1. Statements
2. Quantifiers
3. Counterexamples
4. Compound Statements
5. Conditional Statements
6. More on Truth Tables
7. Problem Solving Strategies

#### Chapter 2: Topics in Set Theory

1. Introduction to Sets
2. Venn Diagrams
3. Cardinality
4. Subsets
5. Union & Intersection
6. Complements
7. The Cartesian Product

#### Chapter 3: Working with Whole Numbers

1. Introduction & Representation Strategies
2. Cardinal, Ordinal & Nominal Numbers
3. Addition & Subtraction of Whole Numbers
4. Properties & Representations of Addition & Subtraction
5. Multiplication of Whole Numbers
6. Properties & Representations of Multiplication
7. Division of Whole Numbers
8. Properties & Representations of Division
9. Exponentiation & Exponent Properties

#### Chapter 4: Topics in Number Theory

1. Prime & Composite Numbers
2. Divisibility Rules for 2, 5 and 10
3. Divisibility Rules for 3, 6 and 9
4. Divisibility Rules for 7 and 11
5. The Greatest Common Factor
6. The Euclidean Algorithm
7. The Lowest Common Multiple

#### Chapter 5: Working with Integers

1. Introduction & Representation Strategies
2. Addition & Subtraction of Integers
3. Multiplication of Integers
4. Division of Integers
5. Exponentiation & Exponent Properties

#### Chapter 6: Working with Fractions and Decimal Numbers

1. Introduction & Representation Strategies for Fractions
2. Addition & Subtraction of Fractions
3. Multiplication & Division of Fractions
4. Fractional Powers & Radical Notation
5. Introduction & Representation Strategies for Decimal Numbers
6. Addition & Subtraction of Decimal Numbers
7. Multiplication & Division of Decimal Numbers
8. Terminating & Repeating Decimal Numbers
9. Irrational Numbers & The Real Number System

#### Chapter 7: Topics in Algebra

1. Representation Strategies
2. Addition & Subtraction of Algebraic Expressions
3. Multiplication & Division of Algebraic Expressions
4. Factoring & Completing the Square
5. Solving Algebraic Equations

#### Chapter 10: Operations in Different Base Systems

1. Addition & Subtraction in Various Base Systems
2. Multiplication in Various Base Systems
3. Division in Various Base Systems
4. Fractions & Decimal Numbers in Various Base Systems
5. An Introduction to Modular Arithmetic

#### Chapter 11: Additional Topics in Algebra

1. Systems of Linear Equations
2. Introduction to Matrices & Vectors
3. Addition, Subtraction & Scalar Multiplication
4. The Dot Product of Vectors
5. Matrix Multiplication
6. Inverse Matrices
7. Revisiting Systems of Linear Equations