Contents 

1. Numbers, Sets and Functions

1. Introduction

2. The Quadratic Formula

3. Elementary Inequalities

4. Sets

5. Set Operations

6. Functions

7. How to Approach Problems

2. Language and Proofs

1. Introduction

2. Two Theorems about Equations

3. Quantifiers and Logical Statements

4. Compound Statements

5. Elementary Proof Techniques

6. How to Approach Problems

3. Induction

1. Introduction

2. Principle of Induction

3. Applications

4. Strong Induction

5. How to Approach Problems

4. Bijection and Cardinality

1. Introduction

2. Representation of Natural Numbers

3. Bijections

4. Injections and Surjections

5. Compositions of Functions

6. Cardinality

7. How to Approach Problems

5. Combinatorial Reasoning

1. Introduction

2. Arrangements and Selections

3. Binomial Coefficients

4. Permutations

5. Functional Digraphs

6. How to Approach Problems

6. Divisibility

1. Introduction

2. Factors and Factorization

3. The Euclidean Algorithm

4. The Dart Board Problem

5. Polynomials