MATH 132 • Midterm I • Discrete and Combinatorial Mathematics

Injective Functions

Example 1

Example 2

Surjective Functions

Example 1

Example 2

Bijective Function

Proof Example For Image of a Function

Proof Example for Preimage of a Function

Example

Definition

Example 1

Countable Sets

Properties of Countable Sets

Example 1

Uncountable Sets

Definition of Divisibility

Example 1

Example 2

Example 3

Division Algorithm

Definition of Modular Arithmetic

Example 1

Properties of Modular Arithmetic

Example 1

Example 2

GCD Greatest Common Divisor

LCM Least Common Multiple

Euclidian Algorithm

Example 1

Bézout Identity

Example 1

Example 2

Example 3

Inverse of a Number in Modular Arithmetic

Fermat's Little Theorem

Solving Linear Congruences

Example 1

Example 2

Chinese Remainder Theorem

Example 1

Example 2

Example 3

Example 4

Introduction

Proof of Formulas by Induction

Example 1

Example 2

Exam-like Question

Exam-like Question

Proof of Divisibility by Induction

Example 1

Example 2

Exam-like Question

Exam-like Question

Proof of Inequality by Induction

Example 1

Example 2

Example 3

Exam-like Question

Exam-like Question

Exam-like Question

Induction Related to Fibonacci

Exam-like Question

Strong Induction

Exam-like Question

Exam-like Question

Exam-like Question

Exam-like Question

Pigeonhole Principle

Example 1

Example 2

Example 3

Example 4

Sets and Functions 1

Cardinality 1

Cardinality 2

Cardinality 3

Cardinality 4

Cardinality 5

Cardinality 6

Cardinality 7

Number Theory 1

Number Theory 2

Number Theory 3

Number Theory 4

Number Theory 5

Number Theory 6

Number Theory 7

Number Theory 8

Number Theory 9

Number Theory 10

Number Theory 11

Number Theory 12

Induction 1

Induction 2

Induction 3

Induction 4

Induction 5

Induction 6

Induction 7

Induction 8

Induction & Number Theory

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3

Pigeonhole Principle 4

Pigeonhole Principle 5

Number Theory

Number Theory

Induction

Cardinality

Pigeonhole Principle

Number Theory - Modular Arithmetic

Number Theory - Chinese Remainder Theorem

Number Theory - Euclidian Algorithm

Cardinality

Induction for Formulas

Induction for Divisibility

Cardinality

Induction

Number Theory

Number Theory

Number Theory

Number Theory