MATH 204 • Midterm II • Discrete Mathematics

Big-O Notation

Example 1

Example 2

Example 3

Example 4

Sum Property of Big-O Notation

Multiplication Property of Big-O Notation

Example 1

Example 2

Big-Omega Notation

Big-Theta Notation

Example 1

Example 2

Linear Search Algorithm

Binary Search Algorithm

Bubble Sort Algorithm

Growth of Functions 1

Growth of Functions 2

Growth of Functions 3

Algorithms 1

Algorithms 2

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

Prime Numbers

Example 1

Example 2

Example 3

GCD Greatest Common Divisor

LCM Least Commun Multiple

Example 1

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

Chinese Remainder Theorem

Example 1

Example 2

Example 3

Example 4

Basic Principles of Counting

Counting Examples

Permutations

Permutations Example

Groups and Circular Permutation Example

Identical Objects Example

Combination

n choose r

Committee Example

Ball Example

Binomial Theorem

Example 1

Example 3

Example 2

Pascal Identity

Vandermonde's Identity

Example 1

Combinatorial Proof

Example 1

Principle Inclusion-Exclusion

Example 1

Example 2

Distributing Objects into Boxes 1

Distributing Objects into Boxes 2

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Pigeonhole Principle

Example 1

Example 2

Example 3

Example 4

Example 5

Introduction

Homogenous Recurrence Relations

Example 1

Example 2

Example 3

Example 4

Non Homogenous Recurrence Relations

Example5

Example 6

Creating Recurrence Relations

Example 7

Example 8

Example 9

Generating Functions

Example 1

Example 2

Example 3

Example 4

Example 5

Extended Binomial Theorem

Counting Problems with Generating Functions

Example 6

Example 7

Example 8

Example 9

Example 10

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

Counting 1

Counting 2

Counting 3

Counting 4

Counting 5

Counting 6

Counting 7

Counting 8

Principle Inclusion - Exclusion 1

Principle Inclusion - Exclusion 2

Pigeonhole Principle 1

Pigeonhole Principle 2

Pigeonhole Principle 3

Pigeonhole Principle 4

Pigeonhole Principle 5

Recurrence Relations 1

Recurrence Relations 2

Recurrence Relations 3

Recurrence Relations 4

Recurrence Relations 5

Recurrence Relations 6

Recurrence Relations 7

Recurrence Relations 8

Recurrence Relations 9

Generating Functions 1

Generating Functions 2

Generating Functions 3

Generating Functions 4

Generating Functions 5

Generating Functions 6

Generating Functions 7

Generating Functions 8

Generating Functions 9

Generating Functions 10

Generating Functions 11

Generating Functions 12

Generating Functions 13

Generating Functions 14

Generating Functions 15

Generating Functions 16

Algorithms (Spring 2019)

Growth of Functions (Spring 2024)

Growth of Functions & Number Theory (Spring 2025)

Modular Arithmetic- True False (Spring 2019)

Modular Arithmetic - Proof (Spring 2019)

Modular Arithmetic - Proof (Spring 2024)

Euclidian Algorithm (Spring 2024)

Euclidian Algorithm (Spring 2025)

Number Theory (Fall 2024)

Number Theory (Fall 2024)

Binomial Coefficient (Spring 2024)

Binomial Identities (Spring 2024)

Binomial Identities (Spring 2025)

Counting (Spring 2019)

Counting (Spring 2019)

Counting (Fall 2024)

Counting (Spring 2024)

Counting (Spring 2025)

Counting (Spring 2025)

Counting (Spring 2025)

Pigeonhole Principle (Fall 2024)

Pigeonhole Principle (Spring 2024)

Short Mixed Questions 1 (Spring 2025)

Short Mixed Questions 2 (Spring 2025)

Recurrence Relations (Spring 2025)

Generating Functions (Spring 2025)