Maths 230: Discrete Mathematics

Students will learn about topics such as logic and proofs, sets and functions, probability, recursion, graph theory, matrices, Boolean algebra and other important discrete math concepts. This course will prepare you to be the best at discrete maths.

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Course Curriculum

1. Ch 1.1 Critical Thinking and Logic in Mathematics
2. Logic
3. Propositions
4. True or False
5. Critical Thinking
6. Lesson Summary
7. Learning Outcomes
8. Quiz 1.1
1. Introduction
2. Logical Fallacy
3. Informal Fallacies
4. Inductive Fallacies
5. Hasty Generalization Fallacy
6. Hasty Generalization Fallacy Examples
7. Avoiding Hasty Generalization
8. Circular Reasoning Fallacy
9. Circular Reasoning Fallacy Examples
10. Avoiding Circular Reasoning
11. Limited Choice Fallacy Examples
12. Avoiding the Limited Choice Fallacy
13. False Cause
14. False Cause Fallacy Examples
15. Avoiding the False Cause Fallacy
16. Lesson Summary
17. Frequently Asked Questions
18. Quiz 1.2
1. Introduction
2. Appeal to Ignorance Fallacy
3. Appeal to Ignorance Examples
4. Appeal to Emotion Fallacy
5. Appeal to Emotion Fallacy Examples
6. Appeal to Popularity Fallacy
7. Appeal to Popularity Fallacy Examples
8. Lesson Summary
9. Frequently Asked Questions
10. Quiz 1.3
1. Introduction
2. Propositions in Logic
3. Negation of proposition
4. What is the Truth Value?
5. Propositional Logic Truth Tables
6. "AND" Truth Table
7. "OR" Truth Table
8. "If-Then" Truth Table
9. "If and Only If" Truth Table
10. Applications of Truth Tables
11. Lesson Summary
12. Frequently Asked Questions
13. Quiz 1.4
1. Introduction
2. Conjunction in Math
3. Conjunction Statement
4. Disjunction statement
5. Disjunction Statement
6. Conjunction vs. Disjunction
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 1.5
1. Introduction
2. What is a Conditional Statement?
3. How to Write a Conditional Statement?
4. Hypothesis and Conclusion of a Conditional Statement
5. Conditional Statement Logic
6. Conditional Statement Examples
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 1.6
1. Introduction
2. Inverse Statement
3. Inverse Statement Example
4. Converse vs. Inverse
5. Converse Logic Statement Example
6. Contrapositive Statement
7. Contrapositive Statement
8. Converse, Inverse, and Contrapositive Statements
9. Lesson Summary
10. Frequently Asked Questions
11. Quiz 1.7
1. Introduction
2. What is a Direct Proof?
3. Direct and Indirect Proofs in Discrete Mathematics
4. How to Write a Direct Proof
5. Direct Proof Induction
6. Lesson Summary
7. Activities
8. FAQs
9. Quiz 1.8
1. Introduction
2. What is a Tautology in Math?
3. Truth Table
4. Tautology Truth Table
5. Examples of Tautology
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 1.9
1. Ch 2.1 Mathematical Sets: Elements, Intersections & Unions
2. Understanding Sets
3. Unions
4. Intersections
5. Lesson Summary
6. Learning Outcome
7. Quiz 2.1
1. Introduction
2. Universal Sets
3. Subsets
4. Union and Intersection
5. Lesson Summary
6. Frequently Asked Questions
7. Quiz 2.2
1. Introduction
2. Complement of a Set: Overview and Terminology
3. What is the Complement of a Set?
4. Properties of the Complement of a Set
5. How to find the Complement of a Set?
6. Complement of a Set Examples
7. Lesson Summary
8. Quiz 2.3
1. Introduction
2. What Is a Set?
3. What Are the Types of Sets?
4. Cardinality of a Set
5. How to Find Cardinality of a Set
6. Cardinality Examples
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 2.4
1. Introduction
2. Definitions
3. Types of Relations
4. Hasse Diagram
5. Semilattice & Lattice
6. Lesson Summary
7. Quiz 2.5
1. Introduction
2. What is a Function?
3. Variables of a Function
4. Domain and Range of a Function
5. Function Graphs
6. Function Examples
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 2.6
1. Introduction
2. What is an Injective Function?
3. What is a Surjective Function?
4. What is a Bijective Function?
5. Cardinality of an Injective Function
6. Injective vs. Surjective vs. Bijective
7. Inverses and Isomorphisms
8. Lesson Summary
9. Frequently Asked Questions
10. Quiz 2.7
1. Ch 3.1 What is a Mathematical Sequence?
2. The Sequence in Math: Definition
3. Understanding Sequences in Math
4. Lesson Summary
5. Quiz 3.1
1. Introduction
2. Sequences
3. Types of Sequences in Mathematics
4. Sequence Formula
5. Sequence Examples
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 3.2
1. Introduction
2. The Arithmetic Sequence of Stadium Seating
3. Creating the Formula of an Arithmetic Sequence
4. Two Standard Formulas of Arithmetic Sequences
5. Finding an Arithmetic Sequence Using Terms
6. Lesson Summary
7. Quiz 3.3
1. Introduction
2. Geometric Sequences of Views of Cat Videos
3. Creating a Formula of a Geometric Sequence
4. Finding a Geometric Sequence Using Terms
5. Lesson Summary
6. Quiz 3.4
1. Introduction
2. Sigma Summation Notation
3. Series to Sigma Notation
4. Sigma Notation Geometric Series
5. Lesson Summary
6. Activities
7. FAQs
8. Quiz 3.5
1. Introduction
2. What is an Arithmetic Series?
3. The Formula for any Arithmetic Series
4. Solving the Michigan Stadium Problem
5. Lesson Summary
6. Quiz 3.6
1. Introduction
2. Geometric Series
3. Geometric Series Formula
4. How to Solve Geometric Series
5. Lesson Summary
6. Frequently Asked Questions
7. Quiz 3.7
1. Introduction
2. Practice Problems
3. Lesson Summary
4. Quiz 3.8
1. Introduction
2. What Is Mathematical Induction?
3. How to Use It
4. Proving a Statement
5. Another Example
6. Lesson Summary
7. Quiz 3.9
1. Introduction
2. What is Proof by Induction?
3. Proof by Induction Steps
4. Choosing the Base Case
5. Writing the Induction
6. Common Mistakes in Proof by Induction
7. Proof by Induction Examples
8. Lesson Summary
9. Quiz 3.10
1. Ch 4.1 Calculating Possible Outcomes: Definition & Formula
2. Possible Outcomes
3. Possible Outcomes Formula
4. Permutations
5. How to Find Possible Outcomes
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 4.1
1. Introduction
2. Combinatorics
3. The Pigeonhole Principle
4. More Examples
5. Lesson Summary
6. Quiz 4.2
1. Introduction
2. Permutation
3. Permutation Formula
4. Permutation Notation
5. How to Calculate Permutations
6. Permutation Examples
7. Combination Probability
8. Lesson Summary
9. Frequently Asked Questions
10. Quiz 4.3
1. Introduction
2. Probability
3. Permutations
4. Calculating Probability of Permutations
5. Lesson Summary
6. Learning Outcome
7. Quiz 4.4
1. Introduction
2. What Is Circular Permutation?
3. Combination vs. Circular Permutation
4. Types of Circular Permutation
5. Fixed vs. Free Circles
6. Circular Permutation Formula
7. Without Repetition
8. With Repetition
9. Multi-Sets
10. Permutation Examples
11. Lesson Summary
12. Frequently Asked Questions
13. Quiz 4.5
1. Introduction
2. What is a Combination?
3. Combination Formula
4. How to solve Combination Problems
5. Permutation vs Combination
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 4.6
1. Introduction
2. What is a Combination?
3. Define Combination
4. The Combination Formula
5. Combinations with Repetition
6. Combinations in Probability Problems
7. Examples of Using Combinations
8. Lesson Summary
9. Frequently Asked Questions
10. Quiz 4.7
1. Ch 5.1 Random Variables: Definition, Types & Examples
2. Random Variable Definition
3. Sample Space Examples
4. Types of Random Variable
5. What is a Discrete Random Variable?
6. What is a Continuous Random Variable?
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 5.1
1. Introduction
2. Discrete Variables
3. How to Find Expected Value?
4. Statistics of Expected Value
5. The Expected Value of a Discrete Random Variable
6. St. Petersburg Paradox
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 5.2
1. Introduction
2. Generating Discrete Probability Distribution
3. Tossing Two Coins
4. Expected Value
5. Roulette: A Game of Chance
6. Lesson Summary
7. Learning Outcomes
8. Quiz 5.3
1. Introduction
2. Changing Data Into Probability
3. Expected Value of the Distribution
4. Lesson Summary
5. Learning Outcomes
6. Quiz 5.4
1. Introduction
2. The Game of Dice
3. Putting It All Together
4. Rolling Three Dice
5. Four-Sided Dice
6. Lesson Summary
7. Learning Outcomes
8. Quiz 5.5
1. Introduction
2. Drawing Cards and Dependent Probabilities
3. Blackjack
4. Lesson Summary
5. Learning Outcomes
6. Quiz 5.6
1. Introduction
2. Probability in Poker
3. Probability of a Royal Flush
4. Probability of Straights and Flushes
5. Lesson Summary
6. Quiz 5.7
1. Introduction
2. Probability in Poker
3. Probability of a Full House
4. Probability of Four of a Kind
5. Probability of Pairs
6. Lesson Summary
7. Quiz 5.8
1. Introduction
2. Understanding Lotteries and Expected Values
3. Pick 4 Lotteries
4. Bonus Number Lotteries: Powerball
5. Lesson Summary
6. Learning Outcomes
7. Quiz 5.9
1. Introduction
2. Games and Expected Values
3. The Process
4. Betting for a Card
5. Insurance Rates
6. Lesson Summary
7. Quiz 5.10
1. Introduction
2. Understanding Discrete Probability
3. Properties of Probability
4. Practice Problems
5. Lesson Summary
6. Learning Outcomes
7. Quiz 5.11
1. Ch 6.1 Binomial Experiments: Definition, Characteristics & Examples
2. Binomial Experiments
3. Understanding Binomial Experiments
4. Identifying Binomial Experiments
5. Lesson Summary
6. Quiz 6.1
1. Introduction
2. Binomial Probabilities
3. Identifying Binomial Probabilities
4. Finding a Binomial Probability
5. Lesson Summary
6. Quiz 6.2
1. Introduction
2. Understanding Binomial Probabilities
3. Practice Problem 1
4. Practice Problem 2
5. Lesson Summary
6. Quiz 6.3
1. Introduction
2. What is Binomial Probability?
3. Binomial Experiment
4. Using the Binomial Distribution Table
5. Cumulative Binomial Distribution
6. Example of Probability Using Distribution Table
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 6.4
1. Introduction
2. What is a Binomial Random Variable?
3. Examples of a Binomial Random Variable
4. Probability Distribution of a Binomial Variable
5. Probability of a Binomial Random Variable
6. Mean and Standard Deviation of Binomial Distribution
7. How to Find the Mean of a Binomial Distribution
8. Expected Value of Binomial Distribution
9. Standard Deviation of Binomial Distribution
10. Standard Deviation of Random Variable
11. Lesson Summary
12. Frequently Asked Questions
13. Quiz 6.5
1. Introduction
2. Understanding Binomial Experiments
3. Binomial Experiment Problems
4. Lesson Summary
5. Quiz 6.6
1. Ch 7.1 Recursive Functions: Definition & Examples
2. What is a Recursive Function?
3. How to Write a Recursive Function
4. Recursive Equation Examples
5. Recursive Function Examples
6. Lesson Summary
7. Frequently Asked Questions
8. Quiz 7.1
1. Introduction
2. What is a Recurrence Relation?
3. Some Recurrence Formulas
4. Linear Recurrence
5. Lesson Summary
6. Frequently Asked Questions
7. Quiz 7.2
1. Introduction
2. Linear Recurrence
3. Types of Linear Recurrence
4. How to Solve Recurrence Relations
5. Characteristic Equation
6. Homogeneous Linear Recurrence Relation
7. Non-Homogeneous Linear Recurrence Relation
8. Applications of Recurrence Relations
9. Lesson Summary
10. Quiz 7.3
1. Introduction
2. What is the Divide-and-Conquer Algorithm?
3. Using the Divide-and-Conquer Approach
4. Divide-and-Conquer Algorithm Examples
5. Master Theorem
6. Advantages of the Divide-and-Conquer Algorithm
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 7.4
1. Introduction
2. Ordinary Generating Functions
3. Scaling a Generating Function
4. Addition of Two Generating Functions
5. Right-Shifting a Sequence
6. Multiplication of Two Sequences
7. Lesson Summary
8. Quiz 7.5
1. Introduction
2. Who Owns What?
3. Basic Set Theory
4. Inclusion-Exclusion with Two Sets
5. Examples with Two Sets
6. Inclusion-Exclusion with Three Sets
7. Examples with Three Sets
8. General Inclusion-Exclusion Principle Formula
9. Lesson Summary
10. Quiz 7.6
1. Ch 8.1 Introduction to Graph Theory
2. Graph Theory
3. A Graph
4. Vertices
5. Edges
6. Loops
7. Lesson Summary
8. Quiz 8.1
1. Introduction
2. A Graph
3. Vertices
4. Edges
5. Paths and Others
6. Lesson Summary
7. Learning Outcomes
8. Quiz 8.2
1. Introduction
2. Graphs in Discrete Mathematics
3. Types of Graphs
4. Uses of Graphs: Example 1
5. Example 2
6. Lesson Summary
7. Quiz 8.3
1. Introduction
2. Defining Graphs
3. Loop
4. Multi-Edges
5. Simple Graph
6. Isomorphism
7. Homomorphism
8. Lesson Summary
9. Quiz 8.4
1. Introduction
2. An Euler Path
3. An Euler Circuit
4. Lesson Summary
5. Quiz 8.5
1. Introduction
2. Euler Paths and Circuits
3. Delivering the Mail
4. The Traveling Salesman
5. The Seven Bridges of Konigsberg
6. Lesson Summary
7. Quiz 8.6
1. Introduction
2. Euler Circuit Definition
3. Fleury's Algorithm
4. Lesson Summary
5. Frequently Asked Questions
6. Quiz 8.7
1. Introduction
2. Euler's Theorem
3. Eulerian Graph
4. Euler's Path Theorem
5. Euler's Cycle Theorem or Euler Circuit in Graph Theory
6. Euler's Sum of Degrees Theorem
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 8.8
1. Introduction
2. A Graph
3. Fleury's Algorithm
4. Eulerizing a Graph
5. Semi-Eulerizing a Graph
6. Lesson Summary
7. Quiz 8.9
1. Introduction
2. Hamiltonian Path
3. Hamiltonian Circuit
4. Difference Between a Hamiltonian Path and a Hamiltonian Circuit
5. Lesson Summary
6. Frequently Asked Questions
7. Quiz 8.10
1. Introduction
2. A Hamilton Circuit
3. A Weighted Graph
4. A Complete Graph
5. Example
6. Lesson Summary
7. Quiz 8.11
1. Introduction
2. The Traveling Salesman Problem
3. Brute Force Method
4. Nearest Neighbor Method
5. Repeated Nearest Neighbor Method
6. Cheapest Link Method
7. Lesson Summary
8. Quiz 8.12
1. Introduction
2. What is Graph Coloring?
3. Coloring a Graph in Discrete Math
4. Chromatic Number
5. Traversing a Graph
6. Breadth-First Search (BFS)
7. Depth First Search (DFS)
8. Lesson Summary
9. Quiz 8.13
1. Introduction
2. What is a Graph?
3. Types of Graphs
4. Representations of Graphs
5. What is an Adjacency Matrix?
6. What is an Adjacency List?
7. Adjacency Matrix Examples
8. Adjacency List Examples
9. Lesson Summary
10. Frequently Asked Questions
11. Quiz 8.14
1. Ch 9.1 What are Trees in Discrete Math? - Definition, Types & Examples
2. Trees in Discrete Math
3. Rooted Tree
4. Directed Tree
5. Binary Tree
6. Properties of a Tree
7. Rooted Tree Diagram
8. Number of Edges in a Tree
9. Rooted Tree Example
10. Lesson Summary
11. Frequently Asked Questions
12. Quiz 9.1
1. Introduction
2. Searching the Tree Structure
3. Search Methods
4. Recap
5. Quiz 9.2
1. Introduction
2. The Value of Organization
3. Advantages and Disadvantages or Organization
4. Albert's Files
5. Lesson Summary
6. Quiz 9.3
1. Introduction
2. Spanning Trees
3. Strategies
4. Lesson Summary
5. Quiz 9.4
1. Introduction
2. Minimum Spanning Tree
3. Minimum Spanning Tree Algorithm
4. Explicit Enumeration
5. Kruskal's Algorithm
6. Prim's Algorithm
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 9.5
1. Ch 10.1 What is a Matrix?
2. What is a defination of Matrix?
3. Matrix Dimensions
4. Matrix Properties
5. Matrix Operations
6. Matrix Addition Rules
7. Matrix Subtraction Rules
8. Matrix Multiplication Rules
9. Matrix: Algebra
10. Lesson Summary
11. Frequently Asked Questions
12. Quiz 10.1
1. Introduction
2. Matrix Math
3. Matrix Notation
4. Equal Matrices
5. Addition of Matrices
6. Subtraction of Matrices
7. Multiplication of Matrices
8. Division of Matrices
9. Lesson Summary
10. Activities
11. solutions
12. FAQs
13. Quiz 10.2
1. Introduction
2. What is an Inverse Matrix?
3. Other Types of Matrices
4. Square Matrix
5. How to Do an Inverse Matrix
6. Inverse Matrix Examples
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 10.3
1. Introduction
2. What Is a Rotation?
3. What Is a Matrix?
4. Rotation Via a Matrix
5. Lesson Summary
6. Quiz 10.4
1. Introduction
2. Transformations
3. What Is a Translation?
4. Matrices to Complete Translations
5. Lesson Summary
6. Quiz 10.5
1. Ch 11.1 What Is Boolean Logic? - Definition, Diagram & Examples
2. Boolean? What's That?
3. Using Booleans Unknowingly
4. It Can't Be That Easy!
5. Lesson Summary
6. Quiz 11.1
1. Introduction
2. What is Boolean Algebra?
3. History of Boolean Algebra
4. Concepts in Boolean Algebra
5. Boolean Algebra Rules
6. Boolean Algebra Theorems
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 11.2
1. Introduction
2. What is a Boolean Expression?
3. How to Write a Boolean Expression
4. Boolean Operators: Definition
5. Boolean Logic Operators
6. Applications: Boolean Coding or Boolean Programming
7. Lesson Summary
8. Frequently Asked Questions
9. Quiz 11.3
1. Introduction
2. Karnaugh Map: Definition
3. A Karnaugh Map: Example
4. Simplifying Boolean Expressions
5. Lesson Summary
6. Quiz 11.4
1. Introduction
2. What Is an ALU?
3. How an ALU Works
4. Lesson Summary
5. Quiz 11.5
1. Introduction
2. Designing Logic Circuits
3. Example 1
4. Example 2
5. Lesson Summary
6. Quiz 11.6
1. Introduction
2. Logic Truth Tables & Logic Gates
3. NAND, NOR, and XOR Logic Gates
4. Functional Completeness
5. Lesson Summary
6. Quiz 11.7
1. Introduction
2. Simplifying Logic Circuits
3. Why Simplify Logic Expressions?
4. Lesson Summary
5. Quiz 11.8
1. Assignment
2. Final Exam

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Ch 1. Introduction to Logic & Proofs

Ch 1.2 Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice

Ch 1.3 Logical Fallacies: Appeals to Ignorance, Emotion or Popularity

Ch 1.4 Propositions, Truth Values and Truth Tables

Ch 1.5 Logical Math Connectors: Conjunctions and Disjunctions

Ch 1.6 Conditional Statements in Math

Ch 1.7 Logic Laws: Converse, Inverse, Contrapositive & Counterexample

Ch 1.8 Direct Proofs: Definition and Applications

Ch 1.9 Tautology in Math: Definition & Examples

Ch 2. Sets & Functions in Discrete Math

Ch 2.2 Universal Set in Math: Definition, Example & Symbol

Ch 2.3 Complement of a Set in Math: Definition & Examples

Ch 2.4 Cardinality & Types of Subsets (Infinite, Finite, Equal, Empty)

Ch 2.5 Partially Ordered Sets & Lattices in Discrete Mathematics

Ch 2.6 What is a Function: Basics and Key Terms

Ch 2.7 Injections, Surjections & Bijections

Ch 3. Sequences, Sums & Induction

Ch 3.2 Introduction to Sequences: Finite and Infinite

Ch 3.3 How to Find and Classify an Arithmetic Sequence

Ch 3.4 Finding and Classifying Geometric Sequences

Ch 3.5 Summation Notation and Mathematical Series

Ch 3.6 How to Calculate an Arithmetic Series

Ch 3.7 How to Calculate a Geometric Series

Ch 3.8 Arithmetic and Geometric Series: Practice Problems

Ch 3.9 Mathematical Induction: Uses & Proofs

Ch 3.10 Proof by Induction: Steps & Examples

Ch 4. Counting Rules, Combinations & Permutations

Ch 4.2 Combinatorics & the Pigeonhole Principle

Ch 4.3 How to Calculate a Permutation

Ch 4.4 How to Calculate the Probability of Permutations

Ch 4.5 Circular Permutation: Formula & Examples

Ch 4.6 Math Combinations: Formula and Example Problems

Ch 4.7 How to Calculate the Probability of Combinations

Ch 5. Discrete Probability

Ch 5.2 Finding & Interpreting the Expected Value of a Discrete Random Variable

Ch 5.3 Developing Discrete Probability Distributions Theoretically & Finding Expected Values

Ch 5.4 Developing Discrete Probability Distributions Empirically & Finding Expected Values

Ch 5.5 Dice: Finding Expected Values of Games of Chance

Ch 5.6 Blackjack: Finding Expected Values of Games of Chance with Cards

Ch 5.7 Poker: Finding Expected Values of High Hands

Ch 5.8 Poker: Finding Expected Values of Low Hands

Ch 5.9 Lotteries: Finding Expected Values of Games of Chance

Ch 5.10 Comparing Game Strategies Using Expected Values: Process & Examples

Ch 5.11 How to Apply Discrete Probability Concepts to Problem Solving

Ch 6. Binomial Probability

Ch 6.2 Finding Binomial Probabilities Using Formulas: Process & Examples

Ch 6.3 Practice Problems for Finding Binomial Probabilities Using Formulas

Ch 6.4 Finding Binomial Probabilities Using Tables

Ch 6.5 Mean & Standard Deviation of a Binomial Random Variable: Formula & Example

Ch 6.6 Solving Problems with Binomial Experiments: Steps & Example

Ch 7. Recursion & Advanced Counting

Ch 7.2 What Is a First-Order Linear Recurrence? - Definition & Uses

Ch 7.3 How to Solve Linear Recurrence Relations

Ch 7.4 Solving Divide-and-Conquer Recurrences

Ch 7.5 Generating Function in Discrete Math: Definition & Examples

Ch 7.6 Inclusion-Exclusion Principle in Combinatorics

Ch 8. Principles of Graphs & Graph Theory

Ch 8.2 Graph Theory Concepts and Terminology

Ch 8.3 Graphs in Discrete Math: Definition, Types & Uses

Ch 8.4 Isomorphism & Homomorphism in Graphs

Ch 8.5 Euler Paths and Euler's Circuits

Ch 8.6 Mathematical Models of Euler's Circuits & Euler's Paths

Ch 8.7 Fleury's Algorithm for Finding an Euler Circuit

Ch 8.8 Euler's Theorems: Circuit, Path & Sum of Degrees

Ch 8.9 Eulerizing Graphs in Math

Ch 8.10 Hamilton Circuits and Hamilton Paths

Ch 8.11 Assessing Weighted & Complete Graphs for Hamilton Circuits

Ch 8.12 Methods of Finding the Most Efficient Circuit

Ch 8.13 Coloring & Traversing Graphs in Discrete Math

Ch 8.14 Adjacency Representations of Graphs in Discrete Math

Ch 9. Trees in Discrete Mathematics

Ch 9.2 How to Traverse Trees in Discrete Mathematics

Ch 9.3 Using Trees for Sorting: Benefits & Disadvantages

Ch 9.4 What is a Spanning Tree? - Properties & Applications

Ch 9.5 Minimum Spanning Tree: Algorithms & Examples

Ch 10. Matrices in Discrete Math

Ch 10.2 Matrix Notation, Equal Matrices & Math Operations with Matrices

Ch 10.3 How to Solve Inverse Matrices

Ch 10.4 Using Matrices to Complete Rotations

Ch 10.5 Using Matrices to Complete Translations