mathispower4u

Most of the videos support the following free discrete math textbook.
Discrete Mathematics, An Open Introduction (3rd Edition)
by Oscar Levin

Introduction andPreliminaries

0.1 What is Discrete Math
What is Discrete Mathematics?

0.2 Mathematical Statements (Playlist)
Mathematical Statements and Logic Connectives
Truth Conditions for Connectives
Implications and Truth Conditions for Implications
Write Math Statements As Symbols and Symbols as Math Statements
Determine Truth Values of Statements from a Given Implication
Introduction to The Converse and Contrapositive of an Implication
Determine the Converse, Inverse, and Contrapositive of an Implication
Converse and Contrapositive Example (Chinese Food and Milk)
Converse and Contrapositive: Drawing Conclusion from an Implication
If And Only If Statements
Given the Truth Value of an Implication and Converse, Find the Truth Value of If And Only If Statements
Necessary and Sufficient Statements
Equivalent Statements to an Implication
Introduction to Predicates and Quantifiers
Predicate and Quantifier Concept Check 1
Predicate and Quantifier Concept Check 2
Determine if Quantified Statements are True or False from a Table

0.3: Introduction to Sets (Playlist)
Introduction to Sets and Set Notation
Determine the Union, Intersection, and Difference of Two Set Given as Lists
Determine Sets Given Using Set Notation (Ex 1)
Determine Sets Given Using Set Notation (Ex 2)
Set Notation: Determine Which Statements are True or False
Determine the Least Element in a Set Given using Set Notation.
Determine the Power Set of a Set and the Cardinality of a Power Set
Determine the Cardinality of Sets Given as Lists
Determine the Cardinality of Sets: Set Notation, Intersection
Determine Sets Involving Unions, Intersections, and Compliments
Determine Sets Involving Unions, Intersections, and Compliments Using a Venn Diagram
The Cartesian Product of Two Sets
Shading Venn Diagrams with Two and Three Sets: Unions and Intersections
Shading Venn Diagrams with Two and Three Sets: Complements
Shading Venn Diagrams with Two and Three Sets: Set Differences
Shading Venn Diagrams with Two and Three Sets: Complements, Intersections, Unions
De Morgan's Laws with Venn Diagrams
De Morgan's Laws: Set Example
Find a Set with Greatest Cardinality that is a Subset of Two Given Sets (Lists)
Find a Set with Greatest Cardinality that is a Subset of Two Given Sets (Set Notation)
Find a Set with Least Cardinality that has Two Given Subsets (Lists)
Find How Many Sets Are a Subset of a Given Set and Have a Given Subset

0.4: Functions (Playlist)

Introduction to Functions (Discrete Math)
Two Line Notation for a Function: Inputs and Outputs
Describing Functions (Discrete Math)
Recursive Functions (Discrete Math)
Determine Function Values for a Recursive Functions
Surjective, Injective, and Bijective Functions
Determine if Functions Given in Two Line Notation are Surjective, Injective, and Bijective
Determine if Various Functions are Surjective, Injective, and Bijective
List All Possible Function Given Domain an Codomain Then Determine if Surjective, Injective, and Bijective (8)
List All Possible Function Given Domain an Codomain Then Determine if Surjective, Injective, and Bijective (9)
Image of a Subset of the Domain and Inverse Image of a Subset of the Codomain

Chapter 1: Counting (Playlist)

1.1: Additive and Multiplicative Principles
Introduction to Counting Using Additive and Multiplicative Principles
Counting Principle With Playing Cards: Picking 1 and 2 Cards (Not Disjoint)
Counting: Neck Wear and Outfits (Additive and Multiplicative Principles)
Counting: Number of Hexadecimal Numbers with Restrictions (And/Or)
Counting: Number of Hexadecimal Strings with Restrictions (And/Or)
The Cardinality of the Union of Two Sets
Determine the Number of Elements in a Large Set that are Multiples of 3 or 5
The Cardinality of the Union of Three Sets
Determine the Number of Elements in a Large Set that Multiples of 3 or 5 or 8
Determine the Greatest and Least Values of the Cardinality of an Intersection and Union
Determine Sum of the Cardinality of the Union and Intersection of Two Sets
The Cardinality of the Union of Three Sets Application: TV Shows

1.2: Binomial Coefficients
Counting Subsets and Subsets of a Specific Cardinality
Determine How Many Subsets Meet Various Conditions (1)
Determine How Many Subsets Meet Various Conditions (2)
Determine How Many Subsets Have More Than a Given Cardinality
Introduction to Bit Strings
Determine the Number of 10-Bit Strings Under Various Conditions
Problem Solving with Bit Strings - Coin Problems
Determine the Number of 9-Bit Strings That Have More Than a Given Number of 1's
Introduction to Lattice Paths
Determine the Number of Shortest Lattice Paths Under Various Conditions
Lattice Paths Application: Driving
Introduction to Binomial Coefficients
Determine Binomial Coefficients
Determine a Coefficient of a Expression of Binomials Raised to Powers
Evaluating Combinations Using Pascal's Triangle
Making Connections: The Many Applications of Combinations
Combinations: The Number of 4 Topping Pizzas

1.3: Combinations and Permutations
Counting: Find the Number of Functions and Bijective Functions (Discrete Math)
Counting: Find the Number of Functions, Injective Functions, and Increasing Functions (Discrete Math)
Counting: Number of Pizza with 3 Toppings and All Possible Pizzas
Counting: Find the Number of Lock Combinations
Counting: Find the Number of 5-Digit Numbers Under Various Conditions
Counting: Books on a Shelf - Arrangements and Alphabetized
Counting: The Number of Types of Quadrilaterals from Two Rows of Points
Counting: The Number of Triangles from an L-Shape of Points
Counting: The Number of Anagrams of Words. (No repeats and repeats)
Counting: The Number of Ordered Groups of Four

1.4: Combinatorial Proofs
Algebraic Proof: C(n,k)=C(n-1,k-1)+C(n-1,k)
Combinatorial Proofs: C(n,k)=C(n-1,k-1)+C(n-1,k)
Algebraic and Combinatorial Proofs: C(n,k)=C(n,n-k)
Combinatorial Proof: 1n+2(n-1)+3(n-2)+…+(n-1)2+n1

1.5: Stars and Bars
Introduction to Stars and Bars Counting Method
Stars and Bars: The Number of Multisets
Stars and Bars: The Number of Ways of Putting Basketballs in Bins
Stars and Bars: The Number of 4-Digit Number with Repetition in Nondecreasing Order
Stars and Bars: The Number of Integers Solutions to x+y+z=8 With Conditions
Stars and Bars: Determine the Number of Outcomes of Rolling 5 Dice (Yahtzee)
Stars and Bars: Determine the Number of Outcomes of 7 Coins of 4 Types
Stars and Bars: The Number of Integer Solutions to w+x+y+z=25 with Different Lower Bounds
Stars and Bars: Number of Discrete Functions, Increasing Functions, and Nondecreasing Functions

1.6: Advanced Counting Using PIE
Stars and Bars with PIE: Find the Number of Meals from a Dollar Menu with Conditions
Introduction to Derangements
Find the Number of Permutations with One Fixed Element Using Derangements
Stars and Bars with PIE: Determine the Number of Ways of Putting Balls in Bins with Upper Bound
Stars and Bars with PIE: Assigning Stars to Students

Chapter 2: Sequences (Playlist)

2.1: Describing Sequences
Introduction to Sequences (Discrete Math)
Determine a Closed Formula for a Given Sequence (1)
Determine a Closed Formula for a Given Sequence (2)
Determine Partial Sums and Recursive and Closed Formulas for Sequences
Given a Recursive Definition of a Sequence, Find Terms and a Closed Formula (1)
Given a Recursive Definition of a Sequence, Find Terms and a Closed Formula (2)
Given a Closed Formula for a Sequence, Find Terms and a Recursive Definition
Introduction to Partial Sums and Partial Products
Given a Sequence, Find Partial Sums and Find a Formula For S_n Involving a_n
Determine Recursive Formulas for Sequences
Given a Recursive Definition, Find Terms of the Sequence
Given a Closed Formula for a Sequence, Find Terms and Find a Closed Formula for a Sequence
Show a Closed Formula for a Sequence Satisfies a Recurrence Relation

2.2: Arithmetic and Geometric Sequences
Introduction to Arithmetic and Geometric Sequences (Discrete Math)
Arithmetic Sequence: Find Recursive Definition, Close Formula, and Number of Terms
Find the Sum of an Arithmetic Sequence and a Closed Formula for a Sequence of Partial Sums (Formula Used)
Find the Sum of an Arithmetic Sequence and a Closed Formula for a Sequence of Partial Sums (Reverse and Add)
Arithmetic Sequence: Find Next Term, Closed Formula, and Partial Sum
Sum of Arithmetic Sequence: Find Number of Terms and Sum with No Formula
Arithmetic Sequence: Find Number of Terms, Second to Last Term, and Partial Sum (Reverse/Add)
Find a Sum of a Geometric Sequence Using Multiply, Shift, and Subtract Method (1)
Find a Sum of a Geometric Sequence Using Multiply, Shift, and Subtract Method (2)
Given 5,x,y,625, Find x and y if the Sequence is Arithmetic or Geometric
Find the Closed Formula for a Sequence that is the Partial Sums of an Arithmetic Sequence
Show that 0.33333… Equals 1/3

2.3: Polynomial Fitting
Introduction to Polynomial Fitting to Find a Closed Formula for a Sequence
Find a Closed Formula for a Sequence Using Polynomial Fitting (Degree 2, by hand)
Find a Closed Formula for a Sequence Using Polynomial Fitting (Degree 2, Aug Matrix)
Find a Closed Formula for a Sequence Using Polynomial Fitting (Degree 3, Aug Matrix)
Find a Closed Formula for a Sequence of Difference Given a_n

2.4: Solving Recurrence Relations
Sequences: Introduction to Solving Recurrence Relations
Solve a Recurrence Relation Using Inspection
Solve a Recurrence Relation Using the Telescoping Technique
Solve a Recurrence Relation Using the Characteristic Root Technique (1 Repeated Root)
Solve a Recurrence Relation Using the Characteristic Root Technique (2 Distinct Roots)
Find a Recurrence Definition and Solve the Recurrence Relation of a Given Sequence
Determine a Recursive Definition and Closed Formula for a Geometric Sequence
Determine and Solve a Recurrence Relation: Path of Tiles Problem

2.5: Induction

Introduction to Proof by Induction: Prove 1+3+5+…+(2n-1)=n^2
Mathematical Induction (older)
Proof by Induction: Prove The Sum of n Squares Formula
Proof by Induction: 4^n - 1 is a Multiple of 3
Proof by Induction: Prove The Sum of n Counting Numbers Formula
Proof by Induction: Prove n^2 < 2^n with n >= 5.
Proof by Strong Induction: If x + 1/x is an Integer Then x^n+1/x^n is an Integer

Chapter 3 Symbolic Logic and Proofs (Playlist)

3.1: Propositional Logic
Introduction to Propositional Logic and Truth Tables
Make Truth Tables for If (P and Q) Then (P or Q) and If (P or Q) Then (P and Q)
Make Truth Tables for P and (If Q Then P) and If (Not P) and (If Q Then P)
Make a Truth Table for If (Not P) Then (Q and R)
Introduction to Logically Equivalent Statements
Determining if Two Statements Are Equivalent Using a Truth Table
Deduction Rules: Modus Ponens and Modul Tollens
Verify the Deduction Rule: If P then Q. If (Not P) Then Q. Therefore Q.
Determine if an Argument is a Deduction Rule or Not: P -> R. Q -> R. R. Therefore P or Q
Determine if an Argument is a Deduction Rule or Not: If (P and Q), Then R. Not P or Not Q. Therefore Not R
Draw Conclusions From the Negation of Statements: Eat and Drink Application
Simplify Statements Using Logically Equivalent Statements
Logically Equivalent Statements: Draw a Conclusion from a False Implication
Introduction to Predicate Logic
Simplify the Negation of Statements with Quantifiers and Predicates

3.2: Proofs
Introduction to Common Mathematical Proof Methods
Introduction to Direct Proofs: If n is even, then n squared is even
Introduction to Proof by Contrapositive: If n squared is even, then n is even
Proof by Contrapositive: If a + b is odd, then a is odd or b is odd
Introduction to Proof by Contradiction: sqrt(2) is irrational
Proof by Contradiction: There are infinitely many primes
Proof by Contradiction: There are no integers x and y such that x^2 = 4y + 2
The Pigeonhole Principle (Proof by Contrapositive)
Introduction to Proof by Counter Example
Proof by Counter Example: Prove a Converse is False
Determine the Negation, Converse, and Contrapositive of a Quantifier Statement (Symbols)
Proof by Cases: For Any Integer, n^3-n is Odd
Proof Exercise: State the Contrapositive, Converse and Negation, Then Prove the Truth Value
Proof Exercise: Determine the Type of Proof to be Used

Chapter 4: Graph Theory (Playlist)

4.1: Definitions

Introduction to Graph Theory
The Definition of a Graph (Graph Theory)
Isomorphic Graphs
Subgraphs and Induced Subgraphs
More Graph Theory Definitions
The Handshake Lemma
Bipartite Graphs and Named Graphs
Handshake Lemma Exercises: Possible Number of Friends
Largest Possible Number of Edges for Various Types of Graphs

4.2: Trees

Introduction to Trees and Properties of Trees
Introduction to Rooted Trees
Given a Rooted Tree, Determine Relationships
Every Tree is a Bipartite Graph
Introduction to Spanning Trees
Given the Definition of a Graph, Determine if the Graph is a Tree
Given a Degree Sequence, Determine if the Graph is a Tree
Given the Graph of a Rooted Tree List the Children, Parents and Siblings of All Vertices
Given a Tree, Does Changing the Root Change the Number of Children and Grandchildren?

4.3: Planar Graphs

Introduction to Planar Graphs and Euler's Formula
Non-Planar Graphs: Proving K5 and K33 are Non-Planar
Introduction Polyhedra Using Euler's Formula
Prove There Are Exactly 5 Regular Polyhedra
Is a Planar Graph Possible Given the Number of Vertices, Edges, and Faces?
Is a Planar Graph Possible Given a Degree Sequence?
Is it Possible for a Connected Graph to be Planar Given Vertices, Edges, and Faces?
Is it Possible for a Graph to be Planar with the Same Number of Vertices and Edges?
Euler's Formula: Find a Missing Face of a Polyhedron

4.4: Coloring

Introduction to Vertex Coloring and the Chromatic Number of a Graph
Upper and Lower Bounds for the Chromatic Number of a Graph
Edge Coloring and the Chromatic Index of a Graph
Determine Which Graphs have a Given Chromatic Number
Find the Chromatic Number of the Given Graphs
Find the Chromatic Number of a Graph that Represents a Cube

4.5: Euler Paths and Circuits

Introduction to Euler Paths and Euler Circuits
Introduction to Hamilton Paths and Hamilton Circuits
Euler Path Application: Road Trip
Determine if Named Graphs Have Euler Paths or Euler Circuits
Euler Path Application: Home Tour Passing Though each Doorway Once
Hamilton Path Application: Home Tour Visiting Each Room Once
Vertex Degree Application: Home Remodel with Odd Number of Doors
For Which Values of n Does K_n have an Euler Path or an Euler Circuit
For Which Values of m and n Does K_m,n have an Euler Path or an Euler Circuit
For Which Values of n Does K_n have a Hamilton Path or a Hamilton Circuit

4.6: Matching in Bipartite Graphs

Introduction to Matching in Bipartite Graphs (Hall's Marriage Theorem)
Proof by Contradiction Using Hall's Marriage Theorem (Playing Cards)
Bipartite Graphs: Determine a Matching of A if Possible
Matching in Bipartite Graphs: Marriage Arrangements

Chapter 5: Additional Topics (Playlist)

5.1: Generating Functions

5.2: Introduction to Number Theory

Intro to Number Theory and The Divisibility Relation
The Division Algorithm and Remainder Classes
Introduction to the Modulo Operator: a mod b with a positive
The Modulo Operator: a mod b with a negative
Introduction to Congruence Modulo n
Congruence Modulo n Properties: Equivalent Relation
Find a Remainder Using Congruences: 3491/9
Use Congruence to Determine Remainders of 2^2019 when Divided by 2, 5, 7, and 9
Find a Remainder Using Congruences: 2^(124)/7
Find a Remainder Using Congruences: 3^(123)/7 (Two Versions)
Simplify a Congruence Using Division
Solving Congruences
Introduction to Solving Linear Diophantine Equations Using Congruence
Application of a Linear Diophantine Equation: Number of Stamps

5.3: Algorithm Analysis
Introduction to Big-O Notation
Introduction to Big-Omega Notation
Introduction to Big-Theta Notation
Compare Algorithm Complexity Given The Execution Time as a Function
Rank the Complexity of Functions
Determine Time Complexity of Code Using Big-O Notation: O(1), O(n), O(n^2)
Determine Time Complexity of Code Using Big-O Notation: O(n+m), O(n*m), O(log(n))
Determine Time Complexity Function and Time Complexity Using Big-O Notation: f(n)=(cn(n-1))/2