Videos
Visit Existsforall Academy’s YouTube channel for the complete collection of videos, as the list below is incomplete. Subscribe on YouTube to get the latest updates on these videos, and like or comment to let me know which topics you enjoy the most!
All
Algebra
Combinatorics
Foundations
Geometry
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-17.png)
Binet’s Formula for Fibonacci Numbers
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-16.png)
Cassini’s Identity for Fibonacci Numbers
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-15.png)
Monty Hall Paradox in Probability
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-14.png)
Chain Rule for Events in Probability
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-13.png)
Classifying the Platonic Solids
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-12.png)
A Criterion for Planar Graphs
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-11.png)
Euler’s Characteristic Formula for Planar Graphs
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-10.png)
Handshaking Lemma in Graph Theory
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-9.png)
Stirling Partition Number of a Set
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-8.png)
Balls & Urns, Sticks & Stones, Stars & Bars
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-7.png)
Counting Surjections in Combinatorics
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-6.png)
Counting Derangements in Combinatorics
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-5.png)
Euler’s Totient Function Formula
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-4.png)
Principle of Inclusion-Exclusion (PIE)
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-3.png)
The Multinomial Theorem
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-2.png)
The Binomial Theorem
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail-1.png)
Vandermonde’s Identity
![](https://existsforall.com/wp-content/uploads/2021/12/Thumbnail.png)
Hockey Stick Identity
![](https://existsforall.com/wp-content/uploads/2021/09/Thumbnail-7.png)
Sum of Squares of a Row of Pascal’s Triangle
![](https://existsforall.com/wp-content/uploads/2021/09/Thumbnail-6.png)
Sum of a Row of Pascal’s Triangle
![](https://existsforall.com/wp-content/uploads/2021/09/Thumbnail-5.png)
Symmetry in Pascal’s Triangle
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Pascal’s Triangle and Pascal’s Identity
![](https://existsforall.com/wp-content/uploads/2021/09/Thumbnail-3.png)
Multinomial Coefficients
![](https://existsforall.com/wp-content/uploads/2021/09/Thumbnail-2.png)
Binomial Coefficients and Combinations
![](https://existsforall.com/wp-content/uploads/2021/09/Thumbnail-1.png)
$k$-to-$1$ Correspondences
![](https://existsforall.com/wp-content/uploads/2021/09/Thumbnail.png)
Counting Permutations
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-29.png)
Counting the Power Set of a Finite Set
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-28.png)
Friends and Strangers in Graph Theory
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-27.png)
Strong Pigeonhole Principle and Reverse
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-26.png)
Casework and Complementary Counting
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-25.png)
What is Combinatorics?
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-24.png)
Trigonometric Vector Cross Product
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-23.png)
Vector Cross Product Derivation
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-22.png)
Trigonometric Dot Product
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-21.png)
Euclidean Triangle Inequality
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-20.png)
Regular Octahedron: Surface Area & Volume
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-19.png)
Regular Tetrahedron: Surface Area & Volume
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-18.png)
Length of a Space Diagonal
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-17.png)
Six Area Formulas for Triangles
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-16.png)
Extended Law of Sines
![](https://existsforall.com/wp-content/uploads/2021/06/Thumnail.png)
Diagonals of a Cyclic Quadrilateral
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-15.png)
Stewart’s Theorem for Triangles
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-14.png)
Ceva’s Theorem for Triangles
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-13.png)
Pitot’s Theorem
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-12.png)
Cyclic Quadrilaterals
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-11.png)
Power of a Point Theorem
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-10.png)
Inscribed Angle Theorem
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-9.png)
Converse of Thales’s Circle Theorem
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-8.png)
Thales’s Circle Theorem
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-7.png)
The Law of Cosines
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-6.png)
Point-Line Distance Formula
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-5.png)
Chebyshev’s Inequality
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-4.png)
Schur’s Inequality
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-3.png)
Cauchy-Schwarz Inequality
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-2.png)
Arithmetic-Geometric Mean Inequality
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail-1.png)
Sophie Germain Identity
![](https://existsforall.com/wp-content/uploads/2021/06/Thumbnail.png)
Difference and Sum of Powers
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-14.png)
Vieta’s Polynomial Formulas
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-13.png)
Polynomial Remainder and Factor Theorems
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-12.png)
Complex Conjugates of Polynomial Roots
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-11.png)
Polynomial Integer Root Theorem
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-10.png)
Polynomial Rational Root Theorem
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-9.png)
Why is $\deg(0)=-\infty$?
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-8.png)
Square Root of a Complex Number
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-7.png)
The Quadratic Formula
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-6.png)
$n^{\text{th}}$ Roots of a Complex Number
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-5.png)
De Moivre’s Formula
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-4.png)
Complex Triangle Inequality
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-3.png)
Triple Angle Trig Identities
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-2.png)
Double & Half Angle Trig Identities
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail-1.png)
Pythagorean Theorem
![](https://existsforall.com/wp-content/uploads/2021/05/Thumbnail.png)
Angle Bisector Theorem
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnail-10.png)
Exterior Angle Theorem
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnail-9.png)
Interior Angle Theorem
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnail-8.png)
Sum of Powers of Positive Integers
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnail-7.png)
Telescoping & Partial Fraction Decomposition
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnail-6.png)
Geometric Series
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnail-5.png)
Arithmetic Series Using Gauss’s Formula
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnail-4.png)
Floor and Ceiling Sum Bounds
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnail-3.png)
Hermite’s Floor Identity
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnail-2.png)
Reverse Triangle Inequality
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnails.png)
Real Triangle Inequality
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnail-1.png)
Compound vs. Simple Interest
![](https://existsforall.com/wp-content/uploads/2021/04/Thumbnail.png)
Bernoulli’s Inequality
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-14.png)
Real Archimedean Property
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-13.png)
Discrete Fubini’s Principle
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-12.png)
Harmonic Series Divergence
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-11.png)
Counting the Pages of a Book
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-10.png)
Logarithmic Change of Base Identity
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail2-1.png)
Rationalizing a Denominator
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-9.png)
Unique Even and Odd Parts of a Function
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-8.png)
Inverses in a Binary Operation are Unique
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-7.png)
Identity Element of a Binary Operation is Unique
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-6.png)
Cantor’s Paradox in Set Theory
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail2.png)
Cantor’s Theorem in Set Theory
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-5.png)
Bijective Function if and only if Inverse Exists
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-4.png)
Bertrand Russell’s Paradox in Set Theory
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-2-1-768x527.png)
Subset Relation is a Partial Order
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-3.png)
Bounded Quantifiers in Logic
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail-2.png)
De Morgan’s Laws in Logic
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The Principle of Explosion in Logic
![](https://existsforall.com/wp-content/uploads/2021/03/Thumbnail.png)
Why Modus Ponens and Modus Tollens are Valid