A Complete Proof of the Singular Value Decomposition

Geometric Proof of the Cauchy-Schwarz Inequality

Did you know that there exists a bijection from [0,1] to (0,1)?

Proving the Subset Sum Problem is NP-Complete | 3-SAT to Subset Sum Reduction

A Demo of Manim Animations Beyond CS/Math

Linear Regression Analysis of Socioeconomic Factors and Crime Rates

Understanding the Binomial Expansion

Proof of Fermat’s Little Theorem and a Note of its Generalization

Solving Summations Cleverly: Finite Geometric Series and Finite Arithmetic-Geometric Series

Proof by Contradiction: Galileo’s Law of Free Fall and Proving √3 is Irrational

x86-64 Assembly Programming: Global Variables and Conditional Set/Move Instructions

Network Flow: Max Flow Problem, Ford-Fulkerson Algorithm, max-flow min-cut theorem

x86-64 Assembly Arithmetic and Bitwise Operations Explained

Explanation of Basic x86-64 Assembly Programming Techniques

Binary Search Trees Explained: Search, Insertion, Deletion

Graphs Explained: Undirected and directed graphs, Euler and Hamiltonian paths, handshaking theorem

Tree Data Structure: Binary trees, expression trees, in-order, pre-order, post-order traversals

Introduction to Data Structures and Algorithms

Greedy Algorithms: Proof of Correctness for Kruskal’s Algorithm

Merge Sort in x86-64 Assembly language

Dynamic Programming: The Knapsack Problem, DP table, implementation in Python

Bipartite Matching. Is there a perfect matching?

Proving the Vertex Cover Problem is NP-Complete | 3-SAT to Vertex Cover Reduction

The SAT Problem: First problem proven to be NP-Complete

Divide and Conquer Algorithms Introduction

Introduction to NP-Complete Problems

What is a B-tree? Properties, Insertion, Deletion.

Red-Black Tree | Properties, Insertion, Deletion, Elementary Operations.

Heap Sort Explained | Pseudocode and Example

Quicksort Explained | Pseudocode and Example

Merge Sort Explained | Pseudocode and Example

Radix Sort Explained | Pseudocode and Example

Counting Sort Explained | Pseudocode and Example

What is the Gaussian Integral?

What is 1 + cos t + cos 2t + … + cos Nt equal to?

Induction and Invariants | Definitions and Examples

Big O Notation, Big Omega Notation, and Big Theta Notation | Definitions and Examples

3D Parametric Heart 💗| Happy Valentine’s Day!

Dijkstra’s Algorithm Explained | Pseudocode and Example

Heap Data Structure | Definition and Example

Deque (Double-ended queue) Data Structure | Definition and Example

Queue Data Structure | Definition and Example

Stack Data Structure | Definition and Example

Linked List Data Structure | Definition and Example

Kruskal’s Algorithm Explained | Pseudocode and Example

Prim’s Algorithm Explained | Pseudocode and Example

Breadth First Search (BFS) Algorithm | Pseudocode and Example

Depth First Search (DFS) Algorithm | Pseudocode and Example

Cute Cat Animation made with Manim

Nezha Wishes Everyone Happy Chinese New Year 哪吒祝大家新年快乐 | Created with Hailuo AI

Happy Chinese New Year of the Snake! 新年快乐！蛇年大吉，万事如意！

Wukong's Weapon Ruyi Staff 金箍棒 | Created with Manim

Parametric Heart Curve in Python | Parametric Equations and Code Included

Computing the Volume of an Ellipsoid and the Area of an Ellipse using the Jacobian Determinant

How to Show the Absolute Value of the Determinant is the Volume of the Parallelepiped (Proof Idea)

Taylor’s Theorem and a Formula for the Remainder (Manim Math Animation)

Manim Animated Hello World Program in x86-64 Assembly

Red Black Tree Insertion

Implementing a While Loop in x86-64 Assembly using 2nd argument of main

Some x86-64 Assembly commands in details