How Can Shazam Identify Any Song in 3 Seconds Inside a Noisy Cafe? Acoustic Fingerprinting, Constellation Maps, and Blind Source Separation
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27 pages
Algorithms
How Do Emergency Hospitals and Cellular Towers Divide Their Territories? The Computational Geometry of Voronoi Diagrams and Delaunay Triangulations
Why Mixing Samples Finds Positives in Fewer Tests: The Mathematics of Group Testing and Combinatorial Search
Why Modern Computers Solve Exponentially Explosive NP-Complete Problems in Seconds: Inside SAT Solvers, CDCL, and Phase Transitions
Why Can Files Be Shrunk Without Losing a Single Character? The Principles and Limits of Lossless Compression — From Shannon Entropy, Huffman, and LZ77 to ANS and LLMs
How Winning Strategies Are Found in Stone-Taking Games: Nim and Combinatorial Game Theory
What Does It Truly Mean to Cut a Cake 'Fairly'? The Mathematics of Fair Division and Envy-Free Mechanisms
Why Computers Can't Add 0.1 and 0.2: The Science of IEEE 754 Floating-Point Arithmetic and Precision Errors
Complete Anatomy of the P vs NP Problem: The Pinnacle of Computational Complexity Theory and the Unsolved Abyss
Linux Completely Fair Scheduler (CFS) Internals: Virtual Runtime and Process Management Driven by Red-Black Trees
How search engines work: collecting the web, organizing information, and finding useful answers
Introduction to Dynamic Programming (DP) and Famous Problems (Knapsack, Fibonacci)
Search in Tree and Graph Data Structures (DFS, BFS, Dijkstra)
Search Algorithms (Principles of Linear, Binary Search and Hash Tables)
Sorting Algorithms Visualized (Bubble, Quick, Merge Sort)
Time and Space Complexity (Introduction to Big O Notation and Examples)
Automata and Formal Language Theory: Behind Regular Expressions and the Chomsky Hierarchy
How Quantum Computers Work and Shor's Algorithm: Why Quantum Computing Can Break Cryptography?
Turing Machines and Computability Theory: Alan Turing's Thought Experiment and the 'Halting Problem'
Gram-Schmidt Process: An Algorithm to Realign Distorted Basis Vectors into Neat, Mutually Orthogonal Vectors
