A detailed explanation of the life of the ancient Greek mathematician Diophantus, his masterpiece 'Arithmetica', Diophantine equations, and the mystery hidden in his epitaph.
An in-depth look at the life of the ancient Greek mathematician Euclid, the impact of his masterpiece 'Elements' on later generations, and his mathematical achievements such as the Euclidean algorithm.
A deep dive into the life of Fibonacci, the spread of Arabic numerals through "Liber Abaci", and the amazing relationship between the Fibonacci sequence and the Golden Ratio hidden in nature.
An in-depth exploration of the life of the ancient Greek mathematician Pythagoras, the Pythagorean theorem, and the philosophy that all is number.
Archimedes of Syracuse. From the 'Eureka' episode to the calculation of pi, the theorem of the sphere and cylinder, and the 'Method' that pioneered calculus, we delve into the life and achievements of ancient Greece's greatest mathematician and physicist.
A complete anatomy of the rendering engine (Blink, WebKit, etc.) mechanism, from the browser loading HTML/CSS/JS to drawing pixels on the screen.
An in-depth look at the next-generation web communication protocol, including why HTTP/3 and the QUIC protocol were created, solving the Head-of-Line Blocking problem, and speeding up connection establishment.
How WebRTC enables direct browser-to-browser communication. A thorough breakdown of complex behind-the-scenes technologies like NAT traversal (STUN/TURN), signaling servers, and the ICE protocol.
A comprehensive guide to all things Wasm, from WebAssembly architecture, compilation process, and JS integration, to its possibilities outside the browser (WASI).
Security measures to protect Web applications from threats. Comprehensively explains from classic XSS and CSRF to modern essential technologies such as CORS, CSP, and SameSite Cookie.
A comprehensive guide to the basics of graph theory. From the bridges of Königsberg to shortest path algorithms like Dijkstra's, Python implementations, and modern machine learning applications, let's explore the mathematics of networks.
An in-depth guide to the Inclusion-Exclusion Principle, an essential mathematical tool for accurately counting elements of multiple overlapping sets without duplication. We explain everything from the basic 2-set case to the general n-set case, using examples, proofs, and application examples.
A detailed explanation of probability models for state transitions, covering the basics and applications of Markov chains.
A detailed explanation of the mathematical structure woven by permutations, combinations, the binomial theorem, and Pascal's triangle.
A detailed explanation of the mathematical background of random walks (the drunkard's walk), from the basics to diffusion phenomena and Brownian motion. A definitive guide including Pólya's recurrence theorem and applications to financial engineering.
A detailed explanation of the mathematical foundations of affine and projective transformations, their expression using homogeneous coordinates, and applications in computer graphics and image processing.
Understand normalization, sensitivity versus positive predictive value, MAP versus posterior prediction, and the assumptions behind four Bayesian applications in AI.
Discover fascinating proofs of the Pythagorean theorem. Explore the beauty of mathematics from Euclid to Einstein through various perspectives.
An in-depth explanation of the beauty of Euler's polyhedron formula (V - E + F = 2) and the world of topology it leads to. Let's explore the charm of invariants, from regular polyhedra to the Euler characteristic.
An in-depth explanation of non-orientable surfaces in topology, specifically the Möbius strip and the Klein bottle, using mathematical formulas and diagrams.
