Mathematics & Physics
Calculus, Algebra & Physics
The Physics of Information: Thermodynamics, Shannon Entropy, and the Limits of Compression
A mathematical breakdown of how Boltzmann's statistical mechanics translates into Shannon's entropy, dictating the physical limits of data structures and network bandwidth.
The Geometry of Cryptography: Modular Arithmetic and Finite Fields
Uncover the mathematical architecture of modern encryption. A deep dive into modular rings, Galois Fields, and the algebraic geometry that powers AES.
Matrix Transformations: Visualizing Linear Algebra for Machine Learning
Stop viewing matrices as data containers. Learn how neural networks use linear algebra as an active engine to geometrically fold, shear, and crush high-dimensional space.
The Calculus of Learning: Understanding Gradients and the Chain Rule
Deconstruct the mathematics of backpropagation. Trace how partial derivatives and the chain rule allow neural networks to navigate high-dimensional error landscapes.
Signal Processing 101: The Math Behind the Fourier Transform
Strip away the black-box algorithms. Understand how complex exponentials and orthogonal projections decompose time-domain chaos into pure frequency.