Blog
Occasional Random thoughts from us.
Why Matrices Are Everywhere in Machine Learning
Datasets, model weights, word embeddings and attention scores are all matrices, and training a large model is mostly matrix multiplication. Here is why, and how researchers keep making that multiplication cheaper.
Linear Algebra for Machine Learning: A Practical Introduction
You don't need a full math degree to use linear algebra in machine learning. Here are the seven ideas that matter most, from dot products to eigenvectors and SVD, each with a worked example and its ML use.
Vectors, Matrices, and Tensors Explained
A number, a list, a grid, a stack of grids: that's the whole ladder from scalars to tensors. Here is what each one is, what "shape" means, and how to estimate the memory an AI model needs.
How Mathematics Makes Computer Animation Possible
Animators set a few key poses; mathematics fills in the thousands of frames between them. Here is how interpolation, splines, easing, inverse kinematics and noise bring characters to life.
The Math Behind 3D Games
A 60 fps game has 16.67 milliseconds to do all its math each frame. Here are the vectors, quaternions, collision tests and physics integrators that fit in that budget.
The Mathematics Behind Computer Graphics
Every image on your screen, from a font to a movie explosion, is built from vectors, matrices, triangles and a cosine. Here is the core math of the graphics pipeline.
Unlocking the Power of Quadratic Functions: Real-World Applications and Problem Solving
Quadratic functions, a cornerstone of algebra, extend far beyond the classroom. They model diverse phenomena, from projectile motion to optimization…
Solving Linear Equations: A Comprehensive Guide with Real-World Applications
Linear equations form the bedrock of algebra and play a crucial role in various real-world applications. Understanding how to solve them is essential for…
Matrices: The Mathematics Behind Computer Graphics
Rotate then move, or move then rotate? With matrices, the order changes the result. Here is how 2D and 3D transformation matrices work, what the determinant tells you, and why every GPU speaks in 4×4 matrices.
Pierre de Fermat: The Enigmatic Prince of Number Theory in the Renaissance
Pierre de Fermat, a name synonymous with mathematical mystique and ingenuity, stands as a towering figure of the Renaissance and early modern periods…
Mastering Mathematical Induction: A Comprehensive Guide to Proofs
Mathematical induction is a fundamental proof technique used to establish the truth of a statement for all natural numbers. It's a powerful tool in the…
Vectors: The Mathematical Language of 3D Graphics
Positions, directions, light rays, velocities and surface orientations are all vectors. Here are the handful of vector operations every 3D program uses, with worked numbers and the graphics problem each one solves.