Math Foundations

Every AI model is just matrix math wearing a fancy hat.

Every neural network is just matrix multiplication with extra steps.

A matrix is a machine that reshapes space. Learn what it does to every point, and you understand the whole transformation.

Derivatives tell you which way is downhill. That is all a neural network needs to learn.

The chain rule is the engine behind every neural network that learns.

Probability is the language AI uses to express uncertainty.

Probability is about what you expect. Bayes' theorem is about what you learn.

Training a neural network is nothing more than finding the bottom of a valley.

Information theory measures surprise. Loss functions are built on it.

High-dimensional data has structure. You find it by looking from the right angle.

SVD is the Swiss Army knife of linear algebra. Every matrix has one. Every data scientist needs one.

Tensors are the common language between data and deep learning. Every image, every sentence, every gradient flows through them.

Floating point is a leaky abstraction. It will bite you during training, and you will not see it coming.

Your distance function defines what "similar" means. Choose wrong and everything downstream breaks.

Statistics is how you know if your model actually works or just got lucky.

Sampling is how AI explores the space of possibilities.

Solving Ax = b is the oldest problem in mathematics that still runs your neural network.

Convex problems have one valley. Neural networks have millions. Knowing the difference matters.

The square root of -1 is not imaginary. It is the key to rotations, frequencies, and half of signal processing.

Every signal is a sum of sine waves. The Fourier transform tells you which ones.

Graphs are the data structure of relationships. If your data has connections, you need graph theory.

Randomness with structure. The math behind random walks, Markov chains, and diffusion models.