AI From Scratch
Phase 01/22 lessons/~23 hours

Math Foundations

The intuition behind every AI algorithm, through code — not textbooks.

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01Linear Algebra IntuitionUp nextEvery AI model is just matrix math wearing a fancy hat.Learn/~60 minutes/Python, Julia02Vectors, Matrices & OperationsEvery neural network is just matrix multiplication with extra steps.Build/~60 minutes/Python, Julia03Matrix TransformationsA matrix is a machine that reshapes space. Learn what it does to every point, and you understand the whole transformation.Build/~75 minutes/Python, Julia04Calculus for Machine LearningDerivatives tell you which way is downhill. That is all a neural network needs to learn.Learn/~60 minutes05Chain Rule & Automatic DifferentiationThe chain rule is the engine behind every neural network that learns.Build/~90 minutes06Probability and DistributionsProbability is the language AI uses to express uncertainty.Learn/~75 minutes07Bayes' TheoremProbability is about what you expect. Bayes' theorem is about what you learn.Build/~75 minutes08OptimizationTraining a neural network is nothing more than finding the bottom of a valley.Build/~75 minutes09Information TheoryInformation theory measures surprise. Loss functions are built on it.Learn/~60 minutes10Dimensionality ReductionHigh-dimensional data has structure. You find it by looking from the right angle.Build/~90 minutes11Singular Value DecompositionSVD is the Swiss Army knife of linear algebra. Every matrix has one. Every data scientist needs one.Build/~120 minutes/Python, Julia12Tensor OperationsTensors are the common language between data and deep learning. Every image, every sentence, every gradient flows through them.Build/~90 minutes13Numerical StabilityFloating point is a leaky abstraction. It will bite you during training, and you will not see it coming.Build/~120 minutes14Norms and DistancesYour distance function defines what "similar" means. Choose wrong and everything downstream breaks.Build/~90 minutes15Statistics for Machine LearningStatistics is how you know if your model actually works or just got lucky.Build/~120 minutes16Sampling MethodsSampling is how AI explores the space of possibilities.Build/~120 minutes17Linear SystemsSolving Ax = b is the oldest problem in mathematics that still runs your neural network.Build/~120 minutes18Convex OptimizationConvex problems have one valley. Neural networks have millions. Knowing the difference matters.Build/~90 minutes19Complex Numbers for AIThe square root of -1 is not imaginary. It is the key to rotations, frequencies, and half of signal processing.Learn/~60 minutes20The Fourier TransformEvery signal is a sum of sine waves. The Fourier transform tells you which ones.Build/~90 minutes21Graph Theory for Machine LearningGraphs are the data structure of relationships. If your data has connections, you need graph theory.Build/~90 minutes22Stochastic ProcessesRandomness with structure. The math behind random walks, Markov chains, and diffusion models.Learn/~75 minutes