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AI Engineering/Phase 01
Foundation

Math Foundations

The linear algebra, calculus and probability you actually use, built by hand.

22 lessons ~31.8 hr
  1. Linear Algebra IntuitionLearn · Free · 1 hEvery AI model is just matrix math wearing a fancy hat.Open
  2. Vectors, Matrices & OperationsBuild · 1 hEvery neural network is just matrix multiplication with extra steps.Needs Full Access
  3. Matrix TransformationsBuild · 1 h 15 minA matrix is a machine that reshapes space. Learn what it does to every point, and you understand the whole transformation.Needs Full Access
  4. Calculus for Machine LearningLearn · 1 hDerivatives tell you which way is downhill. That is all a neural network needs to learn.Needs Full Access
  5. Chain Rule & Automatic DifferentiationBuild · 1 h 30 minThe chain rule is the engine behind every neural network that learns.Needs Full Access
  6. Probability and DistributionsLearn · 1 h 15 minProbability is the language AI uses to express uncertainty.Needs Full Access
  7. Bayes' TheoremBuild · 1 h 15 minProbability is about what you expect. Bayes' theorem is about what you learn.Needs Full Access
  8. OptimizationBuild · 1 h 15 minTraining a neural network is nothing more than finding the bottom of a valley.Needs Full Access
  9. Information TheoryLearn · 1 hInformation theory measures surprise. Loss functions are built on it.Needs Full Access
  10. Dimensionality ReductionBuild · 1 h 30 minHigh-dimensional data has structure. You find it by looking from the right angle.Needs Full Access
  11. Singular Value DecompositionBuild · 2 hSVD is the Swiss Army knife of linear algebra. Every matrix has one. Every data scientist needs one.Needs Full Access
  12. Tensor OperationsBuild · 1 h 30 minTensors are the common language between data and deep learning. Every image, every sentence, every gradient flows through them.Needs Full Access
  13. Numerical StabilityBuild · 2 hFloating point is a leaky abstraction. It will bite you during training, and you will not see it coming.Needs Full Access
  14. Norms and DistancesBuild · 1 h 30 minYour distance function defines what "similar" means. Choose wrong and everything downstream breaks.Needs Full Access
  15. Statistics for Machine LearningBuild · 2 hStatistics is how you know if your model actually works or just got lucky.Needs Full Access
  16. Sampling MethodsBuild · 2 hSampling is how AI explores the space of possibilities.Needs Full Access
  17. Linear SystemsBuild · 2 hSolving Ax = b is the oldest problem in mathematics that still runs your neural network.Needs Full Access
  18. Convex OptimizationBuild · 1 h 30 minConvex problems have one valley. Neural networks have millions. Knowing the difference matters.Needs Full Access
  19. Complex Numbers for AILearn · 1 hThe square root of -1 is not imaginary. It is the key to rotations, frequencies, and half of signal processing.Needs Full Access
  20. The Fourier TransformBuild · 1 h 30 minEvery signal is a sum of sine waves. The Fourier transform tells you which ones.Needs Full Access
  21. Graph Theory for Machine LearningBuild · 1 h 30 minGraphs are the data structure of relationships. If your data has connections, you need graph theory.Needs Full Access
  22. Stochastic ProcessesLearn · 1 h 15 minRandomness with structure. The math behind random walks, Markov chains, and diffusion models.Needs Full Access