InterviewsVector
Original Academy

Legacy mirror · noindex · upstream phase 1

Math Foundations

The intuition behind every AI algorithm, through code.

Provenance: this phase outline and its lesson readings are preserved from ai-engineering-from-scratch by Rohit Ghumare under the MIT License. InterviewsVector does not claim authorship. These archive pages remain available for old links and progress, but are excluded from indexing.

Attributed readings

  1. 01Linear Algebra IntuitionEvery AI model is just matrix math wearing a fancy hat.
  2. 02Vectors, Matrices & OperationsEvery neural network is just matrix multiplication with extra steps.
  3. 03Matrix Transformations & EigenvaluesA matrix is a machine that reshapes space. Learn what it does to every point, and you understand the whole transformation.
  4. 04Calculus for ML: Derivatives & GradientsDerivatives tell you which way is downhill. That is all a neural network needs to learn.
  5. 05Chain Rule & Automatic DifferentiationThe chain rule is the engine behind every neural network that learns.
  6. 06Probability & DistributionsProbability is the language AI uses to express uncertainty.
  7. 07Bayes' Theorem & Statistical ThinkingProbability is about what you expect. Bayes' theorem is about what you learn.
  8. 08Optimization: Gradient Descent FamilyTraining a neural network is nothing more than finding the bottom of a valley.
  9. 09Information Theory: Entropy, KL DivergenceInformation theory measures surprise. Loss functions are built on it.
  10. 10Dimensionality Reduction: PCA, t-SNE, UMAPHigh-dimensional data has structure. You find it by looking from the right angle.
  11. 11Singular Value DecompositionSVD is the Swiss Army knife of linear algebra. Every matrix has one. Every data scientist needs one.
  12. 12Tensor OperationsTensors are the common language between data and deep learning. Every image, every sentence, every gradient flows through them.
  13. 13Numerical StabilityFloating point is a leaky abstraction. It will bite you during training, and you will not see it coming.
  14. 14Norms & DistancesYour distance function defines what "similar" means. Choose wrong and everything downstream breaks.
  15. 15Statistics for MLStatistics is how you know if your model actually works or just got lucky.
  16. 16Sampling MethodsSampling is how AI explores the space of possibilities.
  17. 17Linear SystemsSolving Ax = b is the oldest problem in mathematics that still runs your neural network.
  18. 18Convex OptimizationConvex problems have one valley. Neural networks have millions. Knowing the difference matters.
  19. 19Complex Numbers for AIThe square root of -1 is not imaginary. It is the key to rotations, frequencies, and half of signal processing.
  20. 20The Fourier TransformEvery signal is a sum of sine waves. The Fourier transform tells you which ones.
  21. 21Graph Theory for MLGraphs are the data structure of relationships. If your data has connections, you need graph theory.
  22. 22Stochastic ProcessesRandomness with structure. The math behind random walks, Markov chains, and diffusion models.