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Mathematics & computational learning

The mathematics behind models, algorithms, and intelligent systems

Lessons that explain the mathematics used in real projects, from concept and equations to worked examples and implementation.

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  • LessonProgramming & Scientific ComputingIntermediate

    KKT and interior-point methods: when constraints enter the picture

    From Lagrangians and KKT conditions to barrier methods and Convex QP.

    A numerical-computing lesson connecting Lagrangians, KKT conditions, barrier methods, and Convex QP.

    Modeling, Algorithms & OptimizationSoftware Development & Engineering
  • LessonProgramming & Scientific ComputingBeginner

    What is a residual, and why should a numerical answer be checked?

    From equation residuals to independent checks of numerical solutions.

    A scientific-computing lesson connecting Python implementation with residuals, numerical answers, and independent checks.

    Software Development & EngineeringModeling, Algorithms & Optimization
  • LessonProgramming & Scientific ComputingIntermediate

    Norms, conditioning, and numerical stability

    From residuals and norms to condition numbers and numerical sensitivity.

    A scientific-computing lesson about error, sensitivity, and validation.

    Modeling, Algorithms & OptimizationSoftware Development & Engineering
  • Project explainerProgramming & Scientific ComputingIntermediate

    micrograd: understanding backpropagation through a tiny implementation

    A guided reading of a compact autograd engine and neural-network library, using it to make reverse-mode differentiation concrete.

    A project explainer showing how a small public codebase can make computational graphs, local derivatives, and backpropagation easier to inspect.

    AI & Machine LearningModeling, Algorithms & Optimization

Learning stays connected to real problems

This area is for conceptual, mathematical, and technical lessons, with real connections to projects, research, and solutions.