Learning library

Make the foundations concrete.

Build working knowledge of robotics and machine learning through examples you can change, calculations you can check, and data you can inspect.

Start with the map of machine learning fields to connect tasks, data, learning signals, and model choices.

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99 lessons to explore

Foundations first

  1. Foundations / 8 min read

    A map of machine learning: tasks, signals, and models

    Understand how supervised learning, self-supervision, reinforcement learning, NLP, and deep learning fit together through practical robot and language examples.

  2. Foundations / 9 min read

    NLP: turn robot commands into token probabilities

    Learn natural language processing through a small robot-command corpus. Compare tokenization, unigram and bigram counts, unseen contexts, embeddings, and evaluation.

  3. Foundations / 10 min read

    pandas: select, align, and check a table of robot readings

    Learn pandas Series and DataFrames through robot readings. Compare loc and iloc, inspect label alignment, handle missing values, and check grouped summaries and joins.

  4. Foundations / 9 min read

    Vector norms and normalization: L1, L2, and L∞

    Measure vectors with L1, L2, and infinity norms. Explore unit boundaries, normalize a robot displacement, and distinguish zero vectors from tiny nonzero inputs.

  5. Foundations / 10 min read

    Matrix multiplication: calculate entries and compose transformations

    Learn matrix multiplication through row-column dot products, compatible shapes, and a rotation-and-stretch experiment that shows why transformation order matters.

  6. Foundations / 11 min read

    Cross product: find a normal direction and calculate torque

    Calculate a three-dimensional cross product, follow the right-hand rule, and connect its magnitude to area. Explore signed torque with a movable lever arm and force.

  7. Foundations / 9 min read

    Matrix transpose and inverse: when do they agree?

    Transpose rectangular matrices, calculate a 2×2 inverse, and test when a transpose reverses a transformation. Explore rotations, reflections, and singular maps.

  8. Foundations / 11 min read

    Determinants: signed area, volume, and collapsed directions

    Calculate a determinant, see how its sign records orientation, and connect zero area to singular matrices. Learn why a small determinant alone does not imply poor conditioning.

  9. Foundations / 12 min read

    Rank and null space: reachable outputs and hidden input changes

    Use rank, column space, and null space to understand a linear map. Explore rank-nullity, unreachable targets, and families of solutions with a small matrix experiment.

  10. Foundations / 10 min read

    Projections and least squares: find the closest fit

    Project a vector onto a direction, measure its orthogonal residual, and connect that geometry to least squares, regression, and nonunique coefficients.

  11. Foundations / 12 min read

    Singular value decomposition: directions, gains, and low-rank approximation

    Build an SVD from orthogonal directions and nonnegative gains. See a circle become an ellipse, identify lost directions, and measure the error from keeping one singular component.

  12. Foundations / 11 min read

    Pseudoinverse: choose the smallest least-squares solution

    Understand the Moore–Penrose pseudoinverse through exact and inconsistent systems. Separate residual error from solution norm, inspect projectors, and see how an SVD cutoff changes the problem.