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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.

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99 lessons found

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.