Clawdemy Lessons

How GPUs and TPUs execute model math: SIMT cores and memory tiers, the physics behind arithmetic intensity, and the TPU's systolic-array bet on matmul.

An overview of how modern language models are evaluated: the four benchmark formats, why evaluation is hard, contamination defenses, and the layered stack.

What you will learn about where LLM training tokens come from: six source categories, open datasets, the raw-to-final funnel, and sampling weights.

What this lesson covers and the skills it builds: filtering, deduplication, mixing, and synthetic data, with prerequisites and the technical-not-legal scope.

What this lesson on vectors covers: the three views, the two defining operations, prerequisites (none), and read and practice times.

Overview of the spans and basis lesson: what you will learn, prerequisites, the light algebra involved, and read and practice time estimates.

Overview of rectangular matrices: read a shape to find input and output dimensions, tell embeddings from projections, and place column space and null space.

Overview of the matrix multiplication lesson: composition of transformations, computing products column by column, prerequisites, time, and outcomes.

What this lesson on linear transformations covers: a matrix as the record of where basis vectors land, plus prerequisites, timing, and outcomes.

Orientation to inverses, column space, and null space: what you will learn, prerequisites, and the three equivalent tests for whether a matrix is invertible.

Overview of the eigenvectors lesson: what you will learn, how diagonalization delivers the change-of-basis payoff, prerequisites, and time and difficulty.

A learning guide to the dot product: the two formulas, projection, duality, and its role in attention and cosine similarity, plus prerequisites and timing.

A guide to the determinant: what it scales, how to read it off the unit square, the ad-bc formula, why zero means collapse, and the product rule.

A brief on the 2D cross product: compute the signed area two vectors span, read its sign as orientation, and see it as the determinant you know.

A roadmap to the Cramer's rule lesson: prerequisites, the area-ratio derivation you will build, and what solving a 2x2 system as a determinant ratio covers.

Overview of the change of basis lesson: what you'll learn, the prerequisites (inverses, transformations), and how it sets up eigenvectors.

What this brief covers: functions and polynomials as vectors, the derivative as a matrix, prerequisites, time, and how every track tool generalizes.

Overview of the 3D linear algebra lesson: what you will learn, prerequisites, and how stepping into three dimensions sets up the determinant next.

Overview of the lesson that derives the 3D cross product from duality, with prerequisites, learning outcomes, and the three geometric properties it covers.

An overview of why e^x is its own derivative: the multiplier crossing point, the chain-rule extension to e^(kx), and where e appears in growth and AI.

A guided overview of proving why area equals slope: the area function, the sliver argument giving A'(x)=f(x), and how it yields the fundamental theorem.

A roadmap to deriving sine and cosine derivatives from a point on the unit circle: what you'll learn, prerequisites, and where it fits.

Brief overview of the derivative lesson: the instantaneous-rate paradox, the rise-over-run limit, free-fall velocity, and the secant-to-tangent picture.

An overview of the product rule: why multiplying two derivatives is wrong, how a growing rectangle gives its two terms, plus the examples you will work.

What the power rule lesson covers: deriving d/dt(t^n) = n*t^(n-1) from growing squares and cubes, prerequisites, learning outcomes, and the time needed.