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Math Foundations

25 problems·~10h·4 stages

Build the linear algebra, statistics, probability, and calculus intuition every ML algorithm assumes. You start with vectors and matrix products and finish by computing Jacobians and Hessians by hand. This is the path to take if you want the math to stop feeling like magic.

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Continue path · Vector Addition

What you will learn

  • Compute dot products, matrix products, and determinants by hand
  • Summarize a dataset with mean, variance, correlation, and skewness
  • Apply Bayes' rule and compute expectations for discrete random variables
  • Differentiate numerically and build gradients, Jacobians, and Hessians

1Vectors and Matrices

0/7

Vectors and matrix products are the language every model is written in. Start with addition, scaling, dot products, and norms, then build matrix multiplication, transposes, and determinants.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.

2Describing Data

0/6

Before models, learn to compress a list of numbers into a few meaningful summaries: center, spread, and how two variables move together.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
LabRecommended next stepLogistic Regression, From ScratchEasy

3Change and Uncertainty

0/6

Calculus measures how outputs respond to inputs and probability measures how sure we are. This stage pairs numerical differentiation with Bayes' rule, cosine similarity, and 2x2 eigenvalues.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
LabRecommended next stepNoisy QuadraticMedium

4Toward ML Mathematics

0/6

The tools behind PCA, regression, and ranking: orthonormalization, eigenpair checks, rank correlation, and the Jacobian and Hessian that power backprop.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
LabRecommended next stepNoisy QuadraticMedium

Capstone

Collection

Close the path with one real artifact from the catalog.

Linear Algebra Crash Course

Run the vector and matrix half of this path as one continuous set before moving on to models.