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Math for Machine Learning

31 problems·~8h·4 stages

A single sequence for the mathematics ML actually uses: linear algebra first, then probability and statistics, then calculus, then eigen-decomposition. You implement every operation by hand, from dot products to Jacobians and t-statistics. Start here if you want one path that covers the whole mathematical toolkit.

Your progress

0/31 · 0%

Path readiness 0%Easy 0% · Medium 0% · Hard 0%

Continue path · Vector Addition

What you will learn

  • Operate on vectors and matrices the way models do
  • Reason about rank, eigenvalues, and orthogonalization
  • Compute gradients, Jacobians, and Hessians by hand
  • Use distributions, expectation, and correlation in modeling

1Vectors and Matrix Algebra

0/8

The linear algebra ML runs on: vector arithmetic, dot products, norms, matrix transpose and multiplication, trace, and Hadamard products.

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.

2Probability and Statistics

0/8

The modeling half: expected value and variance, Bayes' rule, the normal CDF, means and variances, Pearson correlation, and one-sample t-statistics.

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 stepCredit Default DetectorMedium

3Calculus and Gradients

0/8

How models improve: numerical derivatives and gradients, directional derivatives, Newton steps, partial derivatives of quadratic forms, and full Jacobians and Hessians.

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

4Eigenvalues and Orthogonality

0/7

Why PCA and spectral methods work: cosine similarity, rank via row reduction, eigenvalues and eigenvectors, orthonormalization, power iteration, and Rayleigh quotients.

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.

Capstone

Pen and paper

Close the path with one real artifact from the catalog.

Norm of a vector projection

A handwritten final check on the projection arithmetic this path drills.