Lessons
Twenty chapters across five parts. Follow them in order, or jump to what you need.
Part 1Algebra and Mathematical Notation
- 1Numbers, Variables, and ExpressionsThe alphabet of mathematics, from ℕ to ℝWeek 1 · 55 min
- 2Equations and InequalitiesSolving, rearranging, and reasoning about relationshipsWeek 1 · 55 min
- 3Powers, Roots, Exponentials, and LogarithmsThe machinery behind loss functions and learning ratesWeek 1 · 65 min
- 4Mathematical Notation for ML PapersSummation, product, sets, indexing, argmin/argmax, and Big-OWeek 1 · 70 min
Part 2Functions and Graphs
Part 3Core Linear Algebra
- 7VectorsArrows, lists, feature vectors, and embeddingsWeek 3 · 75 min
- 8MatricesGrids of numbers that move spaceWeek 4 · 85 min
- 9Systems of Linear EquationsAx = b, Gaussian elimination, and geometric meaningWeek 4 · 75 min
- 10Vector Spaces and Linear TransformationsSpan, independence, basis, rank, and the four subspacesWeek 5 · 80 min
- 11Eigenvalues, Eigenvectors, and PCA IntuitionInvariant directions and the axes of varianceWeek 5 · 85 min
- 12Norms, Distances, and SimilarityMeasuring size, closeness, and alignmentWeek 3 · 65 min
Part 4Calculus
- 13Limits and ContinuityWhat happens as we get arbitrarily closeWeek 6 · 60 min
- 14DerivativesSensitivity, slope, and the rules that compute itWeek 6 · 90 min
- 15Chain Rule and Computational GraphsHow gradients flow backward through compositionWeek 7 · 85 min
- 16Optimization IntuitionMinima, gradient descent, learning rates, and convexityWeek 8 · 80 min
- 17Introductory Partial DerivativesSlopes in many directions and the gradient vectorWeek 7 · 75 min