Math Foundations
Mission. Teach the mathematics that the NumPy/pandas/scikit-learn stack silently assumes.
Scope
- Linear algebra: vectors, matrices, decompositions, geometric intuition
- Probability theory
- Calculus for ML: gradients, the chain rule
- Optimization: convexity, gradient descent
- Discrete math where it pays off
Learning objectives
- Explain what matrix multiplication does geometrically, not just mechanically
- Derive gradient descent by hand for simple objectives
- Read the math in an ML paper's methods section and follow it
Lessons
This track is scaffolded and waiting for content. See the curriculum dashboard for the roadmap and progress across all tracks.
Planned lessons (24)
Wave 2 — breadth (provisional roadmap) — 24 lessons
linear-algebra
- Vectors Magnitude and direction as the atom of data representation.
- Dot Products and Similarity Projections, cosines, and why similarity is a dot product.
- Norms and Distances Measuring size: L1, L2, and what each is for.
- Matrices as Transformations A matrix is a verb: stretching, rotating, projecting space.
- Matrix Multiplication, Geometrically Composing transformations, and why the order matters.
- Linear Systems Elimination, solution sets, and the geometry of solvability.
- Rank, Span, Independence The dimensions of your data and the redundancies inside it.
- Determinants What a determinant measures: volume, orientation, invertibility.
- Eigenvalues and Eigenvectors The directions a transformation doesn't turn, and why ML keeps finding them.
- Singular Value Decomposition The workhorse decomposition behind PCA, compression, and recommender systems.
- Projections and Least Squares The geometry behind every regression you'll fit.
probability
- Sample Spaces and Events Counting outcomes correctly before reasoning about them.
- Conditional Probability and Bayes Updating beliefs when evidence arrives, done carefully.
- Expectation and Variance The mean as an operator, and variance as its second moment.
- Covariance and Correlation Joint behavior of random variables, from the math up.
calculus
- Derivatives as Sensitivity Rates of change: what nudging an input does to an output.
- Gradients Partial derivatives as a vector pointing uphill.
- The Chain Rule Derivatives through composition, the engine of backpropagation.
optimization
- Convexity Bowl-shaped problems you can actually solve to optimality.
- Gradient Descent by Hand Deriving and stepping the update rule yourself.
- Gradient Descent in NumPy The update rule in code, with diagnostics for divergence.
- Constrained Optimization Lagrange multipliers and the boundary of the feasible set.
discrete
- Counting and Combinatorics Permutations, combinations, and counting without listing.
- Graph Theory Essentials Nodes, edges, paths: the structures behind networks and pipelines.