Maths for Machine Learning
The vectors, matrices, derivatives and probability that every machine learning course assumes you already have.
About this track
Almost every machine learning explanation stops to say "recall that the gradient points uphill" or "this is just a dot product" and moves on. This track is where you go to actually see those things, one at a time, with something you can drag.
It starts at the equation of a line and works up through vectors, matrix multiplication, derivatives and probability distributions. Nothing here assumes a maths degree, and nothing is left as an exercise for the reader.
All 13 modules, in teaching order
- 01Equation of a Line (y = mx + c)Learn the equation of a line using an interactive 2D and 3D visualizer. Understand slope and intercept with real examples, live calculations, and guided practice.
- 02LogarithmsInteractive logarithms lesson - explore log curves for any base, the product-to-sum rule, and why log scales tame huge ranges.
- 03ExponentialsInteractive exponentials lesson - growth versus decay, the number e, doubling time, and why exponential always beats polynomial eventually.
- 04Vectors and the Dot ProductInteractive lesson on vectors and the dot product - drag vectors, see magnitude, angle, projection, and why the dot product changes sign at 90 degrees.
- 05Matrix MultiplicationInteractive matrix multiplication - click an output cell to see the row and column that produce it, with the shape rule enforced live.
- 06Derivatives and SlopeInteractive derivatives lesson - drag a point along a curve, shrink the secant to a tangent, and see the limit definition of the derivative in action.
- 07The Chain RuleInteractive chain rule lesson - see how derivatives multiply through composed functions, and why this is exactly what backpropagation computes.
- 08Partial Derivatives and the GradientInteractive partial derivatives and gradient lesson - explore a 2D surface, see partial slopes along each axis, and the gradient arrow pointing uphill.
- 09Mean, Mode and MedianInteractive lesson on mean, mode and median - see how skew and outliers pull the three averages apart, and which one to trust.
- 10Mean, Variance and Standard DeviationInteractive lesson on mean, variance and standard deviation - drag data points, see deviations squared, sigma bands and z-scores computed live.
- 11Probability BasicsInteractive probability basics - sample spaces, events, AND vs OR, independence, and the law of large numbers demonstrated by simulation.
- 12Bayes' TheoremInteractive Bayes theorem lesson - the medical test paradox shown as a natural frequency grid, with adjustable base rate, sensitivity and specificity.
- 13The Normal DistributionInteractive normal distribution lesson - adjust mean and standard deviation, see the 68-95-99.7 rule, z-scores, and the central limit theorem by sampling.