Fit a line to twelve points by hand, then watch gradient descent do it. Learning is a search for the knob settings that make one number — the loss — small.

Drag the points while gradient descent refits, and watch a ball roll down the real loss bowl in 3D. The normal equations land on the very same line in one step.

Drag an outlier and watch the squared, absolute and Huber fits react differently; then see why classifiers are scored with cross-entropy. The loss decides what "good" means.

A probability for every point of the plane, trained live: a linear score squashed by the sigmoid, with the decision boundary where the score is zero.

Slide the polynomial degree on noisy data: training error keeps falling while validation error traces a U. An L2 penalty reins the wild coefficients back in.

k-fold cross-validation, fold by fold, to choose a model honestly — then a data-leakage trap that scores far above chance on pure noise.

Click anywhere: the k closest examples vote. No training at all — just memory — and the regions repaint as k and the distance metric change.

Try every threshold on every feature, keep the split that leaves the purest groups, and recurse. The plane breaks into boxes, one question at a time.

Assign each point to its nearest centre, move each centre to its points' mean, repeat. The objective only ever falls — but a bad start can trap it.

Rotate a 3D cloud, hunt for the direction it spreads most, and flatten it to 2D. The answers are the eigenvectors of its covariance matrix.

Slide a threshold and watch the confusion matrix, precision, recall, F1 and the ROC and PR curves move together — and see 95% accuracy that catches nothing.