Learning guides
Use a worked example to make a prediction, try the matching interactive module, then explain any difference. These guided experiments connect the archive's visualizations to calculations and the assumptions behind them.
Calculus
Connect average change to an instantaneous slope
Work out a secant slope, predict the matching tangents, and understand when the Mean Value Theorem applies.
Probability
Update a probability without ignoring the base rate
Count true and false signals, calculate a posterior probability, and test how changing one assumption changes the answer.
Computer science
Trace a shortest path one decision at a time
Follow Dijkstra's tentative distances, explain relaxation, and distinguish a weighted shortest path from the fewest edges.
A practical learning routine
Write down the input values and your expected result before adjusting a slider. Change one parameter at a time so that you can identify its effect. Read the theory after the experiment, then test a boundary case or an assumption. The module helps you explore; a graph or animation alone is not a proof.
If a displayed result disagrees with your calculation, keep the exact inputs and report a reproducible example. For the complete topic list, explore the modules or visit the module index.