Interactive Tools

Small tools for seeing the core ideas of calculus, statistics, algebra and algorithms by playing with them. I use them in my lessons too.

Calculus

Increase the number of rectangles and watch the sum approach the integral.

Let h approach zero and watch the secant slope become the derivative.

Add terms and watch the polynomial approach the function, and see where convergence stops.

Pick an ε and try to find a δ that works for it; test the definition of a limit by hand.

Pick an interval and see the area under the curve, the z-scores and the matching raw values.

Change n and p and see probabilities such as "at most k" and "at least k" on the bars.

Draw samples from a non-normal population and watch the distribution of their means turn normal.

Take hundreds of samples from the same population and count how many intervals capture the true proportion.

A one-proportion z-test: see the p-value as an area under the curve and watch what the decision depends on.

Add and remove points and see how the line, r and the residuals change.

Race six sorting algorithms on the same array and see their comparison and write counts and their pseudocode.

Explore the Cayley table, centre and subgroups of every group up to order 8, and of A₄.