Interactive math textbooks

There is no excuse for Ron Larson‘s Calculus, the textbook I used in high school. It’s over 1,000 pages long and it’s printed on paper. This may have been acceptable in 1998 when it was first printed, but today I am amazed that it remains in print. That’s because textbooks should be electronic and interactive.

You have to be suspicious of exisitng “interactive” math content, because it may be interactive in a very shallow sense. For example, if you get a hard question wrong then it shows you an easier question. What I’d like to see are interactible examples and figures: Move a point around on the figure and see how things change in real-time.

Strom et al. have done a very good job of this with Immersive Math, an interactive linear algebra textbook. (A paper textbook cannot update its figures in real-time.) They also have hover-tips for referenced theorems and definitions, which is a nice touch. (In a paper textbook you’d have to flip back.)

I made my own demo for solids of revolution, a difficult topic for many students. You can move a slider to see the differential volume element change. But you can also hover over a term, like dA, in the equations to highlight the geometrical interpretation corresponding to the term. Click the animation to be redirected to the demo and try it yourself.

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