# Tutorial notes

From Spivey's Corner

These notes arise out of problems that have been discussed in tutorials or elsewhere.

- A note about places where arguments about automata can be streamlined.
- A family of Haskell expressions whose types grow exponentially.
- A problem associated with the Twelve Days of Christmas.
- A note entitled Kicking around a binomial sum, and another note about a different sum.
- My standard story for explaining the idea of duality in linear programming.
- A note about what WeakHashMap is good for in Java.
- A note about invariants for an algorithm that decides equivalence of deterministic finite automata.
- A note on twice twice twice.