Discrete Mathematics
A few examples of what you can ask Wolfram|Alpha about:
compute binomial coefficients (combinations)
compute a Frobenius number
find partitions of an integer
compute properties of a named graph
compare several graphs
analyze a graph specified by adjacency rules
compute properties of a lattice
compute properties of a root lattice
compare several lattices
compute a possible formula and continuation for a sequence
sum an incompletely specified infinite series
solve a recurrence
specify initial values
find a recurrence satisfied by a given sequence
Ackermann Function
evaluate the Ackermann function