Mathematics
# Discrete Mathematics

compute binomial coefficients (combinations)

30 choose 18
compute a Frobenius number

Frobenius number {4, 7, 12}
find partitions of an integer

integer partitions of 10
compute properties of a named graph

Pappus graph
compare several graphs

Petersen graph, icosahedral graph
analyze a graph specified by adjacency rules

1->2, 2->3, 3->1, 3->4, 4->1
compute properties of a lattice

face-centered cubic
compute properties of a root lattice

A4 root lattice
compare several lattices

simple cubic, simple hexagonal
compute a possible formula and continuation for a sequence

1, 4, 9, 16, 25, ...
sum an incompletely specified infinite series

1/2 + 1/4 + 1/8 + 1/16 + ...
solve a recurrence

g(n+1)=n^2+g(n)
specify initial values

f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2
find a recurrence satisfied by a given sequence

fibonacci(n) recurrence
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Ackermann Function

evaluate the Ackermann function

ackermann[2,3]
what is ackermann 4,1?
ack(2,ack(2,1))