Draw two graphs which have the same number of vertices and the same number of edges, but are not isomorphic. (Hint: I first did this with 4 vertices; can it be done with fewer?)
Next, draw two graphs which have the same number of vertices of each degree, but are not isomorphic. (The same number of degree-0 vertices, the same number of degree-1 vertices, etc. Hint: I first did this with 6 vertices; can it be done with fewer?.)
Write and analyze (i.e. tell me its run-time in big-O notation) a function (method, whatever) which, given such a polynomial and a real value of x, computes the value of the polynomial at x by Horner's method.
Write and analyze a function (or method or whatever) which takes in two polynomials, as above, and computes their sum, another polynomial.
Same thing, computing the product.
Extra credit: Same thing, computing the quotient and the remainder. You may assume that the polynomial you're dividing by has at least one nonzero coefficient.
Note: I gave a very similar polynomial problem to my 344 class last year. I don't recommend copying their programs, for two reasons: (1) I still have last year's programs to compare with, and (2) most of them weren't very good.