1. Difference tables and polynomial fits. Doing it with sums
Doing it with differences
Finding a formula: combinatorial polynomials
Making it formal: the [delta] operator
Going the other way: polynomials to tables
2. Form and function: the algebra of polynomials. Polynomials
3. Complex numbers, complex maps, and trigonometry. Complex numbers
The geometry behind multiplying
Julia sets and the Mandelbrot set.
4. Combinations and locks. Combinatorial proofs and identities
Some approaches to the simplex lock problem
Connections to the Mahler basis.
5. Sums of powers. Summatory polynomials
