My name is Murray and I am a 10th grade student. Me and my friend have recently discovered and proved a theorem of a relitively advanced nature. It is that the the nth difference of an nth degree equation = n! times the coefficient of the highest power. One of my teachers said this theorem is part finite and that she thinks she has seen it before, but she does not remember what it is called, at what level it is taught, who discovered it or when it was invented. I would greatly appretiate answers to any of these questions.

Sincerly, Murray

You have discovered an important fact about "finite differences." Finite difference methods are older than calculus, and are being studied today by those who solve calculus problems on the computer because they lead to a variety of practical computer methods. The coefficients of the nth difference of a polynomial are related to STIRLING NUMBERS OF THE FIRST KIND. You can learn more about these things in a book about numerical analysis.